**SFB 925**Light induced dynamics and control of correlated quantum systems

# Publications

## Project A

### Project A1

#### Electronic decay of core-excited HCl molecules probed by THz streaking

*K. Wenig, M. Wieland, A. Baumann , S. Walther, A. Dimitriou , M. J. Prandolini , O. Schepp , I. Bermúdez Macias, M. Sumfleth , N. Stojanovic, S. Düsterer, J. Rönsch-Schulenburg, E. Zapolnova, R. Pan, M. Drescher, and U. Frühling*

The ultrafast electronic decay of HCl molecules in the time domain after resonant core excitation was measured. Here, a Cl-2p core electron was promoted to the antibonding σ* orbital initiating molecular dissociation, and simultaneously, the electronic excitation relaxes via an Auger decay. For HCl, both processes compete on similar ultrashort femtosecond time scales. In order to measure the lifetime of the core hole excitation, we collinearly superimposed 40 fs soft x-ray pulses with intense terahertz (THz) radiation from the free-electron laser in Hamburg (FLASH). Electrons emitted from the molecules are accelerated (streaked) by the THz electric field where the resulting momentum change depends on the field's phase at the instant of ionization. Evaluation of a time-shift between the delay-dependent streaking spectra of photo- and Auger electrons yields a decay constant of (11 ± 2) fs for LMM Auger electrons. For further validation, the method was also applied to the MNN Auger decay of krypton. Reproduction of the value already published in the literature confirms that a temporal resolution much below the duration of the exciting x-ray pulses can be reached.

Struct. Dyn. 6, 034301 (2019)

#### Roadmap of ultrafast x-ray atomic and molecular physics

*L. Young, K. Ueda, M. Gühr, P. H. Bucksbaum, M. Simon, S. Mukamel, N. Rohringer, K. C. Prince, C. Masciovecchio, M. Meyer, A. Rudenko, D. Rolles, C. Bostedt, M. Fuchs, D. A. Reis, R. Santra, H. Kapteyn, M. Murnane, H. Ibrahim, F. Légaré, et. al.*

X-ray free-electron lasers (XFELs) and table-top sources of x-rays based upon high harmonic generation (HHG) have revolutionized the field of ultrafast x-ray atomic and molecular physics, largely due to an explosive growth in capabilities in the past decade. XFELs now provide unprecedented intensity (1020 W cm−2) of x-rays at wavelengths down to ~1 Ångstrom, and HHG provides unprecedented time resolution (~50 attoseconds) and a correspondingly large coherent bandwidth at longer wavelengths. For context, timescales can be referenced to the Bohr orbital period in hydrogen atom of 150 attoseconds and the hydrogen-molecule vibrational period of 8 femtoseconds; wavelength scales can be referenced to the chemically significant carbon K-edge at a photon energy of ~280 eV (44 Ångstroms) and the bond length in methane of ~1 Ångstrom. With these modern x-ray sources one now has the ability to focus on individual atoms, even when embedded in a complex molecule, and view electronic and nuclear motion on their intrinsic scales (attoseconds and Ångstroms). These sources have enabled coherent diffractive imaging, where one can image non-crystalline objects in three dimensions on ultrafast timescales, potentially with atomic resolution. The unprecedented intensity available with XFELs has opened new fields of multiphoton and nonlinear x-ray physics where behavior of matter under extreme conditions can be explored. The unprecedented time resolution and pulse synchronization provided by HHG sources has kindled fundamental investigations of time delays in photoionization, charge migration in molecules, and dynamics near conical intersections that are foundational to AMO physics and chemistry. This roadmap coincides with the year when three new XFEL facilities, operating at Ångstrom wavelengths, opened for users (European XFEL, Swiss-FEL and PAL-FEL in Korea) almost doubling the present worldwide number of XFELs, and documents the remarkable progress in HHG capabilities since its discovery roughly 30 years ago, showcasing experiments in AMO physics and other applications. Here we capture the perspectives of 17 leading groups and organize the contributions into four categories: ultrafast molecular dynamics, multidimensional x-ray spectroscopies; high-intensity x-ray phenomena; attosecond x-ray science.

#### Observation and Control of Laser-Enabled Auger Decay

*D. Iablonskyi, K. Ueda, Kenichi L. Ishikawa, A. S. Kheifets, P. Carpeggiani, M. Reduzzi, H. Ahmadi, A. Comby, G. Sansone, T. Csizmadia, S. Kuehn, E. Ovcharenko, T. Mazza, M. Meyer, A. Fischer, C. Callegari, O. Plekan, P. Finetti, E. Allaria, E. Ferrari, E. Roussel, D. Gauthier, L. Giannessi, K. C. Prince*

Single-photon laser-enabled Auger decay (spLEAD) is predicted theoretically [B. Cooper and V. Averbukh, Phys. Rev. Lett. 111, 083004 (2013)] and here we report its first experimental observation in neon. Using coherent, bichromatic free-electron laser pulses, we detect the process and coherently control the angular distribution of the emitted electrons by varying the phase difference between the two laser fields. Since spLEAD is highly sensitive to electron correlation, this is a promising method for probing both correlation and ultrafast hole migration in more complex systems.

#### Ultrashort free-electron laser X-ray pulses

*W. Helml, I. Grguras, P. N. Juranic, S. Düsterer, T. Mazza, A. R. Maier, N. Hartmann, M. Ilchen, G. Hartmann, L. Patthey, C. Callegari, J. T. Costello, M. Meyer, R. N. Coffee, A. L. Cavalieri, R. Kienberger*

For the investigation of processes happening on the time scale of the motion of bound electrons, well-controlled X-ray pulses with durations in the few-femtosecond and even sub-femtosecond range are a necessary prerequisite. Novel free-electron lasers sources provide these ultrashort, high-brightness X-ray pulses, but their unique aspects open up concomitant challenges for their characterization on a suitable time scale. In this review paper we describe progress and results of recent work on ultrafast pulse characterization at soft and hard X-ray free-electron lasers. We report on different approaches to laser-assisted time-domain measurements, with specific focus on single-shot characterization of ultrashort X-ray pulses from self-amplified spontaneous emission-based and seeded free-electron lasers. The method relying on the sideband measurement of X-ray electron ionization in the presence of a dressing optical laser field is described first. When the X-ray pulse duration is shorter than half the oscillation period of the streaking field, few-femtosecond characterization becomes feasible via linear streaking spectroscopy. Finally, using terahertz fields alleviates the issue of arrival time jitter between streaking laser and X-ray pulse, but compromises the achievable temporal resolution. Possible solutions to these remaining challenges for single-shot, full time–energy characterization of X-ray free-electron laser pulses are proposed in the outlook at the end of the review.

#### Circular Dichroism in Multiphoton Ionization of Resonantly Excited He+ Ions

*M. Ilchen, N. Douguet, T. Mazza, A. J. Rafipoor et. al.*

Intense, circularly polarized extreme-ultraviolet and near-infrared (NIR) laser pulses are combined to double ionize atomic helium via the oriented intermediate He+(3p) resonance state. Applying angle-resolved electron spectroscopy, we find a large photon helicity dependence of the spectrum and the angular distribution of the electrons ejected from the resonance by NIR multiphoton absorption. The measured circular dichroism is unexpectedly found to vary strongly as a function of the NIR intensity. The experimental data are well described by theoretical modeling and possible mechanisms are discussed.

#### Angle resolved photoelectron spectroscopy of two-color XUV-NIR ionization with polarization control

*S. Düsterer, G. Hartmann, F. Babies, A. Beckmann et. al.*

Electron emission caused by extreme ultraviolet (XUV) radiation in the presence of a strong near infrared (NIR) field leads to multiphoton interactions that depend on several parameters. Here, a comprehensive study of the influence of the angle between the polarization directions of the NIR and XUV fields on the two-color angle-resolved photoelectron spectra of He and Ne is presented. The resulting photoelectron angular distribution strongly depends on the orientation of the NIR polarization plane with respect to that of the XUV field. The prevailing influence of the intense NIR field over the angular emission characteristics for He(1s) and Ne(2p) ionization lines is shown. The underlying processes are modeled in the frame of the strong field approximation (SFA) which shows very consistent agreement with the experiment reaffirming the power of the SFA for multicolor-multiphoton ionization in this regime.

#### Coherent control with a short-wavelength Free Electron Laser

*K.C. Prince, E. Allaria, C. Callegari, R. Cucini et. al*

Extreme ultraviolet and X-ray free-electron lasers (FELs) produce short-wavelength pulses with high intensity, ultrashort duration, well-defined polarization and transverse coherence, and have been utilized for many experiments previously possible only at long wavelengths: multiphoton ionization1, pumping an atomic laser2 and four-wave mixing spectroscopy3. However one important optical technique, coherent control, has not yet been demonstrated, because self-amplified spontaneous emission FELs have limited longitudinal coherence4, 5, 6, 7. Single-colour pulses from the FERMI seeded FEL are longitudinally coherent8, 9, and two-colour emission is predicted to be coherent. Here, we demonstrate the phase correlation of two colours, and manipulate it to control an experiment. Light of wavelengths 63.0 and 31.5 nm ionized neon, and we controlled the asymmetry of the photoelectron angular distribution10, 11 by adjusting the phase, with a temporal resolution of 3 as. This opens the door to new short-wavelength coherent control experiments with ultrahigh time resolution and chemical sensitivity.

#### Angular distribution and circular dichroism in the two-colour XUV+NIR above-threshold ionization of helium

*T. Mazza, M. Ilchen, A. J. Rafipoor, C. Callegari et. al.*

The photoelectron angular distribution and the circular dichroism in two-colour XUV+NIR above-threshold ionization of helium atoms have been investigated both experimentally and theoretically. Circularly polarized XUV pulses from the free electron laser FERMI have been spatially and temporally overlapped with circularly polarized optical pulses in the interaction region with an atomic helium jet. The emitted electrons were energy and angle analyzed by means of a velocity map imaging spectrometer. Asymmetry parameters of the angular distribution were determined and compared to theoretical predictions based on the strong field approximation and perturbation theory, respectively. For low NIR intensities, the ratio of the partial waves in the two-photon ionization process and their relative phase could be deduced. For high NIR intensities, the influence of multi-photon processes is discussed. Circular dichroism was revealed in both cases and is in good agreement with the results of the strong field approximation.

#### Femtosecond dynamics of correlated many-body states in C60 fullerenes

*S. Usenko, M. Schüler, A. Azima, M. Jakob, L.L. Lazzarino, Y. Pavlyukh, A. Przystawik, M. Drescher, T. Laarmann, J. Berakdar*

Fullerene complexes may play a key role in the design of future molecular electronics and nanostructured devices with potential applications in light harvesting using organic solar cells. Charge and energy flow in these systems is mediated by many-body effects. We studied the structure and dynamics of laser-induced multi-electron excitations in isolated C60 by two-photon photoionization as a function of excitation wavelength using a tunable fs UV laser and developed a corresponding theoretical framework on the basis of ab initio calculations. The measured resonance line width gives direct information on the excited state lifetime. From the spectral deconvolution we derive a lower limit for purely electronic relaxation on the order of Tel=10+5-3 fs. Energy dissipation towards nuclear degrees of freedom is studied with time-resolved techniques. The evaluation of the nonlinear autocorrelation trace gives a characteristic time constant of Tvib=400+-100 fs for the exponential decay. In line with the experiment, the observed transient dynamics is explained theoretically by nonadiabatic (vibronic) couplings involving the correlated electronic, the nuclear degrees of freedom (accounting for the Herzberg–Teller coupling), and their interplay.

#### Sensitivity of nonlinear photoionization to resonance substructure in collective excitation

*T. Mazza, A. Karamatskou, M. Ilchen, S. Bakhtiarzadeh, A. J. Rafipoor, P. O’Keeffe, T. J. Kelly, N. Walsh, J. T. Costello, M. Meyer, R. Santra*

Collective behaviour is a characteristic feature in many-body systems, important for developments in fields such as magnetism, superconductivity, photonics and electronics. Recently, there has been increasing interest in the optically nonlinear response of collective excitations. Here we demonstrate how the nonlinear interaction of a many-body system with intense XUV radiation can be used as an effective probe for characterizing otherwise unresolved features of its collective response. Resonant photoionization of atomic xenon was chosen as a case study. The excellent agreement between experiment and theory strongly supports the prediction that two distinct poles underlie the giant dipole resonance. Our results pave the way towards a deeper understanding of collective behaviour in atoms, molecules and solid-state systems using nonlinear spectroscopic techniques enabled by modern short-wavelength light sources.

#### Dichroism in the photoionisation of atoms at XUV Free Electron Lasers

*T. Mazza, E.V. Gryzlova, A.N. Grum-Grzhimailo, A.K. Kazansky, N.M. Kabachnik, M. Meyer*

Two-color photoionization of atomic He has been investigated by angle-integrated and angle-resolved electron spectroscopy. The combined action of intense radiation pulses from the XUV free-electron laser (FEL), FERMI or FLASH, and a synchronized optical laser on the target atom gives rise to a rich sideband structure in the photoemission spectrum. Measurements of the angular distribution parameters and the determination of the circular and linear dichroism for the two-color photoionization enable a detailed analysis of the symmetry of the outgoing electron waves and of the dynamics underlying the multi-photon processes. The experimental results are in excellent agreement with theoretical results obtained using perturbation theory (low intensity regime) and the strong field approximation. For the particular case of two-photon ionization the measurements represent an ideal tool for characterizing certain FEL parameters, here for example the degree and the sign of circular polarization. Finally, new features of the dichroism are theoretically predicted originating from the non-dipole contribution into the photoionization amplitudes.

#### Probing photoelectron angular distributions in molecules with polarization-controlled two-color above-threshold ionization

*T. Leitner, R. Taieb, M. Meyer, Ph. Wernet*

We present polarization-controlled multiphoton two-color above-threshold ionization (TCATI) of molecules. The intensity modulations of valence photoelectron intensities of molecules arising from varying the relative orientation of the linear polarization vectors of femtosecond infrared (IR) and vacuum-ultraviolet (VUV) radiation in TCATI of the highest occupied molecular orbitals of H2O, O2, and N2 are reported. The results on the molecular systems are compared to the 3p photoionization of atomic Ar, which serves as a reference system. Modeling the large differences of the modulation amplitudes within the soft-photon approximation enables us to extract the one-photon-ionization anisotropy parameter β2. Accounting only for the first sideband due to two-photon TCATI by one VUV and one IR photon we find satisfactory agreement between experiment and simulation for H2O and O2. However, the model fails for N2 and possible reasons are discussed. We discuss that the described approach may represent an alternative way of determining photoelectron angular distributions from valence shells of molecules and indicate future directions for modeling TCATI of molecules.

#### Isotope effects in resonant two-color photoionization of Xe in the region of the 5p5(2P1/2)4f [5/2]2 autoionizing state

*E. V. Gryzlova, P. O. Keeffe, D. Cubaynes, G. A. Garcia, L. Nahon, A. N. Grum-Grzhimailo, M. Meyer*

Isotope effects in two-photon two-color photoionization are investigated by a combined theoretical and experimental study of the ionization of xenon atoms. A combination of variable polarization synchrotron and laser radiations are used to excite the 5p5(2P1/2)4f[5/2]2 autoionizing resonance via the intermediate 5p5(2P3/2)5d[3/2]1 state. Electrons and ions are detected in coincidence in order to extract the photoelectron angular distributions and the values of the linear and circular dichroism and to determine how these depend on the isotope. A complete theoretical model of the two-photon process in atoms is given in order to describe these parameters as a function of the polarization of the exciting light sources (both linear and circular polarization). Furthermore, the hyperfine depolarization due to the coupling of the electronic and nuclear angular momenta in the intermediate state is taken into account. The results of the theoretical model are in agreement with the experimental results and allow estimation of the previously unknown hyperfine structure (HFS) constant for the case of overlapping HFS levels.

Isotope effects in resonant two-color photoionization of Xe in the region of the 5p5(2P1/2)4f[5/2]2 autoionizing state (PDF Download Available). Available from: https://www.researchgate.net/publication/275584741_Isotope_effects_in_resonant_two-color_photoionization_of_Xe_in_the_region_of_the_5p52P124f522_autoionizing_state [accessed Feb 17, 2016].

#### Femtosecond all-optical synchronization of an X-ray free-electron laser

*S. Schulz, I. Grguraš, C. Behrens, H. Bromberger, J. T. Costello, M. K. Czwalinna, M. Felber, M. C. Hoffmann, M. Ilchen, H. Y. Liu, T. Mazza, M. Meyer, S. Pfeiffer, P. Prędki, S. Schefer, C. Schmidt, U. Wegner, H. Schlarb, A. L. Cavalieri*

Many advanced applications of X-ray free-electron lasers require pulse durations and time resolutions of only a few femtoseconds. To generate these pulses and to apply them in time-resolved experiments, synchronization techniques that can simultaneously lock all independent components, including all accelerator modules and all external optical lasers, to better than the delivered free-electron laser pulse duration, are needed. Here we achieve all-optical synchronization at the soft X-ray free-electron laser FLASH and demonstrate facility-wide timing to better than 30 fs r.m.s. for 90 fs X-ray photon pulses. Crucially, our analysis indicates that the performance of this optical synchronization is limited primarily by the free-electron laser pulse duration, and should naturally scale to the sub-10 femtosecond level with shorter X-ray pulses.

#### Determining the polarization state of an extreme ultraviolet free-electron laser beam using atomic circular dichroism

*T. Mazza, M. Ilchen, A. J. Rafipoor, C. Callegari, P. Finetti, O. Plekan, K. C. Prince, R. Richter, M. B. Danailov, A. Demidovich, G. De Ninno, C. Grazioli, R. Ivanov, N. Mahne, M. Meyer et al*

Ultrafast extreme ultraviolet and X-ray free-electron lasers are set to revolutionize many domains such as bio-photonics and materials science, in a manner similar to optical lasers over the past two decades. Although their number will grow steadily over the coming decade, their complete characterization remains an elusive goal. This represents a significant barrier to their wider adoption and hence to the full realization of their potential in modern photon sciences. Although a great deal of progress has been made on temporal characterization and wavefront measurements at ultrahigh extreme ultraviolet and X-ray intensities, only few, if any progress on accurately measuring other key parameters such as the state of polarization has emerged. Here we show that by combining ultra-short extreme ultraviolet free electron laser pulses from FERMI with near-infrared laser pulses, we can accurately measure the polarization state of a free electron laser beam in an elegant, non-invasive and straightforward manner using circular dichroism.

#### Accelerator- and laser-based sources of high-field terahertz pulses

*N. Stojanovic, M. Drescher*

At present we are witnessing a rapid development of sources for terahertz (THz) pulses with very strong electromagnetic fields. These pulses are reaching a stage where they can be used to not only probe, but also uniquely control a variety of processes that range from fundamental dynamics in individual atoms and molecules, through phase transitions in solids to a wealth of interactions in biological materials. In this review, we are presenting an overview of two major directions in the generation of such radiation. Large-scale accelerator-based sources offer unprecedented pulse energies coupled with a wide tuning range and extreme repetition rates. Laser-based sources, on the other hand, are laboratory-scale instruments and thus are very attractive in their availability to the wide scientific community. The capabilities of different variants of these THz sources are evaluated and compared with each other. In addition, powerful techniques for the temporal characterization of THz pulses are discussed.

#### Evidence for Chirped Auger-Electron Emission

*B. Schuette, S. Bauch, U. Fruehling, M. Wieland, M. Gensch, E. Ploenjes, T. Gaumnitz, A. Azima, M. Bonitz, M. Drescher*

Auger decay carries valuable information about the electronic structure and dynamics of atoms, molecules, and solids. Here we furnish evidence that under certain conditions Auger electrons are subject to an energetic chirp. The effect is disclosed in time-resolved streaking experiments on the Xe NOO and Kr MNN Auger decay using extreme-ultraviolet pulses from the free-electron laser in Hamburg as well as from a high-order harmonic laser source. The origin of this effect is found to be an exchange of energy between the Auger electron and an earlier emitted correlated photoelectron. The observed time-dependent spectral modulations are understood within an analytical model and confirmed by extensive computer simulations.

### Project A2

#### Shaping femtosecond laser pulses at short wavelength with grazing-incidence optics

*L. L. Lazzarino, M. M. Kazemi, C. Haunhorst, C. Becker, S. Hartwell, M. A. Jakob, A. Przystawik, S. Usenko, D. Kip, I. Hartl, and T. Laarmann*

We present the design of an extreme ultraviolet (XUV) pulse shaper relying on reflective optics. The instrument will allow tailoring of the time-frequency spectrum of femtosecond pulses generated by seeded free-electron lasers (FEL) and high-harmonic generation (HHG) sources down to a central wavelength of ~15 nm. The device is based on the geometry of a 4f grating compressor that is a standard concept in ultrafast laser science and technology. We apply it to shorter wavelengths using grazing-incidence optics operated under ultra-high vacuum conditions. The design blaze angle and the line density of the gratings allow the manipulation of all different harmonics typical for seeded FEL and HHG photon sources without the need of realignment of the instrument and even simultaneously in multi-color experiments. A proof-of-principle pulse shaping experiment using 266 nm laser light has been performed, demonstrating relative phase-control of femtosecond UV pulses.

#### VUV-induced dynamics of the electronically excited C2D4 molecule in a single-color pump-probe experiment

*Oliver Schepp, Arne Baumann, Marek Wieland, Armin Azima, Markus Drescher*

The ultrafast non-adiabatic dynamics of the electronically excited ethylene molecule C2H4 and its deuterated isotopologue C2D4 are studied with time-resolved photoelectron spectroscopy after excitation via irradiation with light in the vacuum ultraviolet spectral range. Sub-20-fs pulses, generated as the fifth harmonic of a Ti:Sa laser system, are split and delayed in an all-reflective Michelson-type interferometer, enabling a single-color pump-probe experiment. In addition to the ultrafast non-adiabatic relaxation process of C2H4, we find more complex dynamics exhibited by the delay-dependent photoelectron yield of C2D4, identified as a signature of the delayed dissociative ionization of the parent ion.

Chemical Physics Letters: X, Volume 3, 1000024 (2019);

DOI: 10.1016/j.cpletx.2019.100024

#### Time-Resolved Dissociation Dynamics of Iodomethane Resulting from Rydberg and Valence Excitation

*Arne Baumann, Dimitrios Rompotis, Oliver Schepp, Marek Wieland, and Markus Drescher*

Rydberg excitations in the vacuum ultraviolet spectral range may open up molecular photoreaction pathways not accessible from lower-lying valence states. Here, single-shot UV/VUV pump–probe spectroscopy was used to study the photodissociation dynamics of iodomethane after 268 nm excitation in the A-band and excitation of the 6p (2E3/2) Rydberg state at 161 nm. By combining weak-field VUV single-photon ionization with sub-10 fs temporal resolution and the superior statistical accuracy of the single-shot technique, sub-30 fs wave packet dynamics upon excitation in the A-band by a UV pump pulse were disclosed. Population transfer from the Rydberg state to the 2 1A1 valence state leading to 100 fs dissociation dynamics was observed by utilizing the same methodology in a VUV-pump/UV-probe scheme.

J. Phys. Chem. A, 2018, 122 (21), pp 4779–4784

DOI: 10.1021/acs.jpca.8b01248

#### Weak-field few-femtosecond VUV photodissociation dynamics of water isotopologues

*A. Baumann, S. Bazzi, D. Rompotis, O. Schepp, A. Azima, M. Wieland, D. Popova-Gorelova, O. Vendrell, R. Santra, M. Drescher*

We present a joint experimental and theoretical study of the VUV-induced dynamics of H2O and its deuterated isotopologues in the first excited state (˜A1B1) utilizing a VUV-pump VUV-probe scheme combined with ab initio classical trajectory calculations. 16-fs VUV pulses centered at 161 nm created by fifth-order harmonic generation are employed for single-shot pump-probe measurements. Combined with a precise determination of the VUV pulses' temporal profile, they provide the necessary temporal resolution to elucidate sub-10-fs dissociation dynamics in the 1+1 photon ionization time window. Ionization with a single VUV photon complements established strong-field ionization schemes by disclosing the molecular dynamics under perturbative conditions. Kinetic isotope effects derived from the pump-probe experiment are found to be in agreement with our by ab initio classical trajectory calculations, taking into account photoionization cross sections for the ground and first excited state of the water cation.

#### Single-shot nonlinear spectroscopy in the vacuum-ultraviolet

*D. Rompotis, A. Baumann, O. Schepp, T. Maltezopoulos, M. Wieland, M. Drescher*

Time-resolved spectroscopy in the vacuum/extreme ultraviolet (VUV/XUV) spectral range promises to disclose ultrafast dynamics in all states of matter. Completing a measurement within a single shot eliminates the influence of experimental parameter fluctuations and enhances its statistical significance. We demonstrate a single-shot temporal metrology scheme operating in the vacuum/extreme-ultraviolet spectral range, combining few-femtosecond resolution in a wide temporal window with high detection efficiency. An anticollinear geometry encodes temporal delay information on the beam propagation coordinate. The spatial distribution of ions created in the common focus is captured with a mass/charge-state-selective ion imaging spectrometer, resulting in a single-shot pump–probe measurement. We demonstrate a proof-of-principle single-shot VUV-pump/VUV-probe experiment by investigating ultrafast dissociation dynamics of O2 excited at 162 nm. The experimental determination of the finite instrument response in the same apparatus enables robust deconvolution of the investigated dynamics well beyond the instrument’s intrinsic temporal resolution.

#### Attosecond interferometry with self-amplified spontaneous emission of a free-electron laser

*Usenko, A. Przystawik, M.A. Jakob, L.L. Lazzarino, G. Brenner, S. Toleikis, Ch. Haunhorst, D. Kip, T. Laarmann*

Light-phase-sensitive techniques, such as coherent multidimensional spectroscopy, are well-established in a broad spectral range, already spanning from radio-frequencies in nuclear magnetic resonance spectroscopy to visible and ultraviolet wavelengths in nonlinear optics with table-top lasers. In these cases, the ability to tailor the phases of electromagnetic waves with high precision is essential. Here we achieve phase control of extreme-ultraviolet pulses from a free-electron laser (FEL) on the attosecond timescale in a Michelson-type all-reflective interferometric autocorrelator. By varying the relative phase of the generated pulse replicas with sub-cycle precision we observe the field interference, that is, the light-wave oscillation with a period of 129 as. The successful transfer of a powerful optical method towards short-wavelength FEL science and technology paves the way towards utilization of advanced nonlinear methodologies even at partially coherent soft X-ray FEL sources that rely on self-amplified spontaneous emission.

#### Split-and-delay unit for FEL interferometry in the XUV spectral range

*S. Usenko, A. Przystawik, L.L. Lazzarino, M.A. Jakob, F. Jacobs, C. Becker, C. Haunhorst, D. Kip, and T. Laarmann*

In this work we present a reflective split-and-delay unit (SDU) developed for interferometric time-resolved experiments utilizing an (extreme ultraviolet) XUV pump–XUV probe scheme with focused free-electron laser beams. The developed SDU overcomes limitations for phase-resolved measurements inherent to conventional two-element split mirrors by a special design using two reflective lamellar gratings. The gratings produce a high-contrast interference signal controlled by the grating displacement in every diffraction order. The orders are separated in the focal plane of the focusing optics, which enables one to avoid phase averaging by spatially selective detection of a single interference state of the two light fields. Interferometry requires a precise relative phase control of the light fields, which presents a challenge at short wavelengths. In our setup the phase delay is determined by an in-vacuum white light interferometer (WLI) that monitors the surface profile of the SDU in real time and thus measures the delay for each laser shot. The precision of the WLI is 1 nm as determined by optical laser interferometry. In the presented experimental geometry it corresponds to a time delay accuracy of 3 as, which enables phase-resolved XUV pump–XUV probe experiments at free-electron laser (FEL) repetition rates up to 60 Hz.

#### Femtosecond dynamics of correlated many-body states in C60 fullerenes

*S. Usenko, M. Schüler, A. Azima, M. Jakob, L.L. Lazzarino, Y. Pavlyukh, A. Przystawik, M. Drescher, T. Laarmann, J. Berakdar*

Fullerene complexes may play a key role in the design of future molecular electronics and nanostructured devices with potential applications in light harvesting using organic solar cells. Charge and energy flow in these systems is mediated by many-body effects. We studied the structure and dynamics of laser-induced multi-electron excitations in isolated C60 by two-photon photoionization as a function of excitation wavelength using a tunable fs UV laser and developed a corresponding theoretical framework on the basis of ab initio calculations. The measured resonance line width gives direct information on the excited state lifetime. From the spectral deconvolution we derive a lower limit for purely electronic relaxation on the order of Tel=10+5-3 fs. Energy dissipation towards nuclear degrees of freedom is studied with time-resolved techniques. The evaluation of the nonlinear autocorrelation trace gives a characteristic time constant of Tvib=400+-100 fs for the exponential decay. In line with the experiment, the observed transient dynamics is explained theoretically by nonadiabatic (vibronic) couplings involving the correlated electronic, the nuclear degrees of freedom (accounting for the Herzberg–Teller coupling), and their interplay.

#### Tracing few-femtosecond photodissociation dynamics on molecular oxygen with a single-color pump-probe scheme in the VUV

*O. Schepp, A. Baumann, D. Rompotis, T. Gebert, A. Azima, M. Wieland, M. Drescher*

#### Efficient generation of below-threshold harmonics for high-fidelity multi-photon physics in the VUV spectral range

*D. Rompotis, T. Gebert, M. Wieland, F. Karimi, M. Drescher*

We demonstrate the generation of microjoule level, sub-20-fs, Ti:Sa fifth-harmonic pulses utilizing a loose-focusing geometry in a long Ar gas cell. The VUV pulses centered at 161.8 nm reach pulse energies of 1.1 μJ per pulse, while the corresponding pulse duration is measured with a second-order, fringe-resolved autocorrelation scheme to be 18±1 fs. Nonresonant, two-photon ionization of Kr and three-photon ionization of Ne verify the fifth-harmonic pulse high-intensity content and indicate the feasibility of multi-photon VUV pump-VUV probe studies of ultrafast atomic and molecular dynamics.

#### Ionisation dynamics of Xe nanoplasma formation studied with XUV fluorescence spectroscopy

*A. Przystawik, L. Schroedter, M. Müller, M. Adolph, C. Bostedt, L. Flückiger, T. Gorkhover, A. Kickermann, M. Krikunova, Nösel, T. Oelze, Y. Ovcharenko, D. Rupp, L. M. Sauppe, S. Schorb, S. Usenko, T. Möller, T. Laarmann*

Intense pulses from a short wavelength free-electron laser turn xenon nanoparticles into a high energy density nanoplasma within femtoseconds. Recently, the generation of multiply charged xenon ions during the initial phase of plasma evolution has been studied by energy-resolved XUV fluorescence detection as a function of cluster size and cluster composition [1]. In the present contribution we give a detailed analysis of the corresponding radiative transitions after resonant excitation of the 4d electron shell at intensities of 2 × 1012 − 2.45 × 1015 W cm−2. The evaluation of charge-state specific fluorescence yields as a function of FEL power density demonstrates that plasma effects such as ionization potential lowering, electron impact excitation, ionization, and energy redistribution govern the laser-induced non-equilibrium dynamics in xenon clusters.

#### Ionization dynamics of XUV excited clusters: the role of inelastic electron collisions

*M. Müller, L. Schroedter, T. Oelze, L. Nösel, A. Przystawik, A. Kickermann, M. Adolph, T. Gorkhover, L. Flückiger, M. Krikunova, M. Sauppe, Y. Ovcharenko, S. Schorb, C. Bostedt, D. Rupp, T. Laarmann, T. Möller*

We report on the ionization and nanoplasma dynamics of small xenon clusters irradiated by intense, short pulses of a short-wavelength free-electron laser. Fluorescence spectroscopy indicates that inelastic electron collisions play a prominent role in the formation of the highest charge states. From the spectral distribution an electron temperature of 27 eV is deduced which corresponds to the average excess energy of the Auger- and photoelectrons ionized from individual atoms but trapped in the cluster core. This suggests that fluorescence spectra reflect a very early stage within the nanoplasma dynamics and shows how a part of the kinetic energy of the plasma electrons trapped in the cluster potential is transferred to the ions.

#### Hidden Charge States in Soft-X-Ray Laser-Produced Nanoplasmas Revealed by Fluorescence Spectroscopy

*L. Schroedter, M. Müller, A. Kickermann, A. Przystawik, S. Toleikis, M. Adolph, L. Flückiger, T. Gorkhover, L. Nösel, M. Krikunova, T. Oelze, Y. Ovcharenko, D. Rupp, M. Sauppe, D. Wolter, S. Schorb, C. Bostedt, T. Möller, T. Laarmann*

Highly charged ions are formed in the center of composite clusters by strong free-electron laser pulses and they emit fluorescence on a femtosecond time scale before competing recombination leads to neutralization of the nanoplasma core. In contrast to mass spectrometry that detects remnants of the interaction, fluorescence in the extreme ultraviolet spectral range provides fingerprints of transient states of high energy density matter. Spectra from clusters consisting of a xenon core and a surrounding argon shell show that a small fraction of the fluorescence signal comes from multiply charged xenon ions in the cluster core. Initially, these ions are as highly charged as the ions in the outer shells of pure xenon clusters with charge states up to at least.

#### A high-harmonic generation source for seeding a free-electron laser at 38 nm

*T. Maltezopoulos, M. Mittenzwey, A. Azima, J. Bödewadt, H. Dachraoui, M. Rehders, C. Lechner, M. Schulz, M. Wieland, T. Laarmann, J. Roßbach, M. Drescher*

Direct seeding with a high-harmonic generation (HHG) source can improve the spectral, temporal, and coherence properties of a free-electron laser (FEL) and shall reduce intensity and arrival-time fluctuations. In the seeding experiment sFLASH at the extreme ultraviolet FEL in Hamburg FLASH, which operates in the self-amplified spontaneous emission mode (SASE), the 21st harmonic of an 800 nm laser is refocused into a dedicated seeding undulator. For seeding, the external light field has to overcome the noise level of SASE; therefore, an efficient coupling between seed pulse and electron bunch is mandatory. Thus, an HHG beam with a proper divergence, width, beam quality, Rayleigh length, pointing stability, single-shot pulse energy, and stability in the 21st harmonic is needed. Here, we present the setup of the HHG source that seeds sFLASH at 38.1 nm, the optimization procedures, and the necessary diagnostics.

#### Generation of the simplest rotational wave packet in a diatomic molecule: Tracing a two-level superposition in the time domain

*A. Przystawik, A. Kickermann, A. Al-Shemmary, S. Düsterer, A. M. Ellis, K. von Haeften, M. Harmand, S. Ramakrishna, H. Redlin, L. Schroedter, M. Schulz, T. Seideman, N. Stojanovic, J. Szekely, F. Tavella, S. Toleikis, T. Laarmann*

We introduce a time-domain approach to explore rotational dynamics caused by intramolecular coupling or the interaction with dissipative media. It pushes the time resolution toward the ultimate limit determined by the rotational period. Femtosecond pulses create a coherent superposition of two rotational states of carbon monoxide. The wave-packet motion is observed by subsequent Coulomb explosion, which results in a time-dependent asymmetry of spatial fragmentation patterns. The asymmetry oscillation prevails for at least 1 ns, covering more than 300 periods with no decoherence. Long time scans will allow weak perturbations of the order of ΔE/E=10−4 to be discerned. Our conclusions are confirmed by a fully quantum-mechanical model.

#### Michelson-type all-reflective interferometric autocorrelation in the VUV regime

*T. Gebert, D. Rompotis, M. Wieland, F. Karimi, A. Azima, M. Drescher*

We demonstrate second-order interferometric autocorrelation of a pulse in the vacuum-ultraviolet (VUV) spectral range using an optical arrangement equivalent to a Michelson interferometer. In an all-reflective design, wavefront splitting is realized with two moveable interdigitated reflective gratings forming a diffraction pattern with well separated orders and an intensity distribution depending on the precisely adjustable path-length difference. An imaging time-of-flight spectrometer is able to spatially select ions created by nonlinear two-photon absorption in the focus of the zeroth diffraction order. This arrangement is used to demonstrate interferometric autocorrelation in krypton with femtosecond VUV pulses at 160 nm wavelength. In addition to the pulse duration, which is already accessible with non-collinear intensity autocorrelation, the full interferometric contrast of the presented approach enables us to extract also information on temporal phases.

### Project A3

#### Inner-shell X-ray absorption spectra of the cationic series NHy+ (y=0-3)

* Sadia Bari, Ludger Inhester, Kaja Schubert, Karolin Mertens, Jan O. Schunck, Simon Dörner, Sascha Deinert, Schwob Lucas, Stefan Schippers, Alfred Müller, Stephan Klumpp and Michael Martins*

On yields following X-ray absorption of the cationic series NH_{y}^{+}(y= 0–3) were measured to identify the characteristic absorption resonances in the energy range of the atomic nitrogen K-edge. Significant changes in the position of the absorption resonances were observed depending on the number of hydrogen atoms bound to the central nitrogen atom. Configuration interaction (CI) calculations were performed to obtain line assignments in the frame of molecular group theory. To validate the calculations, our assignment for the atomic cation N^{+}, measured as a reference, was compared with published theoretical and experimental data.

#### Photoionization and photo- fragmentation of singly charged positive and negative Sc3N@C80 endohedral fullerene ions

* A. Müller, M. Martins, A. L. D. Kilcoyne, R. A. Phaneuf, J. Hellhund, A. _{Borovik,} Jr., K. Holste, S. Bari, T. Buhr, S. Klumpp, A. Perry-Sassmannshausen, S. Reinwardt, S. Ricz, K. Schubert, and S. Schippers*

Photoprocesses of the endohedral fullerene ions S_{c3}N@C_{+80} and S_{c3}N@C_{80}− in the gas phase have been investigated in the photon energy ranges 30–50 eV and 280–420 eV. Single and double ionization as well as single ionization accompanied by the release of a C_{2} dimer were observed as a function of the photon energy for the positive parent ion and double detachment was measured for the negative parent ion. The emphasis of the experiments was on the specific effects of the encapsulated trimetallic nitride cluster S_{c3}N on the observed reactions. Clear evidence of photoexcitation near the Sc *L* edge is obtained with the dominating contributions visible in the one- and two-electron-removal channels. *K*-vacancy production in the encapsulated central nitrogen atom is seen in the single ionization of S_{c3}N@C_{+80} but is much less pronounced in the photoionization-with-fragmentation channel. Comparison of the cross sections near the carbon *K* edge with the corresponding channels measured previously in the photoionization of L_{u3}N@C_{+80} reveal strong similarities. Previously predicted sharp resonance features in the ionization of S_{c3}N@C+80 ions below the Sc *M* edge are not confirmed. The experiments are accompanied by quantum-chemistry calculations in the Hartree-Fock approximation and by model calculations employing density functional theory (DFT).

#### The photonion merged-beams experiment

* Stefan Schippers, Ticia Buhr, Alexander Borovik Jr., Kristof Holste, Alexander Perry-Sassmannshausen, Karolin Mertens, Simon Reinwardt, Michael Martins, Stephan Klumpp, Kaja Schubert, Sadia Bari, Randolf Beerwerth, Stephan Fritzsche, Sandor Ricz, Jonas Hellhund, and Alfred Müller*

The Photon‐Ion Spectrometer at PETRA III—in short, PIPE—is a permanently installed user facility at the "Variable Polarization XUV Beamline" P04 of the synchrotron light source PETRA III operated by DESY in Hamburg, Germany. The careful design of the PIPE ion‐optics in combination with the record‐high photon flux at P04 has lead to a breakthrough in experimental studies of photon interactions with ionized small quantum systems. This short review provides an overview over the published scientific results from photon‐ion merged‐beams experiments at PIPE that were obtained since the start of P04 operations in 2013. The topics covered comprise photoionization of ions of astrophysical relevance, quantitative studies of multi‐electron processes upon inner‐shell photoexcitation and photoionization of negative and positive atomic ions, precision spectroscopy of photoionization resonances, photoionization and photofragmentation of molecular ions, and of endohedral fullerene ions.

#### Ultrafast charge redistribution in small iodine containing molecules

* M. Hollstein, K. Mertens, S. Klumpp, N. Gerken, S. Palutke, I. Baev, G. Brenner, S. Dziarzhytski, M. Meyer, W. Wurth, D. Pfannkuche1, M. Martins*

We present studies on intra-molecular charge redistribution in iodine containing molecules upon iodine-4d photoionization. For this, we employed an XUV-pump-XUV-probe scheme based on time-delayed femtosecond pulses delivered by the free-electron laser at DESY in Hamburg (FLASH). The experimental results show delay dependent and molecule-specific iodine charge state distributions that arise upon multiple iodine-4d photoionization. Using the example of CH_{3}I and CH_{2}I_{2}, we compare the delay-dependent yields of I^{3+}. We model the involved processes using advanced ab initio electronic structure calculations which include electron correlations combined with a classical model of the nuclear motion. The qualitative agreement of our model with the experimental results allows us to relate the observed, strongly molecule-specific efficiencies of the intra-molecular charge rearrangement not only to molecule-specific fragmentation timescales but also to molecule-specific electronic structure and molecular environment.

#### Photoabsorption of the molecular IH cation at the iodine 3d absorption edge

*Stephan Klumpp, Alexander A. Guda, Kaja Schubert, Karolin Mertens, Jonas Hellhund, Alfred Müller, Stefan Schippers, Sadia Bari, and Michael Martins*

Yields of atomic iodine I* ^{q+}* (

*q*≥2) fragments resulting from photoexcitation and photoionization of the target ions IH+ and I+ have been measured in the photon-energy range 610–680 eV, which comprises the thresholds for iodine 3

*d*ionization. The measured ion-yield spectra show two strong and broad resonance features due to the excitation of the 3

*d*electrons into

_{3/2,5/2}*ɛf*states rather similar for both parent ions. In the 3

*d*pre-edge range, excitations into (

*npπ*)-like orbitals and into an additional

*σ*orbital are found for IH+, which have been identified by comparison of the atomic I+ and molecular IH+ data and with the help of (time-dependent) density functional theory (DFT) and atomic Hartree-Fock calculations. The (5

^{∗}*p π*) orbital is almost atomlike, whereas all other resonances of the IH+ primary ion show a more pronounced molecular character, which is deduced from the chemical shifts of the resonances and the theoretical analysis.

#### Photoionization of metastable heliumlike C4+(1s2s 3S1 ) ions: Precision study of intermediate doubly excited states

* A. Müller, E. Lindroth, S. Bari, A. Borovik, Jr., P.-M. Hillenbrand, K. Holste, P. Indelicato, A. L. D. Kilcoyne, S. Klumpp, M. Martins, J. Viefhaus, P. Wilhelm, and S. Schippers*

In a joint experimental and theoretical endeavor, photoionization of metastable C^{4+}(1*s*2*s*^{3}*S*_{1}) ions via intermediate levels with hollow, double-*K*-vacancy configurations 2*s*2*p*, 2*s*3*p*, 2*p*3*s*, 2*p*3*d*, 2*s*4*p*, 2*p*4*s*, and 2*p*4*d* has been investigated. High-resolution photon-ion merged-beams measurements were carried out with the resolving power reaching up to 25 800 which is sufficient to separate the leading fine-structure components of the 2*s*2*p*^{3}*P* term. Many-body perturbation theory was employed to determine level-to-level cross sections for *K*-shell excitation with subsequent autoionization. The resonance energies were calculated with inclusion of electron correlation and radiative contributions. Their uncertainties are estimated to be below ±1 meV. Detailed balance confirms the present photoionization cross-section results by comparison with previous dielectronic-recombination measurements. The high accuracy of the theoretical transition energies together with the present experimental results qualify photoabsorption resonances in heliumlike ions as new, greatly improved energy-reference standards at synchrotron radiation facilities.

#### Near-K-Edge Double and Triple Detachment of the F - Negative Ion: Observation of Direct Two-Electron Ejection by a Single Photon

*A. Müller, A. Borovik, Jr., S. Bari, T. Buhr, K. Holste, M. Martins, A. Perry-Saßmannshausen, R. A. Phaneuf, S. Reinwardt, S. Ricz, K. Schubert, and S. Schippers*

Double and triple detachment of the F^{−}(1*s*^{2}2*s*^{2}2*p*^{6}) negative ion by a single photon have been investigated in the photon energy range 660 to 1000 eV. The experimental data provide unambiguous evidence for the dominant role of direct photodouble detachment with a subsequent single-Auger process in the reaction channel leading to F^{2}+ product ions. Absolute cross sections were determined for the direct removal of a (1*s*+2*p*) pair of electrons from F^{−} by the absorption of a single photon.

#### Soft X-ray Transmission Polarizer Based on Ferromagnetic Thin Films

* L. Müller, G. Hartmann, S. Schleitzer, M. H. Berntsen, M. Walther, R. Rysov, W. Roseker, F. Scholz, J. Seltmann, L. Glaser, J. Viefhaus, K. Mertens, K. Bagschik, R. Frömter, A. De Fanis, I. Shevchuk, K. Medjanik, G. Öhrwall, H. P. Oepen, M. Martins, M. Meyer, and G. Grübel*

A transmission polarizer for producing elliptically polarized soft X-ray radiation from linearly polarized light is presented. The setup is intended for use at synchrotron and free-electron laser beamlines that do not directly offer circularly polarized light for, e.g., X-ray magnetic circular dichroism (XMCD) measurements or holographic imaging. Here, we investigate the degree of ellipticity upon transmission of linearly polarized radiation through a cobalt thin film. The experiment was performed at a photon energy resonant to the Co *L*_{3}-edge, i.e., 778 eV, and the polarization of the transmitted radiation was determined using a polarization analyzer that measures the directional dependence of photo electrons emitted from a gas target. Elliptically polarized radiation can be created at any absorption edge showing the XMCD effect by using the respective magnetic element.

#### Ultrashort free-electron laser X-ray pulses

*W. Helml, I. Grguras, P. N. Juranic, S. Düsterer, T. Mazza, A. R. Maier, N. Hartmann, M. Ilchen, G. Hartmann, L. Patthey, C. Callegari, J. T. Costello, M. Meyer, R. N. Coffee, A. L. Cavalieri, R. Kienberger*

For the investigation of processes happening on the time scale of the motion of bound electrons, well-controlled X-ray pulses with durations in the few-femtosecond and even sub-femtosecond range are a necessary prerequisite. Novel free-electron lasers sources provide these ultrashort, high-brightness X-ray pulses, but their unique aspects open up concomitant challenges for their characterization on a suitable time scale. In this review paper we describe progress and results of recent work on ultrafast pulse characterization at soft and hard X-ray free-electron lasers. We report on different approaches to laser-assisted time-domain measurements, with specific focus on single-shot characterization of ultrashort X-ray pulses from self-amplified spontaneous emission-based and seeded free-electron lasers. The method relying on the sideband measurement of X-ray electron ionization in the presence of a dressing optical laser field is described first. When the X-ray pulse duration is shorter than half the oscillation period of the streaking field, few-femtosecond characterization becomes feasible via linear streaking spectroscopy. Finally, using terahertz fields alleviates the issue of arrival time jitter between streaking laser and X-ray pulse, but compromises the achievable temporal resolution. Possible solutions to these remaining challenges for single-shot, full time–energy characterization of X-ray free-electron laser pulses are proposed in the outlook at the end of the review.

#### Imaging the square of the correlated two-electron wave function of a hydrogen molecule

* M. Waitz, R.Y. Bello, D. Metz, J. Lower, F. Trinter, C. Schober, M. Keiling, U. Lenz, M. Pitzer, K. Mertens, M. Martins, J. Viefhaus, S. Klumpp, T. Weber, L.Ph.H. Schmidt, J.B. Williams, M.S. Schöffler, V.V. Serov, A.S. Kheifets, L. Argenti, A. Palacios, F. Martı́n, T. Jahnke, and R. Dörner*

The toolbox for imaging molecules is well-equipped today. Some techniques visualize the geometrical structure, others the electron density or electron orbitals. Molecules are many-body systems for which the correlation between the constituents is decisive and the spatial and the momentum distribution of one electron depends on those of the other electrons and the nuclei. Such correlations have escaped direct observation by imaging techniques so far. Here, we implement an imaging scheme which visualizes correlations between electrons by coincident detection of the reaction fragments after high energy photofragmentation. With this technique, we examine the H_{2} two-electron wave function in which electron–electron correlation beyond the mean-field level is prominent. We visualize the dependence of the wave function on the internuclear distance. High energy photoelectrons are shown to be a powerful tool for molecular imaging. Our study paves the way for future time resolved correlation imaging at FELs and laser based X-ray sources.

#### Multiple Auger cycle photoionisation of manganese atoms by short soft x-ray pulses

*S. Klumpp, N. Gerken, K. Mertens, M. Richter, B. Sonntag, A. A. Sorokin, M. Braune, K. Tiedtke, P. Zimmermann and M. Martins*

The multiple ionisation of atomic Mn, excited at (photon energy: 52.1 eV) and above (photon energy: 61.1 eV) the discrete giant *3p-3d* resonance, was studied using high irradiation free-electron-laser soft x-ray pulses from the BL2 beamline of FLASH, DESY, Hamburg. In particular, the impact of the giant resonance on the ionisation mechanism was investigated. Ion mass-over-charge spectra were obtained by means of ion time-of-flight spectrometry. For the two photon energies, the yield of the different ionic charge states Mn*q+* (*q* = 0–7) was determined as a function of the irradiance of the soft x-ray pulses. The maximum charge state observed was Mn^{6+} for resonant excitation at 52.1 eV and Mn^{7+} for non-resonant excitation at 61.1 eV at a maximum irradiation of 3 x 10 ^{13} Wcm -^{2} .

#### Two-electron Processes in Multiple Ionization under Strong Soft X-ray Radiation

*M. Ilchen, T. Mazza, E. T. Karamatskos, D. Markellos, S. Bakhtiarzadeh, A. J. Rafipoor, T. J. Kelly, N. Walsh, J. T. Costello, P. O’Keeffe, N. Gerken, M. Martins, P. Lambropoulos, M. Meyer*

In a combined experimental and theoretical study we have investigated the ionization of atomic argon upon irradiation with intense soft-x-ray pulses of 105 eV photon energy from the free-electron laser FLASH. The measured ion yields show charge states up to Ar^{7+}. The comparison with the theoretical study of the underlying photoionization dynamics highlights the importance of excited states in general and of processes governed by electron correlation in particular, namely, ionization with excitation and shake-off, processes usually inaccessible by measurements of ionic yields only. The Ar^{7+} yield shows a clear deviation from the predictions of the commonly used model of sequential ionization via single-electron processes and the observed signal can only be explained by taking into account the full multiplet structure of the involved configurations and by inclusion of two-electron processes. The competing process of two-photon ionization from the ground state of Ar^{6+} is calculated to be orders of magnitude smaller.

#### Soft X-ray multiphoton excitation of small iodine methane derivatives

*K. Mertens, N. Gerken, S. Klumpp, M. Braune and M. Martins*

The fragmentation pattern of the iodine-containing molecules CH_{2}I_{2} and CH_{3}I following a strong multiphoton excitation in the vicinity of the iodine 4d giant resonance regime is studied using soft X-ray free electron laser radiation. A strong difference of the charge distribution and the kinetic energy release (KER) for the two molecules is found. The effects can be attributed to charge rearrangement processes induced by the photoexcitation. The difference in the observed distribution for higher charge states of iodine and carbon fragments is consistent with an over-the-barrier model for the charge rearrangement in the dissociating molecules. The KER for singly ionised carbon fragments indicates an ultrafast charge rearrangement before the dissociation starts.

#### Sensitivity of nonlinear photoionization to resonance substructure in collective excitation

*T. Mazza, A. Karamatskou, M. Ilchen, S. Bakhtiarzadeh, A. J. Rafipoor, P. O’Keeffe, T. J. Kelly, N. Walsh, J. T. Costello, M. Meyer, R. Santra*

Collective behaviour is a characteristic feature in many-body systems, important for developments in fields such as magnetism, superconductivity, photonics and electronics. Recently, there has been increasing interest in the optically nonlinear response of collective excitations. Here we demonstrate how the nonlinear interaction of a many-body system with intense XUV radiation can be used as an effective probe for characterizing otherwise unresolved features of its collective response. Resonant photoionization of atomic xenon was chosen as a case study. The excellent agreement between experiment and theory strongly supports the prediction that two distinct poles underlie the giant dipole resonance. Our results pave the way towards a deeper understanding of collective behaviour in atoms, molecules and solid-state systems using nonlinear spectroscopic techniques enabled by modern short-wavelength light sources.

#### Observation of a Four-Electron Auger Process in Near-K-Edge Photoionization of Singly Charged Carbon Ions

*A. Müller, A. Borovik, Jr., T. Buhr, J. Hellhund, K. Holste, A. L. D. Kilcoyne, S. Klumpp, M. Martins, S. Ricz, J. Viefhaus, S. Schippers*

Single, double, and triple ionization of C^{1+} ions by single photons is investigated in the energy range of 286–326 eV, i.e., in the range from the lowest-energy *K*-vacancy resonances to well beyond the *K*-shell ionization threshold. Clear signatures of C^{1+}(1*s*2*s*^{2}2*p*^{2} ^{2}*D*,^{2}*P*) resonances are found in the triple-ionization channel. The only possible mechanism producing C^{4+}(1*s*^{2}) via these resonances is direct triple-Auger decay, i.e., a four-electron process with simultaneous emission of three electrons.

#### High resolution multi-photon spectroscopy by a tunable free-electron-laser light

*M. Zitnik, A. Mihelic, K. Bucar, M. Kavcic, J.-E. Rubensson, M. Svanquist, J. Söderström, R. Feifel, C. Sathe, Y. Ovcharenko, V. Lyamayev, T. Mazza, M. Meyer, M. Simon, L. Journel, J. Lüning, O. Plekan, M. Coreno, M. Devetta, M. Di Fraia, et. al*

Seeded free electron lasers theoretically have the intensity, tunability, and resolution required for multiphoton spectroscopy of atomic and molecular species. Using the seeded free electron laser FERMI and a novel detection scheme, we have revealed the two-photon excitation spectra of dipole-forbidden doubly excited states in helium. The spectral profiles of the lowest (−1,0)^{+1} ^{1}*S ^{e} *and (0,1)

^{0}

^{1}

*D*resonances display energy shifts in the meV range that depend on the pulse intensity. The results are explained by an effective two-level model based on calculated Rabi frequencies and decay rates.

^{e}#### Time-Dependent Multiphoton Ionization of Xenon in the Soft-X-Ray Regime

*N. Gerken, S. Klumpp, A. A. Sorokin, K. Tiedtke, M. Richter, V. Bürk, K. Mertens, P. Jurani, M. Martins*

The time-dependent multiphoton ionization of xenon atoms is studied with femtosecond pulses in the excitation range of the 4*d* giant resonance at the photon energy of 93 eV. Benefiting from a new operation mode of the free electron laser FLASH, the measurements are performed with varying pulse durations. A strong dependence of the ion charge distribution on the pulse duration allows the different multiphoton mechanisms behind the multiple photoionization of xenon to be disentangled up to a charge state of Xe1^{0+}. The results up to X^{e8+} are well explained by sequences of single photon, multiphoton, and Auger processes, but higher charge state generation suggests the need for collective electron multiphoton excitations.

### Project A4

#### Spectroscopic Signatures of the Dynamical Hydrophobic Solvation Shell Formation

*Henning Kirchberg, Peter Nalbach, Christian Bressler, and Michael Thorwart*When a hydrophilic solute in water is suddenly turned into a hydrophobic species, for instance, by photoionization, a layer of hydrated water molecules forms around the solute on a time scale of a few picoseconds. We study the dynamic buildup of the hydration shell around a hydrophobic solute on the basis of a time-dependent dielectric continuum model. Information about the solvent is spectroscopically extracted from the relaxation dynamics of a test dipole inside a static Onsager sphere in the nonequilibrium solvent. The growth process is described phenomenologically within two approaches. First, we consider a time-dependent thickness of the hydration layer that grows from zero to a finite value over a finite time. Second, we assume a time-dependent complex permittivity within a finite layer region around the Onsager sphere. The layer is modeled as a continuous dielectric with a much slower fluctuation dynamics. We find a time-dependent frequency shift down to the blue of the resonant absorption of the dipole, together with a dynamically decreasing line width, as compared to bulk water. The blue shift reflects the work performed against the hydrogen-bonded network of the bulk solvent and is a directly measurable quantity. Our results are in agreement with an experiment on the hydrophobic solvation of iodine in water.

*J. Phys. Chem. B 123, 2106 (2019)*

#### Transient Metal-Centered States Mediate Isomerization of a Photochromic Ru-Sulfoxide Complex

*A. Cordones, J. Hyuk Lee, K. Hong, H. Cho, K. Garg, M. Boggio-Pasqua, J. Rack, N. Huse, R. W. Schoenlein, T. Kyu Kim*

Ultrafast isomerization reactions underpin many processes in (bio)chemical systems and molecular materials. Understanding the coupled evolution of atomic and molecular structure during isomerization is paramount for control and rational design in molecular science. Here we report transient X-ray absorption studies of the photo-induced linkage isomerization of a Ru-based photochromic molecule. X-ray spectra reveal the spin and valence charge of the Ru atom and provide experimental evidence that metal-centered excited states mediate isomerization. Complementary X-ray spectra of the functional ligand S atoms probe the nuclear structural rearrangements, highlighting the formation of two metal-centered states with different metal-ligand bonding. These results address an essential open question regarding the relative roles of transient charge-transfer and metal-centered states in mediating photoisomerization. Global temporal and spectral data analysis combined with time-dependent density functional theory reveals a complex mechanism for photoisomerization with atomic details of the transient molecular and electronic structure not accessible by other means.

#### Nonequilibrium quantum solvation with a time-dependent Onsager cavity

*Henning Kirchberg, Peter Nalbach, and Michael Thorwart*We formulate a theory of nonequilibrium quantum solvation in which parameters of the solvent are explicitly depending on time. We assume in a simplest approach a spherical molecular Onsager cavity with a time-dependent radius. We analyze the relaxation properties of a test molecular point dipole in a dielectric solvent and consider two cases: (i) a shrinking Onsager sphere and (ii) a breathing Onsager sphere. Due to the time-dependent solvent, the frequency-dependent response function of the dipole becomes time-dependent. For a shrinking Onsager sphere, the dipole relaxation is in general enhanced. This is reflected in a temporally increasing linewidth of the absorptive part of the response. Furthermore, the effective frequency-dependent response function shows two peaks in the absorptive part which are symmetrically shifted around the eigenfrequency. By contrast, a breathing sphere reduces damping as compared to the static sphere. Interestingly, we find a non-monotonous dependence of the relaxation rate on the breathing rate and a resonant suppression of damping when both rates are comparable. Moreover, the linewidth of the absorptive part of the response function is strongly reduced for times when the breathing sphere reaches its maximal extension.

*J. Chem. Phys. 148, 164301 (2018)*

#### UV-Photochemistry of the Disulfide Bond: Evolution of Early Photoproducts from Picosecond X-ray Absorption Spectroscopy at the Sulfur K-Edge

*M. Ochmann, A. Hussain, I. von Ahnen, A. A. Cordones, K. Hong, J. H. Lee, R. Ma, K. Adamczyk, O. Vendrell, T. K. Kim, R. W. Schoenlein, and N. Huse*

We have investigated dimethyl disulfide as the basic moiety for understanding the photochemistry of disulfide bonds, which are central to a broad range of biochemical processes. Picosecond time-resolved X-ray absorption spectroscopy at the sulfur K-edge provides unique element-specific insight into the photochemistry of the disulfide bond initiated by 267 nm femtosecond pulses. We observe a broad but distinct transient induced absorption spectrum which recovers on at least two time scales in the nanosecond range. We employed RASSCF electronic structure calculations to simulate the sulfur-1s transitions of multiple possible chemical species, and identified the methylthiyl and methylperthiyl radicals as the primary reaction products. In addition, we identify disulfur and the CH_{2}S thione as the secondary reaction products of the perthiyl radical that are most likely to explain the observed spectral and kinetic signatures of our experiment. Our study underscores the importance of elemental specificity and the potential of time-resolved X-ray spectroscopy to identify short-lived reaction products in complex reaction schemes that underlie the rich photochemistry of disulfide systems.

#### Transferring the entatic-state principle to copper photochemistry

*B. Maerz, D. Göries, M. Naumova, M. Biednov, G. Neuber, A. Wetzel, S. M. Hofmann, P. Roedig, A. Meents, J. Bielecki, J. Andreasson, K. R. Beyerlein, H. N. Chapman, C. Bressler, W. Zinth, M. Rübhausen, and S. Herres-Pawlis*

The entatic state denotes a distorted coordination geometry of a complex from its typical arrangement that generates an improvement to its function. The entatic-state principle has been observed to apply to copper electron-transfer proteins and it results in a lowering of the reorganization energy of the electron-transfer process. It is thus crucial for a multitude of biochemical processes, but its importance to photoactive complexes is unexplored. Here we study a copper complex—with a specifically designed constraining ligand geometry—that exhibits metal-to-ligand charge-transfer state lifetimes that are very short. The guanidine–quinoline ligand used here acts on the bis(chelated) copper(I) centre, allowing only small structural changes after photoexcitation that result in very fast structural dynamics. The data were collected using a multimethod approach that featured time-resolved ultraviolet–visible, infrared and X-ray absorption and optical emission spectroscopy. Through supporting density functional calculations, we deliver a detailed picture of the structural dynamics in the picosecond-to-nanosecond time range.

#### Probing Transient Valence Orbital Changes with Picosecond Valence-to-Core X-ray Emission Spectroscopy

*A. March, T. Assefa, C. Bömer, C. Bressler, A. Britz, M. Diez, G. Doumy, A. Galler, M. Harder, D. Khakhulin, Z. Németh, M. Pápai, S. Schulz, S. H. Southworth, H. Yavas, L. Young, W. Gawelda, and G. Vankó*

We probe the dynamics of valence electrons in photoexcited [Fe(terpy)_{2}]^{2+} in solution to gain deeper insight into the Fe–ligand bond changes. We use hard X-ray emission spectroscopy (XES), which combines element specificity and high penetration with sensitivity to orbital structure, making it a powerful technique for molecular studies in a wide variety of environments. A picosecond-time-resolved measurement of the complete 1s X-ray emission spectrum captures the transient photoinduced changes and includes the weak valence-to-core (vtc) emission lines that correspond to transitions from occupied valence orbitals to the nascent core-hole. Vtc-XES offers particular insight into the molecular orbitals directly involved in the light-driven dynamics; a change in the metal–ligand orbital overlap results in an intensity reduction and a blue energy shift in agreement with our theoretical calculations and more subtle features at the highest energies reflect changes in the frontier orbital populations.

#### Parametric Down-Conversion of X Rays into the Optical Regime

*A. Schori, C. Bömer, D. Borodin, S. P. Collins, B. Detlefs, M. Moretti Sala, S. Yudovich, and S. Shwartz*

We report the observation of parametrically down-converted x-ray signal photons at photon energies that correspond to idler photons at optical wavelengths. The count-rate dependence on the angles of the input beam and of the detector and on the slit sizes agrees with theory within the experimental uncertainties. The nonlinear susceptibility, which we calculated from the measured efficiencies, is comparable to the nonlinear susceptibility evaluated from the measurements of x-ray and optical wave mixing. The results of the present Letter advance the development of a spectroscopy method for probing valence-electron charges and the microscopic optical response of crystals with atomic-scale resolution.

#### Light-Induced Radical Formation and Isomerization of an Aromatic Thiol in Solution Followed by Time-Resolved X-ray Absorption Spectroscopy at the Sulfur K-Edge

*M. Ochmann, I. von Ahnen, A. A. Cordones, A. Hussain, J. H. Lee, K. Hong, K. Adamczyk, O. Vendrell , T. K. Kim , R. W. Schoenlein, N. Huse*

We applied time-resolved sulfur-1s absorption spectroscopy to a model aromatic thiol system as a promising method for tracking chemical reactions in solution. Sulfur-1s absorption spectroscopy allows tracking multiple sulfur species with a time resolution of ∼70 ps at synchrotron radiation facilities. Experimental transient spectra combined with high-level electronic structure theory allow identification of a radical and two thione isomers, which are generated upon illumination with 267 nm radiation. Moreover, the regioselectivity of the thione isomerization is explained by the resulting radical frontier orbitals. This work demonstrates the usefulness and potential of time-resolved sulfur-1s absorption spectroscopy for tracking multiple chemical reaction pathways and transient products of sulfur-containing molecules in solution.

#### Time-resolved pump and probe x-ray absorption fine structure spectroscopy at beamline P11 at PETRA III

*D. Göries, B. Dicke, P. Roedig, N. Stübe, J. Meyer, A. Galler, W. Gawelda, A. Britz, P. Geßler, H. Sotoudi Namin, A. Beckmann, M. Schlie, M. Warmer, M. Naumova, C. Bressler, M. Rübhausen, E. Weckert, and A. Meents*

We report about the development and implementation of a new setup for time-resolved X-ray absorption fine structure spectroscopy at beamline P11 utilizing the outstanding source properties of the low-emittance PETRA III synchrotron storage ring in Hamburg. Using a high intensity micrometer-sized X-ray beam in combination with two positional feedback systems, measurements were performed on the transition metal complex fac-Tris[2-phenylpyridinato-C2,N]iridium(III) also referred to as fac-Ir(ppy)3. This compound is a representative of the phosphorescent iridium(III) complexes, which play an important role in organic light emitting diode (OLED) technology. The experiment could directly prove the anticipated photoinduced charge transfer reaction. Our results further reveal that the temporal resolution of the experiment is limited by the PETRA III X-ray bunch length of ∼103 ps full width at half maximum (FWHM).

#### Femtosecond X-Ray Scattering Study of Ultrafast Photoinduced Structural Dynamics in Solvated [Co(terpy)2]2+

*E. Basin, T. B. van Driel, K. S. Kjaer, A. O. Dohn, M. Christensen, T. Harlang, P. Chabera, Y. Liu, J. Uhlig, M. Pápai, Z. Németh, R. Hartsock, W. Liang, J. Zhang, R. Alonso-Mori, M. Chollet, J. M. Glawnia, S. Nelsen, D. Sokara, T. A. Assefa, A. Britz, A. Galler, W. Gawelda, C. Bressler, K. J. Gaffney, H. T. Lemke, K. B. Moller, M. M. Nielsen, V. Sundström, G. Vankó, K. Wärmark, S. E. Canton, and K. Haldrup*

We study the structural dynamics of photoexcited [Co(terpy)_{2}]^{2+} in an aqueous solution with ultrafast x-ray diffuse scattering experiments conducted at the Linac Coherent Light Source. Through direct comparisons with density functional theory calculations, our analysis shows that the photoexcitation event leads to elongation of the Co-N bonds, followed by coherent Co-N bond length oscillations arising from the impulsive excitation of a vibrational mode dominated by the symmetrical stretch of all six Co-N bonds. This mode has a period of 0.33 ps and decays on a subpicosecond time scale. We find that the equilibrium bond-elongated structure of the high spin state is established on a single-picosecond time scale and that this state has a lifetime of ∼7 ps.

#### A Multi-MHz Single Shot Data Acquisition Scheme with High Dynamic Range: Pump-Probe X-Ray Experiments at Synchrotrons

*A. Britz, T. Assefa, A. Galler, W. Gawelda, M. Diez, P. Zalden, D. Khakhulin, B. Fernandes, P. Gessler, H. Sotuodi, A. Beckmann, M. Harder, H. Yavas, and C. Bressler*

The technical implementation of a multi-MHz data acquisition scheme for laser-X-ray pump-probe experiments with pulse limited temporal resolution (100 ps) is presented. Such techniques are very attractive to benefit from the high-repetition rates of X-ray pulses delivered from advanced synchrotron radiation sources. Exploiting a synchronized 3.9 MHz laser excitation source, experiments in 60-bunch mode (7.8 MHz) at beamline P01 of the PETRA III storage ring are performed. Hereby molecular systems in liquid solutions are excited by the pulsed laser source and the total X-ray fluorescence yield (TFY) from the sample is recorded using silicon avalanche photodiode detectors (APDs). The subsequent digitizer card samples the APD signal traces in 0.5 ns steps with 12-bit resolution. These traces are then processed to deliver an integrated value for each recorded single X-ray pulse intensity and sorted into bins according to whether the laser excited the sample or not. For each subgroup the recorded single-shot values are averaged over ~107 pulses to deliver a mean TFY value with its standard error for each data point, e.g. at a given X-ray probe energy. The sensitivity reaches down to the shot-noise limit, and signal-to-noise ratios approaching 1000 are achievable in only a few seconds collection time per data point. The dynamic range covers 100 photons pulse-1 and is only technically limited by the utilized APD.

#### Finite difference method accelerated with sparse solvers for structural analysis of the metal-organic complexes

*A. A. Guda, S. A. Guda, M. A. Soldatov, K. A. Lomachenko, A. L. Bugaev, C. Lamberti, W. Gawelda, C. Bressler, G. Smolentsev, A. V. Soldatov, Y. Joly*

Finite difference method (FDM) implemented in the FDMNES software [Phys. Rev. B, 2001, 63, 125120] was revised. Thorough analysis shows, that the calculated diagonal in the FDM matrix consists of about 96% zero elements. Thus a sparse solver would be more suitable for the problem instead of traditional Gaussian elimination for the diagonal neighbourhood. We have tried several iterative sparse solvers and the direct one MUMPS solver with METIS ordering turned out to be the best. Compared to the Gaussian solver present method is up to 40 times faster and allows XANES simulations for complex systems already on personal computers. We show applicability of the software for metal-organic [Fe(bpy)_{3}]^{2+} complex both for low spin and high spin states populated after laser excitation.

#### Observing Solvation Dynamics with Simultaneous Femtosecond X-Ray Emission Spectroscopy and X-ray Scattering

*K. Haldrup, W. Gawelda, R. Abela, R. Alonso-Mori, U. Bergmann, A. Bordage, M. Cammarata, S. Canton, A. O. Dohn, T. Brandt van Driel, D. M. Fritz, A. Galler, P. Glatzel, T. Harlang, K. S. Kjaer, H. T. Lemke, K. B. Moller, Z. Németh, M. Papai, N. Sas, J. Uhlig, D. Zhu, G. Vankó, V. Sundström, M. M. Nielsen, C. Bressler*

In liquid phase chemistry dynamic solute–solvent interactions often govern the path, ultimate outcome, and efficiency of chemical reactions. These steps involve many-body movements on subpicosecond time scales and thus ultrafast structural tools capable of capturing both intramolecular electronic and structural changes, and local solvent structural changes are desired. We have studied the intra- and intermolecular dynamics of a model chromophore, aqueous [Fe(bpy)_{3}]^{2+}, with complementary X-ray tools in a single experiment exploiting intense XFEL radiation as a probe. We monitored the ultrafast structural rearrangement of the solute with X-ray emission spectroscopy, thus establishing time zero for the ensuing X-ray diffuse scattering analysis. The simultaneously recorded X-ray diffuse scattering patterns reveal slower subpicosecond dynamics triggered by the intramolecular structural dynamics of the photoexcited solute. By simultaneous combination of both methods only, we can extract new information about the solvation dynamic processes unfolding during the first picosecond (ps). The measured bulk solvent density increase of 0.2% indicates a dramatic change of the solvation shell around each photoexcited solute, confirming previous ab initio molecular dynamics simulations. Structural changes in the aqueous solvent associated with density and temperature changes occur with ∼1 ps time constants, characteristic for structural dynamics in water. This slower time scale of the solvent response allows us to directly observe the structure of the excited solute molecules well before the solvent contributions become dominant.

#### Visualizing the non-equilibrium dynamics of photoinduced intramolecular electron transfer with femtosecond X-ray pulses

*S. Canton, K. Kjaer, G. Vankó, T. van Driel, S. Adachi, A. Bordage, C. Bressler, P. Chabera, M. Christensen, A. Dohn, A. Galler, W. Gawelda, D. Gosztola, K. Haldrup, T. Harlang, Y. Liu, K. Moller, Z. Németh, S. Nozawa, M. Pápai, T. Sato, Ta. Sato, K. Suarez-Alcantara, T. Togashi, K. Tono, J. Uhlig, D. Vithanage, K. Wärnmark, M. Yabashi, J. Zhang, V. Sundström, and M. Nielsen*

Ultrafast photoinduced electron transfer preceding energy equilibration still poses many experimental and conceptual challenges to the optimization of photoconversion since an atomic-scale description has so far been beyond reach. Here we combine femtosecond transient optical absorption spectroscopy with ultrafast X-ray emission spectroscopy and diffuse X-ray scattering at the SACLA facility to track the non-equilibrated electronic and structural dynamics within a bimetallic donor–acceptor complex that contains an optically dark centre. Exploiting the 100-fold increase in temporal resolution as compared with storage ring facilities, these measurements constitute the first X-ray-based visualization of a non-equilibrated intramolecular electron transfer process over large interatomic distances. Experimental and theoretical results establish that mediation through electronically excited molecular states is a key mechanistic feature. The present study demonstrates the extensive potential of femtosecond X-ray techniques as diagnostics of non-adiabatic electron transfer processes in synthetic and biological systems, and some directions for future studies, are outlined.

#### Optimized finite difference method for the full –potential XANES simulations: application to molecular adsorption geometries in MOFs and metal-ligand intersystem crossing transients

*S. Guda, A. Guda, M. Soldatov, K. Lomachenko, A. Bugaev, C. Lamberti, W. Gawelda, C. Bressler, G. Smolentsev, A. Soldatov, Y. Joly*

Accurate modeling of the X-ray absorption near-edge spectra (XANES) is required to unravel the local structure of metal sites in complex systems and their structural changes upon chemical or light stimuli. Two relevant examples are reported here concerning the following: (i) the effect of molecular adsorption on 3d metals hosted inside metal–organic frameworks and (ii) light induced dynamics of spin crossover in metal–organic complexes. In both cases, the amount of structural models for simulation can reach a hundred, depending on the number of structural parameters. Thus, the choice of an accurate but computationally demanding finite difference method for the ab initio X-ray absorption simulations severely restricts the range of molecular systems that can be analyzed by personal computers. Employing the FDMNES code [ Phys. Rev. B, 2001, 63, 125120] we show that this problem can be handled if a proper diagonalization scheme is applied. Due to the use of dedicated solvers for sparse matrices, the calculation time was reduced by more than 1 order of magnitude compared to the standard Gaussian method, while the amount of required RAM was halved. Ni K-edge XANES simulations performed by the accelerated version of the code allowed analyzing the coordination geometry of CO and NO on the Ni active sites in CPO-27-Ni MOF. The Ni–CO configuration was found to be linear, while Ni–NO was bent by almost 90°. Modeling of the Fe K-edge XANES of photoexcited aqueous [Fe(bpy)_{3}]^{2+} with a 100 ps delay we identified the Fe–N distance elongation and bipyridine rotation upon transition from the initial low-spin to the final high-spin state. Subsequently, the X-ray absorption spectrum for the intermediate triplet state with expected 100 fs lifetime was theoretically predicted.

#### Feasibility of Valence-to-Core X ray Emission Spectroscopy for Tracking Transient Species

*A. M. March, T. A. Assefa, C. Bressler, G. Doumy, A. Galler, W. Gawelda, E. P. Kanter, Z. Németh, M. Pápai, S. H. Southworth, L. Young, G. Vankó*

X-ray spectroscopies, when combined in laser-pump, X-ray-probe measurement schemes, can be powerful tools for tracking the electronic and geometric structural changes that occur during the course of a photoinitiated chemical reaction. X-ray absorption spectroscopy (XAS) is considered an established technique for such measurements, and X-ray emission spectroscopy (XES) of the strongest core-to-core emission lines (Kα and Kβ) is now being utilized. Flux demanding valence-to-core XES promises to be an important addition to the time-resolved spectroscopic toolkit. In this paper we present measurements and density functional theory calculations on laser-excited, solution-phase ferrocyanide that demonstrate the feasibility of valence-to-core XES for time-resolved experiments. We discuss technical improvements that will make valence-to-core XES a practical pump–probe technique.

#### Detailed Characterization of a Nanosecond-lived Excited State: X-ray and Theoretical Investigation of the Quintet State in Photoexcited [Fe(terpy)2]2+

*G. Vankó, A. Bordage, M. Pápai, K. Haldrup, P. Glatzel, A. M. March, G. Doumy, A. Britz, A. Galler, T. A. Assefa, D. Cabaret, A. Juhin, T. B. van Driel, K. S. Kjaer, A. O. Dohn, K. B. Moller, H. T. Lemke, E. Gallo, M. Rovezzi, Z. Németh, E. Rozsàlyi, T. Rozgonyi, J. Uhlig, V. Sundström, M. M. Nielsen, L. Young, S. H. Southworth, C. Bressler, W. Gawelda*

Theoretical predictions show that depending on the populations of the Fe 3d* _{xy}*, 3d

*, and 3*

_{xz}*orbitals two possible quintet states can exist for the high-spin state of the photoswitchable model system [Fe(terpy)*

_{dyz}_{2}]

^{2+}. The differences in the structure and molecular properties of these

^{5}B

_{2}and

^{5}E quintets are very small and pose a substantial challenge for experiments to resolve them. Yet for a better understanding of the physics of this system, which can lead to the design of novel molecules with enhanced photoswitching performance, it is vital to determine which high-spin state is reached in the transitions that follow the light excitation. The quintet state can be prepared with a short laser pulse and can be studied with cutting-edge time-resolved X-ray techniques. Here we report on the application of an extended set of X-ray spectroscopy and scattering techniques applied to investigate the quintet state of [Fe(terpy)

_{2}]

^{2+}80 ps after light excitation. High-quality X-ray absorption, nonresonant emission, and resonant emission spectra as well as X-ray diffuse scattering data clearly reflect the formation of the high-spin state of the [Fe(terpy)

_{2}]

^{2+}molecule; moreover, extended X-ray absorption fine structure spectroscopy resolves the Fe–ligand bond-length variations with unprecedented bond-length accuracy in time-resolved experiments. With ab initio calculations we determine why, in contrast to most related systems, one configurational mode is insufficient for the description of the low-spin (LS)–high-spin (HS) transition. We identify the electronic structure origin of the differences between the two possible quintet modes, and finally, we unambiguously identify the formed quintet state as

^{5}E, in agreement with our theoretical expectations.

#### Hydration shell effects in the relaxation dynamics of photoexcited Fe-II complexes in water

*P. Nalbach, A. J. A. Achner, M. Frey, M. Grosser, C. Bressler, M. Thorwart*

We study the relaxation dynamics of photoexcited Fe-II complexes dissolved in water and identify the relaxation pathway which the molecular complex follows in presence of a hydration shell of bound water at the interface between the complex and the solvent. Starting from a low-spin state, the photoexcited complex can reach the high-spin state via a cascade of different possible transitions involving electronic as well as vibrational relaxation processes. By numerically exact path integral calculations for the relaxational dynamics of a continuous solvent model, we find that the vibrational life times of the intermittent states are of the order of a few ps. Since the electronic rearrangement in the complex occurs on the time scale of about 100 fs, we find that the complex first rearranges itself in a high-spin and highly excited vibrational state, before it relaxes its energy to the solvent via vibrational relaxation transitions. By this, the relaxation pathway can be clearly identified. We find that the life time of the vibrational states increases with the size of the complex (within a spherical model), but decreases with the thickness of the hydration shell, indicating that the hydration shell acts as an additional source of fluctuations.

#### Solvation Dynamics Monitored by Combined X-Ray Spectroscopies and Scattering: Photoinduced Spin Transition in aqueous [Fe(bpy)3]2+

*C. Bressler, W. Gawelda, A. Galler, M. M. Nielsen, V. Sundström, G. Doumy, A. M. March, S. H. Southworth, L. Young, G. Vankó*

We have studied the photoinduced low spin (LS) to high spin (HS) conversion of aqueous Fe(bpy)3 with pulse-limited time resolution. In a combined setup permitting simultaneous X-ray diffuse scattering (XDS) and spectroscopic measurements at a MHz repetition rate we have unraveled the interplay between intramolecular dynamics and the intermolecular caging solvent response with 100 ps time resolution. On this time scale the ultrafast spin transition including intramolecular geometric structure changes as well as the concomitant bulk solvent heating process due to energy dissipation from the excited HS molecule are long completed. The heating is nevertheless observed to further increase due to the excess energy between HS and LS states released on a subnanosecond time scale. The analysis of the spectroscopic data allows precise determination of the excited population which efficiently reduces the number of free parameters in the XDS analysis, and both combined permit extraction of information about the structural dynamics of the first solvation shell.

#### Tracking excited-state charge and spin dynamics in iron coordination complexes

*W. Zhang, R. Alonso-Mori, U. Bergmann, C. Bressler, M. Chollet, A. Galler, W. Gawelda, R. G. Hadt, R. W. Hartsock1, T. Kroll, K. S. Kjær, K. Kubicˇek, H. T. Lemke, H. W. Liang, D. A. Meyer, M. M. Nielsen, C. Purser, J. S. Robinson, et. al*

Crucial to many light-driven processes in transition metal complexes is the absorption and dissipation of energy by 3d electrons1, 2, 3, 4. But a detailed understanding of such non-equilibrium excited-state dynamics and their interplay with structural changes is challenging: a multitude of excited states and possible transitions result in phenomena too complex to unravel when faced with the indirect sensitivity of optical spectroscopy to spin dynamics5 and the flux limitations of ultrafast X-ray sources6, 7. Such a situation exists for archetypal polypyridyl iron complexes, such as [Fe(2,2′-bipyridine)3]2+, where the excited-state charge and spin dynamics involved in the transition from a low- to a high-spin state (spin crossover) have long been a source of interest and controversy6, 7, 8, 9, 10, 11, 12, 13, 14, 15. Here we demonstrate that femtosecond resolution X-ray fluorescence spectroscopy, with its sensitivity to spin state, can elucidate the spin crossover dynamics of [Fe(2,2′-bipyridine)3]2+ on photoinduced metal-to-ligand charge transfer excitation. We are able to track the charge and spin dynamics, and establish the critical role of intermediate spin states in the crossover mechanism. We anticipate that these capabilities will make our method a valuable tool for mapping in unprecedented detail the fundamental electronic excited-state dynamics that underpin many useful light-triggered molecular phenomena involving 3d transition metal complexes.

#### Guest-Host Interactions Investigated by Time-Resolved X-Ray Spectroscopies and Scattering at MHz rates: Solvation Dynamics and Photoinduced Spin Transition in Aquesous [Fe(bipy]3]2+

*K. Haldrup, G. Vankó, W. Gawelda, A. Galler, G. Doumy, A. M. March, E. P. Kanter, A. Bordage, A. Dohn, T. B. van Driel, K. S. Kjaer, H. T. Lemke, S. E. Canton, J. Uhlig, V. Sundström, L. Young, S. Southworth, M. M. Nielsen, C. Bressler*

We have studied the photoinduced low spin (LS) to high spin (HS) conversion of [Fe(bipy)(3)](2+) in aqueous solution. In a laser pump/X-ray probe synchrotron setup permitting simultaneous, time-resolved X-ray diffuse scattering (XDS) and X-ray spectroscopic measurements at a 3.26 MHz repetition rate, we observed the interplay between intramolecular dynamics and the intermolecular caging solvent response with better than 100 ps time resolution. On this time scale, the initial ultrafast spin transition and the associated intramolecular geometric structure changes are long completed, as is the solvent heating due to the initial energy dissipation from the excited HS molecule. Combining information from X-ray emission spectroscopy and scattering, the excitation fraction as well as the temperature and density changes of the solvent can be closely followed on the subnanosecond time scale of the HS lifetime, allowing the detection of an ultrafast change in bulk solvent density. An analysis approach directly utilizing the spectroscopic data in the XDS analysis effectively reduces the number of free parameters, and both combined permit extraction of information about the ultrafast structural dynamics of the caging solvent, in particular, a decrease in the number of water molecules in the first solvation shell is inferred, as predicted by recent theoretical work.

### Project A5

#### Roadmap of ultrafast x-ray atomic and molecular physics

*L. Young, K. Ueda, M. Gühr, P. H. Bucksbaum, M. Simon, S. Mukamel, N. Rohringer, K. C. Prince, C. Masciovecchio, M. Meyer, A. Rudenko, D. Rolles, C. Bostedt, M. Fuchs, D. A. Reis, R. Santra, H. Kapteyn, M. Murnane, H. Ibrahim, F. Légaré, et. al.*

X-ray free-electron lasers (XFELs) and table-top sources of x-rays based upon high harmonic generation (HHG) have revolutionized the field of ultrafast x-ray atomic and molecular physics, largely due to an explosive growth in capabilities in the past decade. XFELs now provide unprecedented intensity (1020 W cm−2) of x-rays at wavelengths down to ~1 Ångstrom, and HHG provides unprecedented time resolution (~50 attoseconds) and a correspondingly large coherent bandwidth at longer wavelengths. For context, timescales can be referenced to the Bohr orbital period in hydrogen atom of 150 attoseconds and the hydrogen-molecule vibrational period of 8 femtoseconds; wavelength scales can be referenced to the chemically significant carbon K-edge at a photon energy of ~280 eV (44 Ångstroms) and the bond length in methane of ~1 Ångstrom. With these modern x-ray sources one now has the ability to focus on individual atoms, even when embedded in a complex molecule, and view electronic and nuclear motion on their intrinsic scales (attoseconds and Ångstroms). These sources have enabled coherent diffractive imaging, where one can image non-crystalline objects in three dimensions on ultrafast timescales, potentially with atomic resolution. The unprecedented intensity available with XFELs has opened new fields of multiphoton and nonlinear x-ray physics where behavior of matter under extreme conditions can be explored. The unprecedented time resolution and pulse synchronization provided by HHG sources has kindled fundamental investigations of time delays in photoionization, charge migration in molecules, and dynamics near conical intersections that are foundational to AMO physics and chemistry. This roadmap coincides with the year when three new XFEL facilities, operating at Ångstrom wavelengths, opened for users (European XFEL, Swiss-FEL and PAL-FEL in Korea) almost doubling the present worldwide number of XFELs, and documents the remarkable progress in HHG capabilities since its discovery roughly 30 years ago, showcasing experiments in AMO physics and other applications. Here we capture the perspectives of 17 leading groups and organize the contributions into four categories: ultrafast molecular dynamics, multidimensional x-ray spectroscopies; high-intensity x-ray phenomena; attosecond x-ray science.

#### Weak-field few-femtosecond VUV photodissociation dynamics of water isotopologues

*A. Baumann, S. Bazzi, D. Rompotis, O. Schepp, A. Azima, M. Wieland, D. Popova-Gorelova, O. Vendrell, R. Santra, M. Drescher*

We present a joint experimental and theoretical study of the VUV-induced dynamics of H2O and its deuterated isotopologues in the first excited state (˜A1B1) utilizing a VUV-pump VUV-probe scheme combined with ab initio classical trajectory calculations. 16-fs VUV pulses centered at 161 nm created by fifth-order harmonic generation are employed for single-shot pump-probe measurements. Combined with a precise determination of the VUV pulses' temporal profile, they provide the necessary temporal resolution to elucidate sub-10-fs dissociation dynamics in the 1+1 photon ionization time window. Ionization with a single VUV photon complements established strong-field ionization schemes by disclosing the molecular dynamics under perturbative conditions. Kinetic isotope effects derived from the pump-probe experiment are found to be in agreement with our by ab initio classical trajectory calculations, taking into account photoionization cross sections for the ground and first excited state of the water cation.

#### State-resolved attosecond reversible and irreversible dynamics in strong optical fields

*M. Sabbar, H. Timmer, Y. Chen, A. K. Pymer, Z. Loh, S. G. Sayres, S. Pabst, R. Santra, S. R. Leone*

Strong-field ionization (SFI) is a key process for accessing real-time quantum dynamics of electrons on the attosecond timescale. The theoretical foundation of SFI was pioneered in the 1960s, and later refined by various analytical models. While asymptotic ionization rates predicted by these models have been tested to be in reasonable agreement for a wide range of laser parameters, predictions for SFI on the sub-laser-cycle timescale are either beyond the scope of the models or show strong qualitative deviations from full quantum-mechanical simulations. Here, using the unprecedented state specificity of attosecond transient absorption spectroscopy, we follow the real-time SFI process of the two valence spin–orbit states of xenon. The results reveal that the irreversible tunnelling contribution is accompanied by a reversible electronic population that exhibits an observable spin–orbit-dependent phase delay. A detailed theoretical analysis attributes this observation to transient ground-state polarization, an unexpected facet of SFI that cannot be captured by existing analytical models that focus exclusively on the production of asymptotic electron/ion yields.

#### Time-dependent configuration-interaction-singles calculation of the 5p-subshell two-photon ionization cross section in xenon

*A. Karamatskou and R. Santra*

The 5p two-photon ionization cross section of xenon in the photon-energy range below the one-photon ionization threshold is calculated within the time-dependent configuration-interaction-singles (TDCIS) method. The TDCIS calculations are compared to random-phase-approximation calculations [Wendin et al., J. Opt. Soc. Am. B 4, 833 (1987)] and are found to reproduce the energy positions of the intermediate Rydberg states reasonably well. The effect of interchannel coupling is also investigated and found to change the cross section of the 5p shell only slightly compared to the intrachannel case.

#### Stability of the time-dependent configuration-interaction-singles method in the attosecond and strong-field regimes: A study of basis sets and absorption methods

*S. Pabst, A. Sytcheva, O. Geffert, R. Santra*

We investigate the behavior of several spatial grid methods and complex absorbers for strong-field and attosecond scenarios when using the time-dependent configuration-interaction singles method to solve the multi-electron time-dependent Schrödinger equation for atoms. We compare the pseudospectral grid, finite-element, and finite-element-discrete-variable-representation (DVR) methods with each other and discuss their advantages and disadvantages. Additionally, we study the performances of complex absorbing potential (CAP) and smooth exterior complex scaling (SES) to absorb the outgoing electron. We find that SES performs generally better than CAP for calculating high-harmonic generation spectra and XUV photoelectron spectra. In both of these cases, the DVR and even more the FEM grid representations show more reliable results—especially when using SES. Both absorbers show drawbacks when calculating photoelectron spectra in the strong-field regime.

#### Maximizing hole coherence in ultrafast photoionization of argon with an optimization by sequential parametrization update

*R. Esteban Goetz, M. Merkel, A. Karamatskou, R. Santra, C. P. Koch*

Photoionization with attosecond pulses populates hole states in the photoion. Superpositions of hole states represent ideal candidates for time-dependent spectroscopy, for example via pump-probe studies. The challenge consists in identifying pulses that create coherent superpositions of hole states while satisfying practical constraints. Here, we employ quantum optimal control to maximize the degree of coherence between these hole states. To this end, we introduce a derivative-free optimization method with sequential parametrization update (SPA optimization). We demonstrate the versatility and computational efficiency of SPA optimization for photoionization in argon by maximizing the coherence between the 3s and 3p0 hole states using shaped attosecond pulses. We show that it is possible to maximize the hole coherence while simultaneously prescribing the ratio of the final hole state populations.

#### Quantum optimal control of photoelectron spectra and angular distributions

*R. E. Goetz, A. Karamatskou, R. Santra, C. P. Koch*

Photoelectron spectra and photoelectron angular distributions obtained in photoionization reveal important information on, e.g., charge transfer or hole coherence in the parent ion. Here we show that optimal control of the underlying quantum dynamics can be used to enhance desired features in the photoelectron spectra and angular distributions. To this end, we combine Krotov's method for optimal control theory with the time-dependent configuration interaction singles formalism and a splitting approach to calculate photoelectron spectra and angular distributions. The optimization target can account for specific desired properties in the photoelectron angular distribution alone, in the photoelectron spectrum, or in both. We demonstrate the method for hydrogen and then apply it to argon under strong XUV radiation, maximizing the difference of emission into the upper and lower hemispheres, in order to realize directed electron emission in the XUV regime.

#### Sensitivity of nonlinear photoionization to resonance substructure in collective excitation

*T. Mazza, A. Karamatskou, M. Ilchen, S. Bakhtiarzadeh, A. J. Rafipoor, P. O’Keeffe, T. J. Kelly, N. Walsh, J. T. Costello, M. Meyer, R. Santra*

Collective behaviour is a characteristic feature in many-body systems, important for developments in fields such as magnetism, superconductivity, photonics and electronics. Recently, there has been increasing interest in the optically nonlinear response of collective excitations. Here we demonstrate how the nonlinear interaction of a many-body system with intense XUV radiation can be used as an effective probe for characterizing otherwise unresolved features of its collective response. Resonant photoionization of atomic xenon was chosen as a case study. The excellent agreement between experiment and theory strongly supports the prediction that two distinct poles underlie the giant dipole resonance. Our results pave the way towards a deeper understanding of collective behaviour in atoms, molecules and solid-state systems using nonlinear spectroscopic techniques enabled by modern short-wavelength light sources.

#### Multielectron dynamics in the tunneling ionization of correlated quantum systems

*M. Hollstein and D. Pfannkuche*

The importance of multielectron dynamics during the tunneling ionization of a correlated quantum system is investigated. By comparison of the solution of the time-dependent Schrödinger equation with the time-dependent configuration-interaction singles approach, we demonstrate the importance of a multielectron description of the tunneling ionization process especially for weakly confined quantum systems. Within this context, we observe that adiabatic driving by an intense light field can even enhance the correlations between still trapped electrons.

#### Wave-packet propagation based calculation of above-threshold ionization in the x-ray regime

*M. Tilley, A. Karamatskou, R. Santra*

We investigate the multi-photon process of above-threshold ionization for the light elements hydrogen, carbon, nitrogen, and oxygen in the hard x-ray regime. Numerical challenges are discussed and by comparing Hartree–Fock–Slater calculations with configuration–interaction–singles results we justify the mean-field potential approach in this regime. We present a theoretical prediction of two-photon above-threshold-ionization cross sections for the mentioned elements. Moreover, we study how the importance of above-threshold ionization varies with intensity. We find that for carbon, at x-ray intensities around ${{10}^{23}}\ {\rm W}\;{\rm c}{{{\rm m}}^{-2}}$, two-photon above-threshold ionization of the K-shell electrons is as probable as one-photon ionization of the L-shell electrons.

#### Theoretical characterization of the collective resonance states underlying the xenon giant dipole resonance

*Yi-Jen Chen (陳怡蓁), Stefan Pabst, Antonia Karamatskou, Robin Santra*

We present a detailed theoretical characterization of the two fundamental collective resonances underlying the xenon giant dipole resonance (GDR). This is achieved consistently by two complementary methods implemented within the framework of the configuration-interaction singles (CIS) theory. The first method accesses the resonance states by diagonalizing the many-electron Hamiltonian using the smooth exterior complex scaling technique. The second method involves a different application of the Gabor analysis to wave-packet dynamics. We identify one resonance at an excitation energy of 74 eV with a lifetime of 27 as and the second at 107eV with a lifetime of 11as. Our work provides a deeper understanding of the nature of the resonances associated with the GDR: a group of close-lying intrachannel resonances splits into two far-separated resonances through interchannel couplings involving the 4d electrons. The CIS approach allows a transparent interpretation of the two resonances as new collective modes. Due to the strong entanglement between the excited electron and the ionic core, the resonance wave functions are not dominated by any single particle-hole state. This gives rise to plasma-like collective oscillations of the 4d shell as a whole.

#### Spin–orbit effects in atomic high-harmonic generation

*S. Pabst, R. Santra*

Spin–orbit interactions lead to small energy gaps between the outermost p1/2 and p3/2 shells of noble gas atoms. Strong-field pulses tunnel-ionize an electron out of either shell resulting in spin–orbit-driven hole motion. These hole dynamics affect the high-harmonic generation (HHG) yield. However, the spectral shape as well as the angular distribution of the HHG emission is not influenced by spin–orbit coupling. We demonstrate the spin–orbit effect on atomic krypton by solving the multi-electron Schrödinger equation with the time-dependent configuration-interaction singles approach. We also provide pulse parameters where this effect can be identified in experiments through an enhancement in the HHG yield as the wavelength of the strong-field pulse increases.

#### Controlling the 2p hole alignment in neon via the 2s-3p Fano resonance

*E. Heinrich-Josties, S. Pabst, R. Santra*

We study the state-resolved production of neon ion after resonant photoionization of Ne via the 2s-3p Fano resonance. We find that by tuning the photon energy across the Fano resonance, a surprisingly high control over the alignment of the final 2p hole along the polarization direction can be achieved. In this way, hole alignments can be created that are otherwise very hard to achieve. The mechanism responsible for this hole alignment is the destructive interference of the direct and indirect (via the autoionizing 2s−13p state) ionization pathways of 2p. By changing the photon energy, the strength of the interference varies and 2p hole alignments with ratios up to 19:1 between 2p0 and 2p±1 holes can be created—an effect normally only encountered in tunnel ionization using strong-field ir pulses. The inclusion of spin-orbit interaction does not change the qualitative feature and leads only to a reduction in the alignment by 2/3. Our study is based on a time-dependent configuration-interaction singles approach, which solves the multichannel time-dependent Schrödinger equation.

#### Calculation of photoelectron spectra within the time-dependent configuration-interaction singles scheme

*A. Karamatskou, S. Pabst, Y.-J. Chen, R. Santra*

We present an extension of the time-dependent configuration-interaction singles (TDCIS) method to the computation of the electron kinetic-energy spectrum in photoionization processes. Especially for strong and long ionizing light pulses, the detection of the photoelectron poses a computational challenge because propagating the outgoing photoelectron wave packet requires large grid sizes. Two different methods that allow for the extraction of the asymptotic photoelectron momentum are compared regarding their methodological and computational performance. The first method follows the scheme of Tong et al. [X. M. Tong, K. Hino, and N. Toshima, Phys. Rev. A 74, 031405(R) (2006)], where the photoelectron wave function is absorbed by a real splitting function. The second method following that presented by Tao and Scrinzi [L. Tao and A. Scrinzi, New J. Phys. 14, 013021 (2012)], measures the flux of the electron wave packet through a surface at a fixed radius. With both methods the full angle- and energy-resolved photoelectron spectrum is obtained. Combined with the TDCIS scheme, it is possible to analyze the dynamics of the outgoing electron in a channel-resolved way and, additionally, to study the dynamics of the bound electrons in the parent ion. As an application, one-photon and above-threshold ionization of argon following strong XUV irradiation are studied via energy- and angle-resolved photoelectron spectra.

#### Introducing many-body physics using atomic spectroscopy

*D. Krebs, S. Pabst, R. Santra*

Atoms constitute relatively simple many-body systems, making them suitable objects for developing an understanding of basic aspects of many-body physics. Photoabsorption spectroscopy is a prominent method to study the electronic structure of atoms and the inherent many-body interactions. In this article, the impact of many-body effects on well-known spectroscopic features, such as Rydberg series, Fano resonances, Cooper minima, and giant resonances, is studied and related many-body phenomena in other fields are outlined. To calculate photoabsorption cross sections, the time-dependent configuration interaction singles (TDCIS) model is employed. The conceptual clearness of TDCIS in combination with the compactness of atomic systems allows for a pedagogical introduction to many-body phenomena.

#### Strong-Field Many-Body Physics and the Giant Enhancement in the High-Harmonic Spectrum of Xenon

*S. Pabst, R. Santra*

We resolve an open question about the origin of the giant enhancement in the high-harmonic generation spectrum of atomic xenon around 100 eV. By solving the many-body time-dependent Schrödinger equation with all 4d, 5s, and 5p orbitals active, we truly demonstrate the enhancement results from the collective many-body excitation induced by the returning photoelectron via two-body interchannel interactions. Without the many-body interactions, which promote a 4d electron into the 5p vacancy created by strong-field ionization, no collective excitation and no enhancement in the high-harmonic generation spectrum exist.

#### Atomic and molecular dynamics triggered by ultrashort light pulses on the atto- to picosecond time scale

*S. Pabst*

Time-resolved investigations of ultrafast electronic and molecular dynamics were not possible until recently. The typical time scale of these processes is in the picosecond to attosecond realm. The tremendous technological progress in recent years made it possible to generate ultrashort pulses, which can be used to trigger, to watch, and to control atomic and molecular motion. This tutorial focuses on experimental and theoretical advances which are used to study the dynamics of electrons and molecules in the presence of ultrashort pulses. In the first part, the rotational dynamics of molecules, which happens on picosecond and femtosecond time scales, is reviewed. Well-aligned molecules are particularly suitable for angle-dependent investigations like x-ray diffraction or strong-field ionization experiments. In the second part, the ionization dynamics of atoms is studied. The characteristic time scale lies, here, in the attosecond to few-femtosecond regime. Although a one-particle picture has been successfully applied to many processes, many-body effects do constantly occur. After a broad overview of the main mechanisms and the most common tools in attosecond physics, examples of many-body dynamics in the attosecond world (e.g., in high-harmonic generation and attosecond transient absorption spectroscopy) are discussed.

#### Adiabaticity and diabaticity in strong-field ionization

*A. Karamatskou, S. Pabst, R. Santra*

If the photon energy is much less than the electron binding energy, ionization of an atom by a strong optical field is often described in terms of electron tunneling through the potential barrier resulting from the superposition of the atomic potential and the potential associated with the instantaneous electric component of the optical field. In the strict tunneling regime, the electron response to the optical field is said to be adiabatic, and nonadiabatic effects are assumed to be negligible. Here, we investigate to what degree this terminology is consistent with a language based on the so-called adiabatic representation. This representation is commonly used in various fields of physics. For electronically bound states, the adiabatic representation yields discrete potential-energy curves that are connected by nonadiabatic transitions. When applying the adiabatic representation to optical strong-field ionization, a conceptual challenge is that the eigenstates of the instantaneous Hamiltonian form a continuum; i.e., there are no discrete adiabatic states. This difficulty can be overcome by applying an analytic-continuation technique. In this way, we obtain a rigorous classification of adiabatic states and a clear characterization of (non)adiabatic and (non)diabatic ionization dynamics. Moreover, we distinguish two different regimes within tunneling ionization and explain the dependence of the ionization probability on the pulse envelope.

#### Real time tracing of valence-shell electronic coherences with attosecond transient absorption spectroscopy

*A. Wirth, R. Santra, E. Goulielmakis*

The chemical properties of atoms, molecules and of more complex systems such as clusters, nanoparticles or condensed matter systems are determined by valence electrons. Real-time control of these properties requires the capability of tracing as well as of driving valence electrons on their native temporal scale of motion, that is, within tens to thousands of attoseconds. Here we detail the technique of attosecond transient absorption spectroscopy. It combines the extreme sensitivity of core-level spectroscopy with the unprecedented temporal resolution offered by the tools of attosecond technology. We use the technique to demonstrate real-time tracing and complete characterization of coherent electron motion triggered by single, double or multiple ionization of atoms exposed to intense, few-cycle pulses. Our work opens the door to high fidelity, time-domain studies and control of electron dynamics in the microcosm.

#### Theory of attosecond transient-absorption spectroscopy of krypton for overlapping pump and probe pulses

*S. Pabst, A. Sytcheva, A. Moulet, A. Wirth, E. Goulielmakis, R. Santra*

We present a fully ab initio calculations for attosecond transient absorption spectroscopy of atomic krypton with overlapping pump and probe pulses. Within the time-dependent configuration interaction singles (TDCIS) approach, we describe the pump step (strong-field ionization using a near-infrared pulse) as well as the probe step (resonant electron excitation using an extreme-ultraviolet pulse) from first principles. We extend our TDCIS model and account for the spin-orbit splitting of the occupied orbitals. We discuss the spectral features seen in a recent attosecond transient absorption experiment [ A. Wirth et al. Science 334 195 (2011)]. Our results support the concept that the transient absorption signal can be directly related to the instantaneous hole population even during the ionizing pump pulse. Furthermore, we find strong deformations in the absorption lines when the overlap of pump and probe pulses is maximum. These deformations can be described by relative phase shifts in the oscillating ionic dipole. We discuss possible mechanisms contributing to these phase shifts. Our finding suggests that the nonperturbative laser dressing of the entire N-electron wave function is the main contributor.

#### Impact of multichannel and multipole effects on the Cooper minimum in the high-order-harmonic spectrum of argon

*S. Pabst, L. Greenman, D. A. Mazziotti, R. Santra*

We investigate the relevance of multiple-orbital and multipole effects during high-harmonic generation (HHG). The time-dependent configuration interaction singles (TDCIS) approach is used to study the impact of the detailed description of the residual electron-ion interaction on the HHG spectrum. We find that the shape and position of the Cooper minimum in the HHG spectrum of argon changes significantly whether or not interchannel interactions are taken into account. The HHG yield can be underestimated by up to 2 orders of magnitude in the energy region of 30–50 eV. We show that the argument of low ionization probability is not sufficient to justify ignoring multiple-orbital contributions. Additionally, we find the HHG yield is sensitive to the nonspherical multipole character of the electron-ion interaction.

### Project A6

#### Quantum point spread function for imaging trapped few-body systems with a quantum gas microscope

*M. Pyzh, S. Krönke, C. Weitenberg, P. Schmelcher*

Quantum gas microscopes, which image the atomic occupations in an optical lattice, have opened a new avenue to the exploration of many-body lattice systems. Imaging trapped systems after freezing the density distribution by ramping up a pinning lattice leads, however, to a distortion of the original density distribution, especially when its structures are on the scale of the pinning lattice spacing. We show that this dynamics can be described by a filter, which we call in analogy to classical optics a quantum point spread function. Using a machine learning approach, we demonstrate via several experimentally relevant setups that a suitable deconvolution allows for the reconstruction of the original density distribution. These findings are both of fundamental interest for the theory of imaging and of immediate importance for current quantum gas experiments.

#### Spectral properties and breathing dynamics of a few-body Bose–Bose mixture in a 1D harmonic trap

*M. Pyzh, S. Krönke, C. Weitenberg, P. Schmelcher*

We investigate a few-body mixture of two bosonic components, each consisting of two particles confined in a quasi one-dimensional harmonic trap. By means of exact diagonalization with a correlated basis approach we obtain the low-energy spectrum and eigenstates for the whole range of repulsive intra- and inter-component interaction strengths. We analyse the eigenvalues as a function of the inter-component coupling, covering hereby all the limiting regimes, and characterize the behaviour in-between these regimes by exploiting the symmetries of the Hamiltonian. Provided with this knowledge we study the breathing dynamics in the linear-response regime by slightly quenching the trap frequency symmetrically for both components. Depending on the choice of interactions strengths, we identify 1 to 3 monopole modes besides the breathing mode of the centre of mass coordinate. For the uncoupled mixture each monopole mode corresponds to the breathing oscillation of a specific relative coordinate. Increasing the inter-component coupling first leads to multi-mode oscillations in each relative coordinate, which turn into single-mode oscillations of the same frequency in the composite-fermionization regime.

#### Superfluidity and relaxation dynamics of a laser-stirred 2D Bose gas

*Singh V. P., Weitenberg C., Dalibard J., Mathey L.*

We investigate the superfluid behavior of a two-dimensional (2D) Bose gas of ^{87}Rb atoms using classical field dynamics. In the experiment by R. Desbuquois et al. [Nat. Phys. 8, 645 (2012)], a 2D quasicondensate in a trap is stirred with a blue-detuned laser beam along a circular path around the trap center. Here, we study this experiment from a theoretical perspective. The heating induced by stirring increases rapidly above a velocity vc, which we define as the critical velocity. We identify the superfluid, the crossover, and the thermal regime by a finite, a sharply decreasing, and a vanishing critical velocity, respectively. We demonstrate that the onset of heating occurs due to the creation of vortex-antivortex pairs. A direct comparison of our numerical results to the experimental ones shows a good agreement, if a systematic shift of the critical phase-space density is included. We relate this shift to the absence of thermal equilibrium between the condensate and the thermal wings, which were used in the experiment to extract the temperature. We expand on this observation by studying the full relaxation dynamics between the condensate and the thermal cloud.

#### Implementing supersymmetric dynamics in ultracold-atom systems

*M. Lahrz, C. Weitenberg, L. Mathey*

Supersymmetric systems derive their properties from conserved supercharges which form a supersymmetric algebra. These systems naturally factorize into two subsystems, which, when considered as individual systems, have essentially the same eigenenergies, and their eigenstates can be mapped onto each other. We propose a Mach-Zehnder interference experiment to detect supersymmetry in quantum-mechanical systems, which can be realized with current technology. To demonstrate this interferometric technique, we first propose a one-dimensional ultracold-atom setup to realize a pair of supersymmetric systems. Here, a single-atom wave packet evolves in a superposition of the subsystems and gives an interference contrast that is sharply peaked if the subsystems form a supersymmetric pair. Second, we propose a two-dimensional setup that implements supersymmetric dynamics in a synthetic gauge field.

#### Observation of topological Bloch-state defects and their merging transition

*M. Tarnowski, M. Nuske, N. Fläschner, B. Rem, D. Vogel, L. Freystatzky, K. Sengstock, L. Mathey, C. Weitenberg*

Topological defects in Bloch bands, such as Dirac points in graphene, and their resulting Berry phases play an important role for the electronic dynamics in solid state crystals. Such defects can arise in systems with a two-atomic basis due to the momentum-dependent coupling of the two sublattice states, which gives rise to a pseudo-spin texture. The topological defects appear as vortices in the azimuthal phase of this pseudo-spin texture. Here, we demonstrate a complete measurement of the azimuthal phase in a hexagonal optical lattice

employing a versatile method based on time-of-flight imaging after off-resonant lattice modulation. Furthermore we map out the merging transition of the two Dirac points induced by beam imbalance. Our work paves the way to accessing geometric properties in general multi-band systems also with spin-orbit coupling and interactions.

Phys. Rev. Lett. 118, 240403 (2017)

https://arxiv.org/abs/1703.02813

#### Emulating molecular orbitals and electronic dynamics with ultracold atoms

*D.-S. Lühmann, C. Weitenberg, K. Sengstock*

In the recent years, ultracold atoms in optical lattices have proven their great value as quantum simulators for studying strongly-correlated phases and complex phenomena in solid-state systems. Here we reveal their potential as quantum simulators for molecular physics and propose a technique to image the three-dimensional molecular orbitals with high resolution. The outstanding tunability of ultracold atoms in terms of potential and interaction offer fully-adjustable model systems for gaining deep insight into the electronic structure of molecules. We study the orbitals of an artificial benzene molecule and discuss the effect of tunable interactions in its conjugated pi electron system with special regard to localization and spin order. The dynamical timescale of ultracold atom simulators are on the order milliseconds which allow for the time-resolved monitoring of a broad range of dynamical processes. As an example, we compute the hole dynamics in the conjugated pi system of the artificial benzene molecule.

## Project B

### Project B2

#### High-resolution resonant inelastic extreme ultraviolet scattering from orbital and spin excitations in a Heisenberg antiferromagnet

*A. Caretta, M. Dell'Angela, Y. Chuang, A. M. Kalashnikova, R. V. Pisarev, D. Bossini, F. Hieke, W. Wurth, B. Casarin, R. Ciprian, F. Parmigiani, S. Wexler, L. A. Wray, M. Malvestuto*

We report a high-resolution resonant inelastic extreme ultraviolet (EUV) scattering study of the quantum Heisenberg antiferromagnet KCoF_{3}. By tuning the EUV photon energy to the cobalt *M*_{23} edge, a complete set of low-energy 3*d* spin-orbital excitations is revealed. These low-lying electronic excitations are modeled using an extended multiplet-based mean-field calculation to identify the roles of lattice and magnetic degrees of freedom in modifying the resonant inelastic x-ray scattering (RIXS) spectral line shape. We have demonstrated that the temperature dependence of RIXS features upon the antiferromagnetic ordering transition enables us to probe the energetics of short-range spin correlations in this material.

#### Extreme ultraviolet resonant inelastic X-ray scattering (RIXS) at a seeded free-electron laser

*M. Dell’Angela, F. Hieke, M. Malvestuto, L. Sturari, S. Bajt, I. V. Kozhevnikov, J. Ratanapreechachai, A. Caretta, B. Casarin, F. Glerean, A. M. Kalashnikova, R. V. Pisarev, Y.-D. Chuang, G. Manzoni, F. Cilento, R. Mincigrucci, A. Simoncig, E. Principi, C. Masciovecchio, L. Raimondi, N. Mahne, C. Svetina, M. Zangrando, R. Passuello, G. Gaio, M. Prica, M. Scarcia, G. Kourousias, R. Borghes, L. Giannessi, W. Wurth and F. Parmigiani*

In the past few years, we have been witnessing an increased interest for studying materials properties under non-equilibrium conditions. Several well established spectroscopies for experiments in the energy domain have been successfully adapted to the time domain with sub-picosecond time resolution. Here we show the realization of high resolution resonant inelastic X-ray scattering (RIXS) with a stable ultrashort X-ray source such as an externally seeded free electron laser (FEL). We have designed and constructed a RIXS experimental endstation that allowed us to successfully measure the d-d excitations in KCoF_{3} single crystals at the cobalt M_{2,3}-edge at FERMI FEL (Elettra-Sincrotrone Trieste, Italy). The FEL-RIXS spectra show an excellent agreement with the ones obtained from the same samples at the MERIXS endstation of the MERLIN beamline at the Advanced Light Source storage ring (Berkeley, USA). We established experimental protocols for performing time resolved RIXS experiments at a FEL source to avoid X ray-induced sample damage, while retaining comparable acquisition time to the synchrotron based measurements. Finally, we measured and modelled the influence of the FEL mixed electromagnetic modes, also present in externally seeded FELs, and the beam transport with ~120 meV experimental resolution achieved in the presented RIXS setup.

#### The role of space charge in spin-resolved photoemission experiments

*A. Fognini, G. Salvatella, T.U. Michlmayr, C. Wetli, U. Ramsperger, T. Bähler, F. Sorgenfrei, M. Beye, A. Eschenlohr, N. Pontius, C. Stamm, F. Hieke, M. Dell‘Angela, S. de Jong, R. Kukreja, N. Gerasimova, V. Rybnikov, H. Redlin, J. Raabe, W. Wurth et.*

Spin-resolved photoemission is one of the most direct ways of measuring the magnetization of a ferromagnet. If all valence band electrons contribute, the measured average spin polarization is proportional to the magnetization. This is even the case if electronic excitations are present, and thus is of particular interest for studying the response of the magnetization to a pump laser pulse. Here, we demonstrate the feasibility of ultrafast spin-resolved photoemission using free electron laser (FEL) radiation and investigate the effect of space charge on the detected spin polarization. The sample is exposed to the radiation of the FEL FLASH in Hamburg. Surprisingly, the measured spin polarization depends on the fluence of the FEL radiation: a higher FEL fluence reduces the measured spin polarization. Space-charge simulations can explain this effect. These findings have consequences for future spin-polarized photoemission experiments using pulsed photon sources.

#### Ultrafast reduction of the total magnetization in iron

*A. Fognini, T. U. Michlmayr, G. Salvatella, C. Wetli, U. Ramsperger, T. Bähler, F.Sorgenfrei, M. Beye, A. Eschenlohr, N. Pontius, C. Stamm, F. Hieke, M. Dell'Angela, S. de Jong, R. Kukreja, N. Gerasimova, V. Rybnikov, H. Redlin, W. Wurth, et. al*

Surprisingly, if a ferromagnet is exposed to an ultrafast laser pulse, its apparent magnetization is reduced within less than a picosecond. Up to now, the total magnetization, i.e., the average spin polarization of the whole valence band, was not detectable on a sub-picosecond time scale. Here, we present experimental data, confirming the ultrafast reduction of the total magnetization. Soft x-ray pulses from the free electron laser in Hamburg (FLASH) extract polarized cascade photoelectrons from an iron layer excited by a femtosecond laser pulse. The spin polarization of the emitted electrons is detected by a Mott spin polarimeter.

#### Speed limit of the insulator metal-transition in magnetite

*S. de Jong, R. Kukreja, C. Trabant, N. Pontius, C.F. Chang, T. Kachel, M. Beye, F. Sorgenfrei, C. H. Back, B. Bräuer, W.F. Schlotter, J.J. Turner, O. Krupin, M. Doehler, D. Zhu, M.A. Hossain, W. Wurth, D. Fausti, F. Novelli, M. Esposito, et. al*

As the oldest known magnetic material, magnetite (Fe3O4) has fascinated mankind for millennia. As the first oxide in which a relationship between electrical conductivity and fluctuating/localized electronic order was shown, magnetite represents a model system for understanding correlated oxides in general. Nevertheless, the exact mechanism of the insulator–metal, or Verwey, transition has long remained inaccessible. Recently, three-Fe-site lattice distortions called trimerons were identified as the characteristic building blocks of the low-temperature insulating electronically ordered phase9. Here we investigate the Verwey transition with pump–probe X-ray diffraction and optical reflectivity techniques, and show how trimerons become mobile across the insulator–metal transition. We find this to be a two-step process. After an initial 300 fs destruction of individual trimerons, phase separation occurs on a 1.5±0.2 ps timescale to yield residual insulating and metallic regions. This work establishes the speed limit for switching in future oxide electronics.

### Project B3

#### Observation of a Chirality-Induced Exchange-Bias Effect

*K. Chen, A. Philippi-Kobs, V. Lauter, A. Vorobiev, E. Dyadkina, V. Yu. Yakovchuk, S. Stolyar, D. Lott*

Chiral magnetism that manifests in the existence of skyrmions or chiral domain walls offers an alternative way for creating anisotropies in magnetic materials that might have large potential for application in future spintronic devices. Here we show experimental evidence for an alternative type of in-plane exchange-bias effect present at room temperature that is created from a chiral 90∘ domain wall at the interface of a ferrimagnetic-ferromagnetic Dy-Co/Ni-Fe bilayer system. The chiral interfacial domain wall forms due to the exchange coupling of Ni-Fe and Dy-Co at the interface and the presence of Dzyaloshinskii-Moriya interaction in the Dy-Co layer. As a consequence of the preferred chirality of the interfacial domain wall, the sign of the exchange-bias effect can be reversed by changing the perpendicular orientation of the Dy-Co magnetization. The chirality-created tunable exchange bias in Dy-Co/Ni-Fe is very robust against high in-plane magnetic fields (μ0H≤6T) and does not show any aging effects. Therefore, it overcomes the limitations of conventional exchange-bias systems.

#### Direct Visualization of Spatial Inhomogeneity of Spin Stripes Order in La1.72Sr0.28NiO4

* Gaetano Campi, Nicola Poccia, Boby Joseph, Antonio Bianconi, Shrawan Mishra, James Lee, Sujoy Roy, Agustinus Agung Nugroho, Marcel Buchholz, Markus Braden, Christoph Trabant, Alexey Zozulya, Leonard Müller, Jens Viefhaus, Christian Schüßler-Langeheine 9, Michael Sprung and Alessandro Ricci *

In several strongly correlated electron systems, the short range ordering of defects, charge and local lattice distortions are found to show complex inhomogeneous spatial distributions. There is growing evidence that such inhomogeneity plays a fundamental role in unique functionality of quantum complex materials. La1.72Sr0.28NiO4 is a prototypical strongly correlated perovskite showing spin stripes order. In this work we present the spatial distribution of the spin order inhomogeneity by applying micro X-ray diffraction to La1.72Sr0.28NiO4, mapping the spin-density-wave order below the 120 K onset temperature. We find that the spin-density-wave order shows the formation of nanoscale puddles with large spatial fluctuations. The nano-puddle density changes on the microscopic scale forming a multiscale phase separation extending from nanoscale to micron scale with scale-free distribution. Indeed spin-density-wave striped puddles are disconnected by spatial regions with negligible spin-density-wave order. The present work highlights the complex spatial nanoscale phase separation of spin stripes in nickelate perovskites and opens new perspectives of local spin order control by strain.

#### Spatial and temporal pre-alignment of an X-ray split-and-delay unit by laser light interferometry

*Roseker, W. ; Lee, S. ; Walther, M. ; Rysov, R. ; Sprung, M. ; Gruebel, G.*

We present a novel experimental setup for performing a precise pre-alignment of a hard X-ray split-and-delay unit based on low coherence light interferometry and high-precision penta-prisms. A split-and-delay unit is a sophisticated perfect crystal-optics device that splits an incoming X-ray pulse into two sub-pulses and generates a controlled time-delay between them. While the availability of a split-and-delay system will make ultrafast time-correlation and X-ray pump-probe experiments possible at free-electron lasers, its alignment process can be very tedious and time-consuming due to its complex construction. By implementing our experimental setup at beamline P10 of PETRA III, we were able to reduce the time of alignment to less than 3 h. We also propose an alternate method for finding the zero-time delay crossing without the use of X-rays or pulsed laser sources. The successful demonstration of this method brings prospect for operating the split-and-delay systems under alignment-time-critical environments such as X-ray free electron laser facilities.

Review of scientific instruments 90(4), 045106 (2019) [10.1063/1.5089496]

#### Towards ultrafast dynamics with split-pulse X-ray photon correlation spectroscopy at free electron laser sources

*Roseker, W. ; Hruszkewycz, S. O. ; Lehmkühler, F. ; Walther, M. ; Schulte-Schrepping, H. ; LEE, S. ; Osaka, T. ; Strüder, L. ;Hartmann, R. ; Sikorski, M. ; Song, S. ; Robert, A. ; Fuoss, P. H. ; Sutton, M. ; Stephenson, G. B. ; Grübel, G.*

One of the important challenges in condensed matter science is to understand ultrafast, atomic-scale fluctuations that dictate dynamic processes in equilibrium and non-equilibrium materials. Here, we report an important step towards reaching that goal by using a state-of-the-art perfect crystal based split-and-delay system, capable of splitting individual X-ray pulses andintroducing femtosecond to nanosecond time delays. We show the results of an ultrafast hard X-ray Photon Correlation Spectroscopy experiment at LCLS where split X-ray pulses were used to measure the dynamics of gold nanoparticles suspended in hexane. We show how reliable speckle contrast values can be extracted even from very low intensity free electron laser(FEL) speckle patterns by applying maximum likelihood fitting, thus demonstrating the potential of a split-and-delay approach for dynamics measurements at FEL sources. This will enable the characterization of equilibrium and, importantly also reversible non-equilibrium processes in atomically disordered materials.

Nature Communications 9(1), 1704 (2018) [10.1038/s41467-018-04178-9]

https://www.nature.com/articles/s41467-018-04178-9.epdf

#### Note: Soft X-ray transmission polarizer based on ferromagnetic thin films

*Mueller, L. ; Hartmann, G. ; Schleitzer, S. ; Berntsen, M. H. ; Walther, M. ; Rysov, R. ; Roseker, W. ; Scholz, F. ; Seltmann, J. ;Glaser, L. ; Viefhaus, J. ; Mertens, K. ; Bagschik, K. ; Frömter, R. ; De Fanis, A. ; Shevchuk, I. ; Medjanik, K. ; Öhrwall, G. ;Oepen, H. P. ; Martins, M. ; Meyer, M. ; Grübel, G.*

A transmission polarizer for producing elliptically polarized soft X-ray radiation from linearly polarized light is presented. The setup is intended for use at synchrotron and free-electron laser beamlines that do not directly offer circularly polarized light for, e.g., X-ray magnetic circular dichroism (XMCD) measurements or holographic imaging. Here, we investigate the degree of ellipticity upon transmission of linearly polarized radiation through a cobalt thin film. The experiment was performed at a photon energy resonant to the Co L3-edge, i.e., 778 eV, and the polarization of the transmitted radiation was determined using a polarization analyzer that measures the directional dependence of photo electrons emitted from a gas target. Elliptically polarized radiation can be created at any absorption edge showing the XMCD effect by using the respective magnetic element.

Review of scientific instruments 89(3), 036103 - (2018) [10.1063/1.5018396]

#### Employing soft x-ray resonant magnetic scattering to study domain sizes and anisotropy in Co/Pd multilayers

*K. Bagschik, R. Frömter, J. Bach, B. Beyersdorff, L. Müller, S. Schleitzer, M. Hårdensson Berntsen, C. Weier, R. Adam, J. Viefhaus, C. M. Schneider, G. Grübel, H. P. Oepen*

It is demonstrated that the magnetic diffraction pattern of the isotropic disordered maze pattern is well described utilizing a gamma distribution of domain sizes in a one-dimensional model. From the analysis, the mean domain size and the shape parameter of the distribution are obtained. The model reveals an average domain size that is significantly different from the value that is determined from the peak position of the structure factor in reciprocal space. As a proof of principle, a wedge-shaped (CotÅ/Pd10Å)8 multilayer film, that covers the thickness range of the spin-reorientation transition, has been used. By means of soft x-ray resonant magnetic scattering (XRMS) and imaging techniques the thickness-driven evolution of the magnetic properties of the cobalt layers is explored. It is shown that minute changes of the domain pattern concerning domain size and geometry can be investigated and analyzed due to the high sensitivity and lateral resolution of the XRMS technique. The latter allows for the determination of the magnetic anisotropies of the cobalt layers within a thickness range of a few angstroms.

#### Spatial coherence determination from the Fourier analysis of a resonant soft X-ray magnetic speckle pattern

*K. Bagschik, R. Frömter, L. Müller, W. Roseker, J. Bach, P. Staeck, C. Thönnißen, S. Schleitzer, M. H. Berntsen, C. Weier, R. Adam, J. Viefhaus, C. M. Schneider, G. Grübel, H. P. Oepen*

We present a method to determine the two-dimensional spatial coherence of synchrotron radiation in the soft X-ray regime by analyzing the Fourier transform of the magnetic speckle pattern from a ferromagnetic film in a multidomain state. To corroborate the results, a Young’s double-pinhole experiment has been performed. The transverse coherence lengths in vertical and horizontal direction of both approaches are in a good agreement. The method presented here is simple and gives a direct access to the coherence properties of synchrotron radiation without nanostructured test objects.

#### Indirect excitation of ultrafast demagnetization

*B. Vodungbo, et.al.*

Does the excitation of ultrafast magnetization require direct interaction between the photons of the optical pump pulse and the magnetic layer? Here, we demonstrate unambiguously that this is not the case. For this we have studied the magnetization dynamics of a ferromagnetic cobalt/palladium multilayer capped by an IR-opaque aluminum layer. Upon excitation with an intense femtosecond-short IR laser pulse, the film exhibits the classical ultrafast demagnetization phenomenon although only a negligible number of IR photons penetrate the aluminum layer. In comparison with an uncapped cobalt/palladium reference film, the initial demagnetization of the capped film occurs with a delayed onset and at a slower rate. Both observations are qualitatively in line with energy transport from the aluminum layer into the underlying magnetic film by the excited, hot electrons of the aluminum film. Our data thus confirm recent theoretical predictions.

#### Characterization of spatial coherence of synchrotron radiation with non-redundant arrays of apertures

*P. Skopintsev, A. Singer, J. Bach, L. Müller, B. Beyersdorff, S. Schleitzer, O. Gorobtsov, A. Shabalin, R. P. Kurta, D. Dzhigaev, O. M. Yefanov, L. Glaser, A. Sakdinawat, G. Grübel, R. Frömter, H. P. Oepen, J. Viefhaus, I. A. Vartanyants*

A method to characterize the spatial coherence of soft X-ray radiation from a single diffraction pattern is presented. The technique is based on scattering from non-redundant arrays (NRAs) of slits and records the degree of spatial coherence at several relative separations from 1 to 15 µm, simultaneously. Using NRAs the spatial coherence of the X-ray beam at the XUV X-ray beamline P04 of the PETRA III synchrotron storage ring was measured as a function of different beam parameters. To verify the results obtained with the NRAs, additional Young's double-pinhole experiments were conducted and showed good agreement.

#### Imaging Ultrafast Demagnetization Dynamics after a Spatially Localized Optical Excitation

*C. von Korff Schmising, B. Pfau, M. Schneider, C. M. Günther, M. Giovannella, J. Perron, B. Vodungbo, L. Müller, F. Capotondi, E. Pedersoli, N. Mahne, J. Lüning, S. Eisebitt*

Ultrashort, coherent x-ray pulses of a free-electron laser are used to holographically image the magnetization dynamics within a magnetic domain pattern after creation of a localized excitation via an optical standing wave. We observe a spatially confined reduction of the magnetization within a couple of hundred femtoseconds followed by its slower recovery. Additionally, the experimental results show evidence of a spatial evolution of magnetization, which we attribute to ultrafast transport of nonequilibrium spin-polarized electrons for early times and to a fluence-dependent remagnetization rate for later times.

#### Endstation for ultrafast magnetic scattering experiments at the free-electron laser in Hamburg

*L. Müller, C. Gutt, S. Streit-Nierobisch, M. Walther, S. Schaffert, B. Pfau, J. Geilhufe, F. Büttner, S. Flewett, C. M. Günther, S. Eisebitt, A. Kobs, M. Hille, D. Stickler, R. Frömter, H. P. Oepen, J. Lüning, G. Grübel*

An endstation for pump–probe small-angle X-ray scattering (SAXS) experiments at the free-electron laser in Hamburg (FLASH) is presented. The endstation houses a solid-state absorber, optical incoupling for pump–probe experiments, time zero measurement, sample chamber, and detection unit. It can be used at all FLASH beamlines in the whole photon energy range offered by FLASH. The capabilities of the setup are demonstrated by showing the results of resonant magnetic SAXS measurements on cobalt-platinum multilayer samples grown on freestanding Si3N4 membranes and pump-laser-induced grid structures in multilayer samples.

#### Invited Article: Coherent imaging using seeded free-electron laser pulses with variable polarization: First results and research opportunities

*F. Capotondi, E. Pedersoli, N. Mahne, R. H. Menk, G. Passos, L. Raimondi, C. Svetina, G. Sandrin, M. Zangrando, M. Kiskinova, S. Bajt, M. Barthelmess, H. Fleckenstein, H. N. Chapman, J. Schulz, S. Schleitzer, L. Müller, C. Gutt, G. Grübel, et. al*

FERMI@Elettra, the first vacuum ultraviolet and soft X-ray free-electron laser (FEL) using by default a “seeded” scheme, became operational in 2011 and has been opened to users since December 2012. The parameters of the seeded FERMI FEL pulses and, in particular, the superior control of emitted radiation in terms of spectral purity and stability meet the stringent requirements for single-shot and resonant coherent diffraction imaging (CDI) experiments. The advantages of the intense seeded FERMI pulses with variable polarization have been demonstrated with the first experiments performed using the multipurpose experimental station operated at the diffraction and projection imaging (DiProI) beamline. The results reported here were obtained with fixed non-periodic targets during the commissioning period in 2012 using 20–32 nm wavelength range. They demonstrate that the performance of the FERMI FEL source and the experimental station meets the requirements of CDI, holography, and resonant magnetic scattering in both multi- and single-shot modes. Moreover, we present the first magnetic scattering experiments employing the fully circularly polarized FERMI pulses. The ongoing developments aim at pushing the lateral resolution by using shorter wavelengths provided by double-stage cascaded FERMI FEL-2 and probing ultrafast dynamic processes using different pump-probe schemes, including jitter-free seed laser pump or FEL-pump/FEL-probe with two color FEL pulses generated by the same electron bunch.

#### Breakdown of the X-Ray Resonant Magnetic Scattering Signal during Intense Pulses of Extreme Ultraviolet Free-Electron-Laser Radiation

*L. Müller, C. Gutt, B. Pfau, S. Schaffert, J. Geilhufe, F. Büttner, J. Mohanty, S. Flewett, R. Treusch, S. Düsterer, H. Redlin, A. Al-Shemmary, M. Hille, A. Kobs, R. Frömter, H. P. Oepen, B. Ziaja, N. Medvedev, S.-K. Son, R. Thiele, R. Santra, et. al.*

We present results of single-shot resonant magnetic scattering experiments of Co/Pt multilayer systems using 100 fs long ultraintense pulses from an extreme ultraviolet (XUV) free-electron laser. An x-ray-induced breakdown of the resonant magnetic scattering channel during the pulse duration is observed at fluences of 5 J/cm2. Simultaneously, the speckle contrast of the high-fluence scattering pattern is significantly reduced. We performed simulations of the nonequilibrium evolution of the Co/Pt multilayer system during the XUV pulse duration. We find that the electronic state of the sample is strongly perturbed during the first few femtoseconds of exposure leading to an ultrafast quenching of the resonant magnetic scattering mechanism.

#### Nanoscale spin reversal by non-local angular momentum transfer following ultrafast laser excitation in ferrimagnetic GdFeCo

*C. E. Graves, A. H. Reid, T. Wang, B. Wu, S. de Jong, K. Vahaplar, I. Radu, D. P. Bernstein, M. Messerschmidt, L. Müller, R. Coffee, M. Bionta, S. W. Epp, R. Hartmann, N. Kimmel, et. al.*

Ultrafast laser techniques have revealed extraordinary spin dynamics in magnetic materials that equilibrium descriptions of magnetism cannot explain. Particularly important for future applications is understanding non-equilibrium spin dynamics following laser excitation on the nanoscale, yet the limited spatial resolution of optical laser techniques has impeded such nanoscale studies. Here we present ultrafast diffraction experiments with an X-ray laser that probes the nanoscale spin dynamics following optical laser excitation in the ferrimagnetic alloy GdFeCo, which exhibits macroscopic all-optical switching. Our study reveals that GdFeCo displays nanoscale chemical and magnetic inhomogeneities that affect the spin dynamics. In particular, we observe Gd spin reversal in Gd-rich nanoregions within the first picosecond driven by the non-local transfer of angular momentum from larger adjacent Fe-rich nanoregions. These results suggest that a magnetic material’s microstructure can be engineered to control transient laser-excited spins, potentially allowing faster (~ 1 ps) spin reversal than in present technologies.

#### Ultrafast optical demagnetization manipulates nanoscale spin structure in domain walls

*B. Pfau, S. Schaffert, L. Müller, C. Gutt, A. Al-Shemmary, F. Büttner, R. Delaunay, S. Düsterer, S. Flewett, R. Frömter, J. Geilhufe, E. Guehrs, C.M. Günther, R. Hawaldar, M. Hille, N. Jaouen, A. Kobs, K. Li, J. Mohanty, H. Redlin et. al*

During ultrafast demagnetization of a magnetically ordered solid, angular momentum has to be transferred between the spins, electrons, and phonons in the system on femto- and picosecond timescales. Although the intrinsic spin-transfer mechanisms are intensely debated, additional extrinsic mechanisms arising due to nanoscale heterogeneity have only recently entered the discussion. Here we use femtosecond X-ray pulses from a free-electron laser to study thin film samples with magnetic domain patterns. We observe an infrared-pump-induced change of the spin structure within the domain walls on the sub-picosecond timescale. This domain-topography-dependent contribution connects the intrinsic demagnetization process in each domain with spin-transport processes across the domain walls, demonstrating the importance of spin-dependent electron transport between differently magnetized regions as an ultrafast demagnetization channel. This pathway exists independent from structural inhomogeneities such as chemical interfaces, and gives rise to an ultrafast spatially varying response to optical pump pulses.

#### Femtosecond Single-Shot Imaging of Nanoscale Ferromagnetic Order in Co/Pd Multilayers Using Resonant X-Ray Holography

*Tianhan Wang et al.*

We present the first single-shot images of ferromagnetic, nanoscale spin order taken with femtosecond x-ray pulses. X-ray-induced electron and spin dynamics can be outrun with pulses shorter than 80 fs in the investigated fluence regime, and no permanent aftereffects in the samples are observed below a fluence of 25 mJ/cm2. Employing resonant spatially muliplexed x-ray holography results in a low imaging threshold of 5 mJ/cm2. Our results open new ways to combine ultrafast laser spectroscopy with sequential snapshot imaging on a single sample, generating a movie of excited state dynamics.

### Project B4

#### Probing the fluctuations of the optical properties in time-resolved spectroscopy

*F. Randi, M. Esposito, F. Giusti, F. Parmigiani, O. Misochko, D. Fausti, M. Eckstein*

We show that, in optical pump-probe experiments on bulk samples, the statistical distribution of the intensity of ultrashort light pulses after interaction with a nonequilibrium complex material can be used to measure the time-dependent noise of the current in the system. We illustrate the general arguments for a photoexcited Peierls material. The transient noise spectroscopy allows us to measure to what extent electronic degrees of freedom dynamically obey the fluctuation-dissipation theorem, and how well they thermalize during the coherent lattice vibrations. The proposed statistical measurement developed here provides a new general framework to retrieve dynamical information on the excited distributions in nonequilibrium experiments, which could be extended to other degrees of freedom of magnetic or vibrational origin.

#### Nonequilibrium GW+EDMFT: Antiscreening and inverted populations from nonlocal correlations

*D. Golez, L. Boehnke, H. Strand, M. Eckstein, P. Werner*

We study the dynamics of screening in photodoped Mott insulators with long-ranged interactions using a nonequilibrium implementation of the *GW* plus extended dynamical mean-field theory formalism. Our study demonstrates that the complex interplay of the injected carriers with bosonic degrees of freedom (charge fluctuations) can result in long-lived transient states with properties that are distinctly different from those of thermal equilibrium states. Systems with strong nonlocal interactions are found to exhibit a self-sustained population inversion of the doublons and holes. This population inversion leads to low-energy antiscreening which can be detected in time-resolved electron-energy-loss spectra.

#### Nonequilibrium steady states and transient dynamics of conventional superconductors under phonon driving

*Y. Murakami, N. Tsuji, M. Eckstein, P. Werner*

We perform a systematic analysis of the influence of phonon driving on the superconducting Holstein model coupled to heat baths by studying both the transient dynamics and the nonequilibrium steady state (NESS) in the weak and strong electron-phonon coupling regimes. Our study is based on the nonequilibrium dynamical mean-field theory, and for the NESS we present a Floquet formulation adapted to electron-phonon systems. The analysis of the phonon propagator suggests that the effective attractive interaction can be strongly enhanced in a parametric resonant regime because of the Floquet side bands of phonons. While this may be expected to enhance the superconductivity (SC), our fully self-consistent calculations, which include the effects of heating and nonthermal distributions, show that the parametric phonon driving generically results in a suppression or complete melting of the SC order. In the strong coupling regime, the NESS always shows a suppression of the SC gap, the SC order parameter, and the superfluid density as a result of the driving, and this tendency is most prominent at the parametric resonance. Using the real-time nonequilibrium DMFT formalism, we also study the dynamics towards the NESS, which shows that the heating effect dominates the transient dynamics, and SC is weakened by the external driving, in particular at the parametric resonance. In the weak coupling regime, we find that the SC fluctuations above the transition temperature are generally weakened under the driving. The strongest suppression occurs again around the parametric resonances because of the efficient energy absorption.

#### Slowdown of the Electronic Relaxation Close to the Mott Transition

*Sharareh Sayyad and Martin Eckstein*

We investigate the time-dependent reformation of the quasiparticle peak in a correlated metal near the Mott transition, after the system is quenched into a hot electron state and equilibrates with an environment which is colder than the Fermi-liquid crossover temperature. Close to the transition, we identify a purely electronic bottleneck time scale, which depends on the spectral weight around the Fermi energy in the bad metallic phase in a nonlinear way. This time scale can be orders of magnitude larger than the bare and renormalized electronic hopping time, so that a separation of electronic and lattice time scales may break down. The results are obtained using nonequilibrium dynamical mean-field theory and a slave-rotor representation of the Anderson impurity model.

#### Versatile approach to spin dynamics in correlated electron systems

*Malte Behrmann, Alexander I. Lichtenstein, Mikhail I. Katsnelson, and Frank Lechermann*

Time-dependent spin phenomena in condensed matter are most often either described in the weakly correlated limit of metallic Stoner-Slater-like magnetism via band theory or in the strongly correlated limit of Heisenberg-like interacting spins in an insulator. However, many experimental studies, e.g., of (de)magnetization processes, focus on itinerant local-moment materials, such as transition metals and various of their compounds. We here present a general theoretical framework that is capable of addressing correlated spin dynamics, also in the presence of a vanishing charge gap. A real-space implementation of the time-dependent rotational-invariant slave boson methodology allows us to treat nonequilibrium spins numerically fast and efficiently beyond linear response as well as beyond the band-theoretical or Heisenberg limit.

#### Nonequilibrium itinerant-electron magnetism: a time-dependent mean-field theory

*A. Secchi, A. I. Lichtenstein, and M. I. Katsnelson*

We study the dynamical magnetic susceptibility of a strongly correlated electronic system in the presence of a time-dependent hopping field, deriving a generalized Bethe-Salpeter equation that is valid also out of equilibrium. Focusing on the single-orbital Hubbard model within the time-dependent Hartree-Fock approximation, we solve the equation in the nonequilibrium adiabatic regime, obtaining a closed expression for the transverse magnetic susceptibility. From this, we provide a rigorous definition of nonequilibrium (time-dependent) magnon frequencies and exchange parameters, expressed in terms of nonequilibrium single-electron Green's functions and self-energies. In the particular case of equilibrium, we recover previously known results.

#### Photo-induced gap closure in an excitonic insulator

*D. Golež, P. Werner, M. Eckstein*

We study the dynamical phase transition out of an excitonic insulator phase after photoexcitation using a time-dependent extension of the self-consistent GW method. We connect the evolution of the photoemission spectra to the dynamics of the excitonic order parameter and identify two dynamical phase transition points marked by a slowdown in the relaxation: one critical point is connected with the trapping in a nonthermal state with reduced exciton density and the second corresponds to the thermal phase transition. The transfer of kinetic energy from the photoexcited carriers to the exciton condensate is shown to be the main mechanism for the gap melting. We analyze the low energy dynamics of screening, which strongly depends on the presence of the excitonic gap, and argue that it is difficult to interpret the static component of the screened interaction as the effective interaction of some low energy model. Instead we propose a phenomenological measure for the effective interaction which indicates that screening has minor effects on the low energy dynamics.

#### Nonequilibrium self-energy functional approach to the dynamical Mott transition

*F. Hofmann, M. Eckstein, M. Potthoff*

The real-time dynamics of the Fermi-Hubbard model, driven out of equilibrium by quenching or ramping the interaction parameter, is studied within the framework of the nonequilibrium self-energy functional theory. A dynamical impurity approximation with a single auxiliary bath site is considered as a reference system and the time-dependent hybridization is optimized as prescribed by the variational principle. The dynamical two-site approximation turns out to be useful to study the real-time dynamics on short and intermediate time scales. Depending on the strength of the interaction in the final state, two qualitatively different response regimes are found. For both weak and strong couplings, qualitative agreement with previous results of nonequilibrium dynamical mean-field theory is found. The two regimes are sharply separated by a critical point at which the low-energy bath degree of freedom decouples in the course of time. We trace the dependence of the critical interaction of the dynamical Mott transition on the duration of the interaction ramp from sudden quenches to adiabatic dynamics, and therewith link the dynamical to the equilibrium Mott transition.

#### Non-equilibrium variational-cluster approach to real-time dynamics in the Fermi-Hubbard model

*Felix Hofmann, Martin Eckstein, Michael Potthoff*

The non-equilibrium variational-cluster approach is applied to study the real-time dynamics of the double occupancy in the one-dimensional Fermi-Hubbard model after different fast changes of hopping parameters. A simple reference system, consisting of isolated Hubbard dimers, is used to discuss different aspects of the numerical implementation of the approach in the general framework of non-equilibrium self-energy functional theory. Opposed to a direct solution of the Euler equation, its time derivative is found to serve as numerically tractable and stable conditional equation to fix the time-dependent variational parameters.

Journal of Physics: Conference Series, Volume 696, conference 1 (2016)

#### Phonon-Pump Extreme-Ultraviolet-Photoemission Probe in Graphene: Anomalous Heating of Dirac Carriers by Lattice Deformation

*Isabella Gierz, Matteo Mitrano, Hubertus Bromberger, Cephise Cacho, Richard Chapman, Emma Springate, Stefan Link, Ulrich Starke, Burkhard Sachs, Martin Eckstein, Tim O. Wehling, Mikhail I. Katsnelson, Alexander Lichtenstein, and Andrea Cavalleri*

We modulate the atomic structure of bilayer graphene by driving its lattice at resonance with the in-plane *E _{1u}* lattice vibration at 6.3

*μ*m. Using time- and angle-resolved photoemission spectroscopy (tr-ARPES) with extreme-ultraviolet (XUV) pulses, we measure the response of the Dirac electrons near the

*K*point. We observe that lattice modulation causes anomalous carrier dynamics, with the Dirac electrons reaching lower peak temperatures and relaxing at faster rate compared to when the excitation is applied away from the phonon resonance or in monolayer samples. Frozen phonon calculations predict dramatic band structure changes when the

*E*vibration is driven, which we use to explain the anomalous dynamics observed in the experiment.

_{1u}#### Large-amplitude spin oscillations triggered by nonequilibrium strongly correlated t2g electrons

*M. Behrmann, F. Lechermann*

Laser-induced ultrafast (fs) magnetization experiments in antiferromagnets have recently attracted large attention, paving the road for inherently fast spin dynamics in the THz regime without invoking stray fields. The technical importance is emphasized by the rising new research field of antiferromagnetic (AFM) spintronics, where superexchange-dominated strongly correlated compounds provide an interesting materials playground. An intriguing question is whether the Coulomb interaction may be a key to control AFM order on ultrafast time scales. Therefore, we study (de)magnetization processes in a time-dependent multiorbital Hubbard model, focusing on t2g electrons in a wider doping range. Depending on filling, we reveal large-amplitude spin oscillations via interaction quenches from the antiferromagnetic or paramagnetic state. Nonequilibrium ultrafast spin-orientation effects in prominent correlated transition-metal oxides are therefrom predicted.

#### Fermi Condensation Near van Hove Singularities Within the Hubbard Model on the Triangular Lattice

*D. Yudin, D. Hirschmeier, H. Hafermann, O. Eriksson, A. I. Lichtenstein, M. I. Katsnelson*

The proximity of the Fermi surface to van Hove singularities drastically enhances interaction effects and leads to essentially new physics. In this work we address the formation of flat bands (“Fermi condensation”) within the Hubbard model on the triangular lattice and provide a detailed analysis from an analytical and numerical perspective. To describe the effect we consider both weak-coupling and strong-coupling approaches, namely the renormalization group and dual fermion methods. It is shown that the band flattening is driven by correlations and is well pronounced even at sufficiently high temperatures, of the order of 0.1–0.2 of the hopping parameter. The effect can therefore be probed in experiments with ultracold fermions in optical lattices.

#### Extended dynamic Mott transition in the two-band Hubbard model out of equilibrium

*M. Behrmann, M. Fabrizio, F. Lechermann*

We reformulate the time-dependent Gutzwiller approximation by M. Schiró and M. Fabrizio, [Phys. Rev. Lett. 105, 076401 (2010)] in the framework of slave-boson mean-field theory, which is used to investigate the dynamical Mott transition of the generic two-band Hubbard model at half filling upon an interaction quench. Interorbital fluctuations lead to notable changes with respect to the single-band case. The singular dynamical transition is replaced by a broad regime of long-lived fluctuations between metallic and insulating states, accompanied by intriguing precursor behavior. A mapping to a spin model proves helpful to analyze the different regions in terms of the evolution of an Ising-like order parameter. Contrary to the static case, singlet occupations remain vital in the Mott-insulating regime with finite Hund's exchange.

#### Non-equilibrium magnetic interactions in strongly correlated systems

*A. Secchi, S. Brener, A. I. Lichtenstein, M. I. Katsnelson*

We formulate a low-energy theory for the magnetic interactions between electrons in the multi-band Hubbard model under non-equilibrium conditions determined by an external time-dependent electric field which simulates laser-induced spin dynamics. We derive expressions for dynamical exchange parameters in terms of non-equilibrium electronic Green functions and self-energies, which can be computed, e.g., with the methods of time-dependent dynamical mean-field theory. Moreover, we find that a correct description of the system requires, in addition to exchange, a new kind of magnetic interaction, that we name twist exchange, which formally resembles Dzyaloshinskii–Moriya coupling, but is not due to spin–orbit, and is actually due to an effective three-spin interaction. Our theory allows the evaluation of the related time-dependent parameters as well.

#### Competing orders in Na_xCoO_2 from strong correlations on a two-particle level

*L. Boehnke, F. Lechermann*

Based on dynamical mean-field theory with a continuous-time quantum Monte-Carlo impurity solver, static as well as dynamic spin and charge susceptibilites for the phase diagram of the sodium cobaltate system Na$_x$CoO$_2$ are discussed. The approach includes important vertex contributions to the q-dependent two-particle response functions by means of a local approximation to the irreducible vertex function in the particle-hole channel. A single-band Hubbard model suffices to reveal several charge- and spin-instability tendencies in accordance with experiment, including the stabilization of an effective kagome sublattice close to x=0.67, without invoking the doping-dependent Na-potential landscape. The in-plane antiferromagnetic-to-ferromagnetic crossover is additionally verified by means of the computed Korringa ratio. Moreover an intricate high-energy mode in the transverse spin susceptiblity is revealed, pointing towards a strong energy dependence of the effective intersite exchange.

Phys. Rev. B 85, 115128 (2012)

http://arxiv.org/abs/1012.5943

### Project B5

#### Non-collinear spin states in bottom-up fabricated atomic chains

*M. Steinbrecher, R. Rausch, Khai Ton That, J. Hermenau, A.A. Khajetoorians, M. Potthoff, R. Wiesendanger, J. Wiebe*

Non-collinear spin states with unique rotational sense, such as chiral spin-spirals, are recently heavily investigated because of advantages for future applications in spintronics and information technology and as potential hosts for Majorana Fermions when coupled to a superconductor. Tuning the properties of such spin states, e.g., the rotational period and sense, is a highly desirable yet difficult task. Here, we experimentally demonstrate the bottom-up assembly of a spin-spiral derived from a chain of iron atoms on a platinum substrate using the magnetic tip of a scanning tunneling microscope as a tool. We show that the spin-spiral is induced by the interplay of the Heisenberg and Dzyaloshinskii-Moriya components of the Ruderman-Kittel-Kasuya-Yosida interaction between the iron atoms. The relative strengths and signs of these two components can be adjusted by the interatomic iron distance, which enables tailoring of the rotational period and sense of the spin-spiral.

#### Anomalous spin precession under a geometrical torque

*C. Stahl, M. Potthoff*

Precession and relaxation predominantly characterize the real-time dynamics of a spin driven by a magnetic field and coupled to a large Fermi sea of conduction electrons. We demonstrate an anomalous precession with frequency higher than the Larmor frequency or with inverted orientation in the limit where the electronic motion adiabatically follows the spin dynamics. For a classical spin, the effect is traced back to a geometrical torque resulting from a finite spin Berry curvature.

#### Enforcing conservation laws in nonequilibrium cluster perturbation theory

*C. Gramsch, M. Potthoff*

Using the recently introduced time-local formulation of the nonequilibrium cluster perturbation theory (CPT), we construct a generalization of the approach such that macroscopic conservation laws are respected. This is achieved by exploiting the freedom for the choice of the starting point of the all-order perturbation theory in the intercluster hopping. The proposed conserving CPT is a self-consistent propagation scheme which respects the conservation of energy, particle number, and spin, which treats short-range correlations exactly up to the linear scale of the cluster, and which represents a mean-field-like approach on length scales beyond the cluster size. Using Green's functions, conservation laws are formulated as local constraints on the local spin-dependent particle and the doublon density. We consider them as conditional equations to self-consistently fix the time-dependent intracluster one-particle parameters. Thanks to the intrinsic causality of the CPT, this can be set up as a step-by-step time propagation scheme with a computational effort scaling linearly with the maximum propagation time and exponentially in the cluster size. As a proof of concept, we consider the dynamics of the two-dimensional, particle-hole-symmetric Hubbard model following a weak interaction quench by simply employing two-site clusters only. Conservation laws are satisfied by construction. We demonstrate that enforcing them has strong impact on the dynamics. While the doublon density is strongly oscillating within plain CPT, a monotonic relaxation is observed within the conserving CPT.

#### Filling-dependent doublon dynamics in the one-dimensional Hubbard model

*R. Rausch and M. Potthoff*

The fate of a local two-hole doublon excitation in the one-dimensional Fermi-Hubbard model is systematically studied for strong Hubbard interaction U in the entire filling range using the density-matrix renormalization group (DMRG) and the Bethe ansatz. For strong U, two holes at the same site form a compound object whose decay is impeded by the lack of phase space. Still, a partial decay is possible on an extremely short time scale where phase-space arguments do not yet apply. We argue that the initial decay and the resulting intermediate state are relevant for experiments performed with ultracold atoms loaded into an optical lattice as well as for (time-resolved) CVV Auger-electron spectroscopy. The detailed discussion comprises the mixed ballistic-diffusive real-time propagation of the doublon through the lattice, its partial decay on the short time scale as a function of filling and interaction strength, as well as the analysis of the decay products, which are metastable on the intermediate time scale that is numerically accessible and which show up in the two-hole excitation (Auger) spectrum. The ambivalent role of singly occupied sites is key to understanding the doublon physics; for high fillings, ground-state configurations with single occupancies are recognized to strongly relax the kinematic constraints and to open up decay channels. For fillings close to half-filling, however, their presence actually blocks the doublon decay. Finally, the analysis of the continua in the two-hole spectrum excludes a picture where the doublon decays into unbound electron holes for generic fillings, different from the limiting case of the completely filled band. We demonstrate that the decay products as well as the doublon propagation should rather be understood in terms of Bethe ansatz eigenstates.

#### Nonequilibrium self-energy functional approach to the dynamical Mott transition

*F. Hofmann, M. Eckstein, M. Potthoff*

The real-time dynamics of the Fermi-Hubbard model, driven out of equilibrium by quenching or ramping the interaction parameter, is studied within the framework of the nonequilibrium self-energy functional theory. A dynamical impurity approximation with a single auxiliary bath site is considered as a reference system and the time-dependent hybridization is optimized as prescribed by the variational principle. The dynamical two-site approximation turns out to be useful to study the real-time dynamics on short and intermediate time scales. Depending on the strength of the interaction in the final state, two qualitatively different response regimes are found. For both weak and strong couplings, qualitative agreement with previous results of nonequilibrium dynamical mean-field theory is found. The two regimes are sharply separated by a critical point at which the low-energy bath degree of freedom decouples in the course of time. We trace the dependence of the critical interaction of the dynamical Mott transition on the duration of the interaction ramp from sudden quenches to adiabatic dynamics, and therewith link the dynamical to the equilibrium Mott transition.

#### Inertia effects in the real-time dynamics of a quantum spin coupled to a Fermi sea

*M. Sayad, R. Rausch, M. Potthoff*

Spin dynamics in the Kondo impurity model, initiated by suddenly switching the direction of a local magnetic field, is studied by means of the time-dependent density-matrix renormalization group. Quantum effects are identified by systematic computations for different spin quantum numbers S and by comparing with tight-binding spin-dynamics theory for the classical-spin Kondo model. We demonstrate that, besides the conventional precessional motion and relaxation, the quantum-spin dynamics shows nutation, similar to a spinning top. Opposed to semiclassical theory, however, the nutation is efficiently damped on an extremely short time scale. The effect is explained in the large-S limit as quantum dephasing of the eigenmodes in an emergent two-spin model that is weakly entangled with the bulk of the system. We argue that, apart from the Kondo effect, the damping of nutational motion is essentially the only characteristics of the quantum nature of the spin. Qualitative agreement between quantum and semiclassical spin dynamics is found down to S=1/2.

#### One-step theory of two-photon photoemission

*J. Braun, R. Rausch, M. Potthoff, H. Ebert*

A theoretical frame for two-photon photoemission is derived from the general theory of pump-probe photoemission, assuming that not only the probe but also the pump pulse is sufficiently weak. This allows us to use a perturbative approach to compute the lesser Green function within the Keldysh formalism. Two-photon photoemission spectroscopy is a widely used analytical tool to study nonequilibrium phenomena in solid materials. Our theoretical approach aims at a material-specific, realistic, and quantitative description of the time-dependent spectrum based on a picture of effectively independent electrons as described by the local-density approximation in band-structure theory. To this end we follow Pendry's one-step theory of the photoemission process as close as possible and heavily make use of concepts of relativistic multiple-scattering theory, such as the representation of the final state by a time-reversed low-energy electron diffraction state. The formalism allows for a quantitative calculation of the time-dependent photocurrent for moderately correlated systems like simple metals or more complex compounds like topological insulators. An application to the Ag(100) surface is discussed in detail.

#### Relaxation of a classical spin coupled to a strongly correlated electron system

*M. Sayad, R. Rausch, M. Potthoff*

A classical spin which is antiferromagnetically coupled to a system of strongly correlated conduction electrons is shown to exhibit unconventional real-time dynamics which cannot be described by Gilbert damping. Depending on the strength of the local Coulomb interaction U, the two main electronic dissipation channels, namely transport of excitations via correlated hopping and via excitations of correlation-induced magnetic moments, become active on largely different time scales. We demonstrate that correlations can lead to a strongly suppressed relaxation which so far has been observed in purely electronic systems only and which is governed here by proximity to the divergent magnetic time scale in the infinite-U limit.

#### Time-dependent Mott transition in the periodic Anderson model with nonlocal hybridization

*F. Hofmann, M. Potthoff*

The time-dependent Mott transition in a periodic Anderson model with off-site, nearest-neighbor hybridization is studied within the framework of nonequilibrium self-energy functional theory. Using the two-site dynamical-impurity approximation, we compute the real-time dynamics of the optimal variational parameter and of different observables initiated by sudden quenches of the Hubbard-U and identify the critical interaction. The time-dependent transition is orbital selective, i.e., in the final state, reached in the long-time limit after the quench to the critical interaction, the Mott gap opens in the spectral function of the localized orbitals only. We discuss the dependence of the critical interaction and of the final-state effective temperature on the hybridization strength and point out the various similarities between the nonequilibrium and the equilibrium Mott transition. It is shown that these can also be smoothly connected to each other by increasing the duration of a U-ramp from a sudden quench to a quasi-static process. The physics found for the model with off-site hybridization is compared with the dynamical Mott transition in the single-orbital Hubbard model and with the dynamical crossover found for the real-time dynamics of the conventional Anderson lattice with on-site hybridization.

#### Multiplons in the two-hole excitation spectra of the one-dimensional Hubbard model

*R. Rausch, M. Potthoff*

Using the density-matrix renormalization group in combination with the Chebyshev polynomial expansion technique, we study the two-hole excitation spectrum of the one-dimensional Hubbard model in the entire filling range from the completely occupied band (n = 2) down to half-filling (n = 1). For strong interactions, the spectra reveal multiplon physics, i.e., relevant final states are characterized by two (doublon), three (triplon), four (quadruplon) and more holes, potentially forming stable compound objects or resonances with finite lifetime. These give rise to several satellites in the spectra with largely different spectral weights as well as to different two-hole, doublon–hole, two-doublon etc continua. The complex multiplon phenomenology is analyzed by interpreting not only local and k-resolved two-hole spectra but also three- and four-hole spectra for the Hubbard model and by referring to effective low-energy models. In addition, a filter-operator technique is presented and applied which allows to extract specific information on the final states at a given excitation energy. While multiplons composed of an odd number of holes do neither form stable compounds nor well-defined resonances unless a nearest-neighbor density interaction V is added to the Hamiltonian, the doublon and the quadruplon are well-defined resonances. The k-resolved four-hole spectrum at n = 2 represents an interesting special case where a completely stable quadruplon turns into a resonance by merging with the doublon–doublon continuum at a critical wave vector. For all fillings with $n\gt 1$, the doublon lifetime is strongly k-dependent and is even infinite at the Brillouin zone edges as demonstrated by k-resolved two-hole spectra. This can be traced back to the 'hidden' charge-SU(2) symmetry of the model which is explicitly broken off half-filling and gives rise to a massive collective excitation, even for arbitrary higher-dimensional but bipartite lattices.

#### Lehmann representation of the nonequilibrium self-energy

*C. Gramsch, M. Potthoff*

It is shown that the nonequilibrium self-energy of an interacting lattice-fermion model has a unique Lehmann representation. Based on the construction of a suitable noninteracting effective medium, we provide an explicit and numerically practicable scheme to construct the Lehmann representation for the self-energy, given the Lehmann representation of the single-particle nonequilibrium Green's function. This is of particular importance for an efficient numerical solution of Dyson's equation in the context of approximations where the self-energy is obtained from a reference system with a small Hilbert space. As compared to conventional techniques to solve Dyson's equation on the Keldysh contour, the effective-medium approach allows us to reach a maximum propagation time, which can be several orders of magnitude longer. This is demonstrated explicitly by choosing the nonequilibrium cluster-perturbation theory as a simple approach to study the long-time dynamics of an inhomogeneous initial state after a quantum quench in the Hubbard model on a 10×10 square lattice. We demonstrate that the violation of conservation laws is moderate for weak Hubbard interaction and that the cluster approach is able to describe prethermalization physics.

#### Spin dynamics and relaxation in the classical-spin Kondo-impurity model beyond the Landau-Lifschitz-Gilbert equation

*M. Sayad, M. Potthoff*

The real-time dynamics of a classical spin in an external magnetic field and local exchange coupled to an extended one-dimensional system of non-interacting conduction electrons is studied numerically. Retardation effects in the coupled electron-spin dynamics are shown to be the source for the relaxation of the spin in the magnetic field. Total energy and spin is conserved in the non-adiabatic process. Approaching the new local ground state is therefore accompanied by the emission of dispersive wave packets of excitations carrying energy and spin and propagating through the lattice with Fermi velocity. While the spin dynamics in the regime of strong exchange coupling J is rather complex and governed by an emergent new time scale, the motion of the spin for weak J is regular and qualitatively well described by the Landau–Lifschitz–Gilbert (LLG) equation. Quantitatively, however, the full quantum–classical hybrid dynamics differs from the LLG approach. This is understood as a breakdown of weak-coupling perturbation theory in J in the course of time. Furthermore, it is shown that the concept of the Gilbert damping parameter is ill-defined for the case of a one-dimensional system.

#### Crossover from conventional to inverse indirect magnetic exchange in the depleted Anderson lattice

*M. W. Aulbach, I. Titvinidze, M. Potthoff*

We investigate the finite-temperature properties of an Anderson lattice with regularly depleted impurities. The physics of this model is ruled by two different magnetic exchange mechanisms: conventional Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction at weak hybridization strength V and an inverse indirect magnetic exchange (IIME) at strong V, both favoring a ferromagnetic ground state. The stability of ferromagnetic order against thermal fluctuations is systematically studied by static mean-field theory for an effective low-energy spin-only model emerging perturbatively in the strong-coupling limit as well as by dynamical mean-field theory for the full model. The Curie temperature is found at a maximum for a half-filled conduction band and at intermediate hybridization strengths in the crossover regime between RKKY and IIME.

#### One-step theory of pump-probe photoemission

*J. Braun, R. Rausch, M. Potthoff, J. Minár, H. Ebert*

A theoretical framework for pump-probe photoemission is presented. The approach is based on a general formulation using the Keldysh formalism for the lesser Green's function to describe the real-time evolution of the electronic degrees of freedom in the initial state after a strong pump pulse that drives the system out of equilibrium. The final state is represented by a time-reversed low-energy electron-diffraction state. Our one-step description is related as close as possible to Pendry's original formulation of the photoemission process. The formalism allows for a quantitative calculation of time-dependent photocurrent for simple metals where a picture of effectively independent electrons is assumed to be reliable. The theory is worked out for valence- and core-electron excitations. It comprises the study of different relativistic effects as a function of the pump-probe delay.

#### Non-equilibrium variational-cluster approach to real-time dynamics in the Fermi-Hubbard model

*Felix Hofmann, Martin Eckstein, Michael Potthoff*

The non-equilibrium variational-cluster approach is applied to study the real-time dynamics of the double occupancy in the one-dimensional Fermi-Hubbard model after different fast changes of hopping parameters. A simple reference system, consisting of isolated Hubbard dimers, is used to discuss different aspects of the numerical implementation of the approach in the general framework of non-equilibrium self-energy functional theory. Opposed to a direct solution of the Euler equation, its time derivative is found to serve as numerically tractable and stable conditional equation to fix the time-dependent variational parameters.

Journal of Physics: Conference Series, Volume 696, conference 1

#### Cooperation of different exchange mechanisms in confined magnetic systems

*A. Schwabe, M. Hänsel, M. Potthoff*

The diluted Kondo lattice model is investigated at strong antiferromagnetic local exchange couplings J, where almost-local Kondo clouds drastically restrict the motion of conduction electrons, giving rise to the possibility of quantum localization of conduction electrons for certain geometries of impurity spins. This localization may lead to the formation of local magnetic moments in the conduction-electron system, and the inverse indirect magnetic exchange (IIME) provided by virtual excitations of the Kondo singlets couples those local moments to the remaining electrons. Exemplarily, we study the one-dimensional two-impurity Kondo model with impurity spins near the chain ends, which supports the formation of conduction-electron magnetic moments at the edges of the chain for sufficiently strong J. Employing degenerate perturbation theory as well as analyzing spin gaps numerically by means of the density-matrix renormalization group, it is shown that the low-energy physics of the model can be well captured within an effective antiferromagnetic Ruderman–Kittel–Kasuya–Yosida-like two-spin model (“RKKY from IIME”) or within an effective central-spin model, depending on edge-spin distance and system size.

#### Nonequilibrium self-energy functional theory

*F. Hofmann, M. Eckstein, E. Arrigoni, M. Potthoff*

The self-energy functional theory (SFT) is generalized to describe the real-time dynamics of correlated lattice-fermion models far from thermal equilibrium. This is achieved by starting from a reformulation of the original equilibrium theory in terms of double-time Green's functions on the Keldysh-Matsubara contour. With the help of a generalized Luttinger-Ward functional, we construct a functional Ω̂[Σ] which is stationary at the physical (nonequilibrium) self-energy Σ and which yields the grand potential of the initial thermal state Ω at the physical point. Nonperturbative approximations can be defined by specifying a reference system that serves to generate trial self-energies. These self-energies are varied by varying the reference system's one-particle parameters on the Keldysh-Matsubara contour. In the case of thermal equilibrium, this approach reduces to the conventional SFT. Contrary to the equilibrium theory, however, “unphysical” variations, i.e., variations that are different on the upper and the lower branches of the Keldysh contour, must be considered to fix the time dependence of the optimal physical parameters via the variational principle. Functional derivatives in the nonequilibrium SFT Euler equation are carried out analytically to derive conditional equations for the variational parameters that are accessible to a numerical evaluation via a time-propagation scheme. Approximations constructed by means of the nonequilibrium SFT are shown to be inherently causal, internally consistent, and to respect macroscopic conservation laws resulting from gauge symmetries of the Hamiltonian. This comprises the nonequilibrium dynamical mean-field theory but also dynamical-impurity and variational-cluster approximations that are specified by reference systems with a finite number of degrees of freedom. In this way, nonperturbative and consistent approximations can be set up, the numerical evaluation of which is accessible to an exact-diagonalization approach.

#### Dynamical symmetry between spin and charge excitations studied by a plaquette mean-field approach in two dimensions

*P. Jurgenowski, M. Potthoff*

The real-time dynamics of local occupation numbers in a Hubbard model on a 6×6 square lattice is studied by means of the nonequilibrium generalization of the cluster-perturbation theory. The cluster approach is adapted to studies of two-dimensional lattice systems by using concepts of multiple-scattering theory and a component decomposition of the nonequilibrium Green's function on the Keldysh-Matsubara contour. We consider “classical” initial states formed as tensor products of states on 2×2 plaquettes and trace the effects of the interplaquette hopping in the final-state dynamics. Two different initially excited states are considered on an individual plaquette, a fully polarized staggered spin state (Néel) and a fully polarized charge-density wave (CDW). The final-state dynamics is constrained by a dynamical symmetry; i.e., the time-evolution operator and certain observables are invariant under an antiunitary transformation composed of time reversal, an asymmetric particle-hole, and a staggered sign transformation. We find an interesting interrelation between this dynamical symmetry and the separation of energy and time scales: In the case of a global excitation with all plaquettes excited, the initial Néel and the initial CDW states are linked by the transformation. This prevents an efficient relaxation of the CDW state on the short time scale governing the dynamics of charge degrees of freedom. Contrarily, the CDW state is found to relax much faster than the Néel state in the case of a local excitation on a single plaquette where the symmetry relation between the two states is broken by the coupling to the environment.

#### Inverse indirect magnetic exchange

*A. Schwabe, I. Titvinidze, M. Potthoff*

Magnetic moments strongly coupled to the spins of conduction electrons in a nanostructure can confine the conduction-electron motion due to scattering at almost localized Kondo singlets. We study the resulting local-moment formation in the conduction-electron system and the magnetic exchange coupling mediated by the Kondo singlets. Its distance dependence is oscillatory and induces robust ferro- or antiferromagnetic order in multi-impurity systems.

#### Doublon dynamics in the extended Fermi-Hubbard model

*F. Hofmann, M. Potthoff*

#### Krylov-space approach to the equilibrium and nonequilibrium single-particle Green's function

*M. Balzer, N. Gdaniec, M.Potthoff*

#### Nonequilibrium cluster perturbation theory

*M. Balzer, M. Potthoff*

### Project B6

#### Ultrafast momentum imaging of pseudospin-flip excitations in graphene

*S. Aeschlimann, R. Krause, M. Chávez-Cervantes, H. Bromberger, R. Jago, E. Mali, A. Al-Temimy, C. Coletti, A. Cavalleri, I. Gierz*

The pseudospin of Dirac electrons in graphene manifests itself in a peculiar momentum anisotropy for photoexcited electron-hole pairs. These interband excitations are in fact forbidden along the direction of the light polarization and are maximum perpendicular to it. Here, we use time- and angle-resolved photoemission spectroscopy to investigate the resulting unconventional hot carrier dynamics, sampling carrier distributions as a function of energy, and in-plane momentum. We first show that the rapidly-established quasithermal electron distribution initially exhibits an azimuth-dependent temperature, consistent with relaxation through collinear electron-electron scattering. Azimuthal thermalization is found to occur only at longer time delays, at a rate that depends on the substrate and the static doping level. Further, we observe pronounced differences in the electron and hole dynamics in n-doped samples. By simulating the Coulomb- and phonon-mediated carrier dynamics we are able to disentangle the influence of excitation fluence, screening, and doping, and develop a microscopic picture of the carrier dynamics in photoexcited graphene. Our results clarify new aspects of hot carrier dynamics that are unique to Dirac materials, with relevance for photocontrol experiments and optoelectronic device applications.

#### Enhanced electron-phonon coupling in graphene with periodically distorted lattice

*E. Pomarico, M. Mitrano, H. Bromberger, M. A. Sentef, A. Al-Temimy, C. Coletti, A. Stohr, S. Link, U. Starke, C. Cacho, R. Chapman, E. Springate, A. Cavalleri, I. Gierz*

Electron-phonon coupling directly determines the stability of cooperative order in solids, including superconductivity, charge, and spin density waves. Therefore, the ability to enhance or reduce electron-phonon coupling by optical driving may open up new possibilities to steer materials' functionalities, potentially at high speeds. Here, we explore the response of bilayer graphene to dynamical modulation of the lattice, achieved by driving optically active in-plane bond stretching vibrations with femtosecond midinfrared pulses. The driven state is studied by two different ultrafast spectroscopic techniques. First, terahertz time-domain spectroscopy reveals that the Drude scattering rate decreases upon driving. Second, the relaxation rate of hot quasiparticles, as measured by time- and angle-resolved photoemission spectroscopy, increases. These two independent observations are quantitatively consistent with one another and can be explained by a transient threefold enhancement of the electron-phonon coupling constant. The findings reported here provide useful perspective for related experiments, which reported the enhancement of superconductivity in alkali-doped fullerites when a similar phonon mode was driven.

#### Electronic-structural dynamics in graphene

*A. Cavalleri, I. Gierz*

We review our recent time- and angle-resolved photoemission spectroscopy experiments, which measure the transient electronic structure of optically driven graphene. For pump photon energies in the near infrared (ℏω_{pump}=950 meV), we have discovered the formation of a population-inverted state near the Dirac point, which may be of interest for the design of THz lasing devices and optical amplifiers. At lower pump photon energies (ℏω_{pump}<400 meV), for which interband absorption is not possible in doped samples, we find evidence for free carrier absorption. In addition, when mid-infrared pulses are made resonant with an infrared-active in-plane phonon of bilayer graphene (ℏω_{pump}=200 meV), a transient enhancement of the electron-phonon coupling constant is observed, providing interesting perspective for experiments that report light-enhanced superconductivity in doped fullerites in which a similar lattice mode was excited. All the studies reviewed here have important implications for applications of graphene in optoelectronic devices and for the dynamical engineering of electronic properties with light.

Structural Dynamics 3, 051301 (2016)

#### Phonon-Pump Extreme-Ultraviolet-Photoemission Probe in Graphene: Anomalous Heating of Dirac Carriers by Lattice Deformation

*Isabella Gierz, Matteo Mitrano, Hubertus Bromberger, Cephise Cacho, Richard Chapman, Emma Springate, Stefan Link, Ulrich Starke, Burkhard Sachs, Martin Eckstein, Tim O. Wehling, Mikhail I. Katsnelson, Alexander Lichtenstein, and Andrea Cavalleri*

We modulate the atomic structure of bilayer graphene by driving its lattice at resonance with the in-plane *E _{1u}* lattice vibration at 6.3

*μ*m. Using time- and angle-resolved photoemission spectroscopy (tr-ARPES) with extreme-ultraviolet (XUV) pulses, we measure the response of the Dirac electrons near the

*K*point. We observe that lattice modulation causes anomalous carrier dynamics, with the Dirac electrons reaching lower peak temperatures and relaxing at faster rate compared to when the excitation is applied away from the phonon resonance or in monolayer samples. Frozen phonon calculations predict dramatic band structure changes when the

*E*vibration is driven, which we use to explain the anomalous dynamics observed in the experiment.

_{1u}### Project B7

#### Probing dynamics in quantum materials with femtosecond X-rays

*M. Buzzi, M. Först, R. Mankowsky, and A. Cavalleri*

Optical pulses are routinely used to drive dynamic changes in the properties of solids. In quantum materials, many new phenomena have been discovered, including ultrafast transitions between electronic phases, switching of ferroic orders and non-equilibrium emergent behaviours, such as photoinduced superconductivity. Understanding the underlying non-equilibrium physics requires detailed measurements of multiple microscopic degrees of freedom at ultrafast time resolution. Femtosecond X-rays are key to this endeavour, as they can probe the dynamics of structural, electronic and magnetic degrees of freedom. Here, we review a series of representative experimental studies in which ultrashort X-ray pulses from free-electron lasers have been used, opening up new horizons for materials research.

#### Pressure tuning of light-induced superconductivity in K3C60

*A. Cantaluppi, M. Buzzi, G. Jotzu, D. Nicoletti, M. Mitrano, D. Pontiroli, M. Riccò, A. Perucchi, P. Di Pietro, A. Cavalleri*

Optical excitation at terahertz frequencies has emerged as an effective means to dynamically manipulate complex materials. In the molecular solid K_{3}C_{60}, short mid-infrared pulses transform the high-temperature metal into a non-equilibrium state with the optical properties of a superconductor. Here we tune this effect with hydrostatic pressure and find that the superconducting-like features gradually disappear at around 0.3 GPa. Reduction with pressure underscores the similarity with the equilibrium superconducting phase of K_{3}C_{60}, in which a larger electronic bandwidth induced by pressure is also detrimental for pairing. Crucially, our observation excludes alternative interpretations based on a high-mobility metallic phase. The pressure dependence also suggests that transient, incipient superconductivity occurs far above the 150 K hypothesized previously, and rather extends all the way to room temperature.

#### Probing the Interatomic Potential of Solids with Strong-Field Nonlinear Phononics

*A. von Hoegen, R. Mankowsky, M. Fechner, M. Först, A. Cavalleri*

Nonlinear optical techniques at visible frequencies have long been applied to condensed matter spectroscopy. However, because many important excitations of solids are found at low energies, much can be gained from the extension of nonlinear optics to mid-infrared and terahertz frequencies. For example, the nonlinear excitation of lattice vibrations has enabled the dynamic control of material functions. So far it has only been possible to exploit second-order phonon nonlinearities9 at terahertz field strengths near one million volts per centimetre. Here we achieve an order-of-magnitude increase in field strength and explore higher-order phonon nonlinearities. We excite up to five harmonics of the A_{1} (transverse optical) phonon mode in the ferroelectric material lithium niobate. By using ultrashort mid-infrared laser pulses to drive the atoms far from their equilibrium positions, and measuring the large-amplitude atomic trajectories, we can sample the interatomic potential of lithium niobate, providing a benchmark for ab initio calculations for the material. Tomography of the energy surface by high-order nonlinear phononics could benefit many aspects of materials research, including the study of classical and quantum phase transitions.

#### Transiently enhanced interlayer tunneling in optically driven high Tc superconductors

*J. Okamoto, W. Hu, A. Cavalleri, L. Mathey*

Recent pump-probe experiments reported an enhancement of superconducting transport along the c axis of underdoped YBa_{2}Cu_{3}O_{6+δ} (YBCO), induced by a midinfrared optical pump pulse tuned to a specific lattice vibration. To understand this transient nonequilibrium state, we develop a pump-probe formalism for a stack of Josephson junctions, and we consider the tunneling strengths in the presence of modulation with an ultrashort optical pulse. We demonstrate that a transient enhancement of the Josephson coupling can be obtained for pulsed excitation and that this can be even larger than in a continuously driven steady state. Especially interesting is the conclusion that the effect is largest when the material is parametrically driven at a frequency immediately above the plasma frequency, in agreement with what is found experimentally. For bilayer Josephson junctions, an enhancement similar to that experimentally is predicted below the critical temperature *T _{c}*. This model reproduces the essential features of the enhancement measured below

*T*. To reproduce the experimental results above

_{c}*T*, we will explore extensions of this model, such as in-plane and amplitude fluctuations, elsewhere.

_{c}#### Anomalous relaxation kinetics and charge density wave correlations in underdoped BaPb1-xBixO3

*D. Nicoletti, E. Casandruc, D. Fu, P. Giraldo-Gallo, I. Fisher, A. Cavalleri*

We present measurements of transient photoconductivity in BaPb_{1−x}Bi_{x}O_{3} (BPBO)––a poorly understood material belonging to the bismuthate family, which has been coined “the other high-temperature superconductor.” The phase diagram of BPBO encompasses charge-density-wave (CDW) order in BaBiO_{3} (x = 1), through superconductivity for intermediate compositions, to bad metal behavior in BaPbO_{3} (x = 0). We present evidence for the coexistence of CDW order and superconductivity for underdoped compositions of BPBO––something that has been discussed previously, but never definitively established. These results are especially timely given that CDW correlations have recently been found in some underdoped cuprate superconductors, pointing toward a surprising commonality between some aspects of these materials. Our measurements also put energy scales on the associated charge order.

#### Ultrafast momentum imaging of pseudospin-flip excitations in graphene

*S. Aeschlimann, R. Krause, M. Chávez-Cervantes, H. Bromberger, R. Jago, E. Mali, A. Al-Temimy, C. Coletti, A. Cavalleri, I. Gierz*

The pseudospin of Dirac electrons in graphene manifests itself in a peculiar momentum anisotropy for photoexcited electron-hole pairs. These interband excitations are in fact forbidden along the direction of the light polarization and are maximum perpendicular to it. Here, we use time- and angle-resolved photoemission spectroscopy to investigate the resulting unconventional hot carrier dynamics, sampling carrier distributions as a function of energy, and in-plane momentum. We first show that the rapidly-established quasithermal electron distribution initially exhibits an azimuth-dependent temperature, consistent with relaxation through collinear electron-electron scattering. Azimuthal thermalization is found to occur only at longer time delays, at a rate that depends on the substrate and the static doping level. Further, we observe pronounced differences in the electron and hole dynamics in n-doped samples. By simulating the Coulomb- and phonon-mediated carrier dynamics we are able to disentangle the influence of excitation fluence, screening, and doping, and develop a microscopic picture of the carrier dynamics in photoexcited graphene. Our results clarify new aspects of hot carrier dynamics that are unique to Dirac materials, with relevance for photocontrol experiments and optoelectronic device applications.

#### Enhanced electron-phonon coupling in graphene with periodically distorted lattice

*E. Pomarico, M. Mitrano, H. Bromberger, M. A. Sentef, A. Al-Temimy, C. Coletti, A. Stohr, S. Link, U. Starke, C. Cacho, R. Chapman, E. Springate, A. Cavalleri, I. Gierz*

Electron-phonon coupling directly determines the stability of cooperative order in solids, including superconductivity, charge, and spin density waves. Therefore, the ability to enhance or reduce electron-phonon coupling by optical driving may open up new possibilities to steer materials' functionalities, potentially at high speeds. Here, we explore the response of bilayer graphene to dynamical modulation of the lattice, achieved by driving optically active in-plane bond stretching vibrations with femtosecond midinfrared pulses. The driven state is studied by two different ultrafast spectroscopic techniques. First, terahertz time-domain spectroscopy reveals that the Drude scattering rate decreases upon driving. Second, the relaxation rate of hot quasiparticles, as measured by time- and angle-resolved photoemission spectroscopy, increases. These two independent observations are quantitatively consistent with one another and can be explained by a transient threefold enhancement of the electron-phonon coupling constant. The findings reported here provide useful perspective for related experiments, which reported the enhancement of superconductivity in alkali-doped fullerites when a similar phonon mode was driven.

#### Nonlinear light–matter interaction at terahertz frequencies

*D. Nicoletti, A. Cavalleri*

Strong optical pulses at mid-infrared and terahertz frequencies have recently emerged as powerful tools to manipulate and control the solid state and especially complex condensed matter systems with strongly correlated electrons. The recent developments in high-power sources in the 0.1–30 THz frequency range, both from table-top laser systems and from free-electron lasers, have provided access to excitations of molecules and solids, which can be stimulated at their resonance frequencies. Amongst these, we discuss free electrons in metals, superconducting gaps and Josephson plasmons in layered superconductors, and vibrational modes of the crystal lattice (phonons), as well as magnetic excitations. This review provides an overview and illustrative examples of how intense terahertz transients can be used to resonantly control matter, with particular focus on strongly correlated electron systems and high-temperature superconductors.

#### Possible light-induced superconductivity in K3C60 at high temperature

*M. Mitrano, A. Cantaluppi, D. Nicoletti, S. Kaiser, A. Perucchi, S. Lupi, P. Di Pietro, D. Pontiroli, M. Riccò, S. R. Clark, D. Jaksch, and A. Cavalleri*

The non-equilibrium control of emergent phenomena in solids is an important research frontier, encompassing effects such as the optical enhancement of superconductivity1. Nonlinear excitation2,3 of certain phonons in bilayer copper oxides was recently shown to induce superconducting-like optical properties at temperatures far greater than the superconducting transition temperature, T*c* (refs 4, 5, 6). This effect was accompanied by the disruption of competing charge-density-wave correlations7,8, which explained some but not all of the experimental results. Here we report a similar phenomenon in a very different compound, K_{3}C_{60}. By exciting metallic K_{3}C_{60} with mid-infrared optical pulses, we induce a large increase in carrier mobility, accompanied by the opening of a gap in the optical conductivity. These same signatures are observed at equilibrium when cooling metallic K_{3}C_{60} below T*c* (20 kelvin). Although optical techniques alone cannot unequivocally identify non-equilibrium high-temperature superconductivity, we propose this as a possible explanation of our results.

#### Theory of Enhanced Interlayer Tunneling in Optically Driven High-Tc Superconductors

*Jun-ichi Okamoto, Andrea Cavalleri, and Ludwig Mathey*

Motivated by recent pump-probe experiments indicating enhanced coherent c-axis transport in underdoped YBCO, we study Josephson junctions periodically driven by optical pulses. We propose a mechanism for this observation by demonstrating that a parametrically driven Josephson junction shows an enhanced imaginary part of the low-frequency conductivity when the driving frequency is above the plasma frequency, implying an effectively enhanced Josephson coupling. We generalize this analysis to a bilayer system of Josephson junctions modeling YBCO. Again, the Josephson coupling is enhanced when the pump frequency is blue detuned to either of the two plasma frequencies of the material. We show that the emergent driven state is a genuine, nonequilibrium superconducting state, in which equilibrium relations between the Josephson coupling, current fluctuations, and the critical current no longer hold.

#### Electronic-structural dynamics in graphene

*A. Cavalleri, I. Gierz*

We review our recent time- and angle-resolved photoemission spectroscopy experiments, which measure the transient electronic structure of optically driven graphene. For pump photon energies in the near infrared (ℏω_{pump}=950 meV), we have discovered the formation of a population-inverted state near the Dirac point, which may be of interest for the design of THz lasing devices and optical amplifiers. At lower pump photon energies (ℏω_{pump}<400 meV), for which interband absorption is not possible in doped samples, we find evidence for free carrier absorption. In addition, when mid-infrared pulses are made resonant with an infrared-active in-plane phonon of bilayer graphene (ℏω_{pump}=200 meV), a transient enhancement of the electron-phonon coupling constant is observed, providing interesting perspective for experiments that report light-enhanced superconductivity in doped fullerites in which a similar lattice mode was excited. All the studies reviewed here have important implications for applications of graphene in optoelectronic devices and for the dynamical engineering of electronic properties with light.

Structural Dynamics 3, 051301 (2016)

#### Wavelength-dependent optical enhancement of superconducting interlayer coupling in La1.885Ba0.115CuO4

*E. Casandruc, D. Nicoletti, S. Rajasekaran, Y. Laplace, V. Khanna, G. D. Gu, J. P. Hill, and A. Cavalleri*

We analyze the pump wavelength dependence for the photoinduced enhancement of interlayer coupling in La_{1.88}5Ba_{0.115}CuO_{4}, which is promoted by optical melting of the stripe order. In the equilibrium superconducting state (*T<TC*=13K) in which stripes and superconductivity coexist, time-domain terahertz spectroscopy reveals a photoinduced blueshift of the Josephson plasma resonance after excitation with optical pulses polarized perpendicular to the CuO_{2} planes. In the striped nonsuperconducting state (*T _{C}<T<T_{SO}*≃40K) a transient plasma resonance similar to that seen below

*T*appears from a featureless equilibrium reflectivity. Most strikingly, both these effects become stronger upon tuning of the pump wavelength from the midinfrared to the visible, underscoring an unconventional competition between stripe order and superconductivity, which occurs on energy scales far above the ordering temperature.

_{C}#### Redistribution of phase fluctuations in a periodically driven cuprate superconductor

*R. Höppner, B. Zhu, T. Rexin, A. Cavalleri, and L. Mathey*

We study the thermally fluctuating state of a bilayer cuprate superconductor under the periodic action of a staggered field oscillating at optical frequencies. This analysis distills essential elements of the recently discovered phenomenon of light-enhanced coherence in YBa_{2}Cu_{3}O_{6+x}, which was achieved by periodically driving infrared active apical oxygen distortions. The effect of a staggered periodic perturbation is studied using a Langevin and Fokker-Planck description of driven, coupled Josephson junctions, which represent two neighboring pairs of layers and their two plasmons. In a toy model including only two junctions, we demonstrate that the external driving leads to a suppression of phase fluctuations of the low-energy plasmon, an effect which is amplified via the resonance of the high-energy plasmon. When extending the modeling to the full layers, we find that this reduction becomes far more pronounced, with a striking suppression of the low-energy fluctuations, as visible in the power spectrum. We also find that this effect acts on the in-plane fluctuations, which are reduced on long length scales. All these findings provide a physical framework to describe light control in cuprates.

#### Phonon-Pump Extreme-Ultraviolet-Photoemission Probe in Graphene: Anomalous Heating of Dirac Carriers by Lattice Deformation

*Isabella Gierz, Matteo Mitrano, Hubertus Bromberger, Cephise Cacho, Richard Chapman, Emma Springate, Stefan Link, Ulrich Starke, Burkhard Sachs, Martin Eckstein, Tim O. Wehling, Mikhail I. Katsnelson, Alexander Lichtenstein, and Andrea Cavalleri*

We modulate the atomic structure of bilayer graphene by driving its lattice at resonance with the in-plane *E _{1u}* lattice vibration at 6.3

*μ*m. Using time- and angle-resolved photoemission spectroscopy (tr-ARPES) with extreme-ultraviolet (XUV) pulses, we measure the response of the Dirac electrons near the

*K*point. We observe that lattice modulation causes anomalous carrier dynamics, with the Dirac electrons reaching lower peak temperatures and relaxing at faster rate compared to when the excitation is applied away from the phonon resonance or in monolayer samples. Frozen phonon calculations predict dramatic band structure changes when the

*E*vibration is driven, which we use to explain the anomalous dynamics observed in the experiment.

_{1u}## Project C

### Project C1

#### Twisted superfluid phase in the extended one-dimensional Bose-Hubbard

* D.-S. Lühmann*

In one-dimensional systems a twisted superfluid phase is found which is induced by a spontaneous breaking of the time-reversal symmetry. Using the density-matrix renormalization group allows us to show that the excitation energy gap closes exponentially causing a quasidegenerate ground state. The two degenerate ground states are connected by the time-reversal symmetry which manifests itself in an alternating complex phase of the long-range correlation function. The quantum phase transition to the twisted superfluid is driven by pair tunneling processes in an extended Bose-Hubbard model. The phase boundaries of several other phases are discussed including a supersolid, a pair superfluid, and a pair supersolid phase as well as a highly unconventional Mott insulator with a degenerate ground state and a staggered pair correlation function.

#### Breaking inversion symmetry in a state-dependent honeycomb lattice: Artificial graphene with tunable band gap

* M. Weinberg, C. Staarmann, C. Ölschläger, J. Simonet, K. Sengstock*

Here, we present the application of a novel method for controlling the geometry of a state-dependent honeycomb lattice: The energy offset between the two sublattices of the honeycomb structure can be adjusted by rotating the atomic quantization axis. This enables us to continuously tune between a homogeneous graphene-like honeycomb lattice and a triangular lattice and to open an energy gap at the characteristic Dirac points. We probe the symmetry of the lattice with microwave spectroscopy techniques and investigate the behavior of atoms excited to the second energy band. We find a striking influence of the energy gap at the Dirac cones onto the lifetimes of atoms in the excited band.

#### Symmetry-broken momentum distributions induced by matter-wave diffraction during time-of-flight expansion of ultracold atoms

* M. Weinberg, O. Jürgensen, C. Ölschläger, D.-S. Lühmann, K. Sengstock, J. Simonet*

We study several effects which lead to symmetry-broken momentum distributions of quantum gases released from optical lattices. In particular, we demonstrate that interaction within the first milliseconds of the time-of-flight expansion can strongly alter the measurement of the initial atomic momentum distribution. For bosonic mixtures in state-dependent lattices, inter-species scattering processes lead to a symmetry breaking in momentum space. The underlying mechanism is identified to be diffraction of the matter wave from the total density lattice, which gives rise to a timedependent interaction potential. Our findings are of fundamental relevance for the interpretation of time-of-flight measurements and for the study of exotic quantum phases such as the twisted superfluid. Beyond that, the observed matter-wave diraction can also be used as an interferometric probe. In addition, we report on diffraction from the state-dependent standing light field, which leads to the same symmetry-broken momentum distributions, even for single component condensates.

#### Emulating molecular orbitals and electronic dynamics with ultracold atoms

*D.-S. Lühmann, C. Weitenberg, K. Sengstock*

In the recent years, ultracold atoms in optical lattices have proven their great value as quantum simulators for studying strongly-correlated phases and complex phenomena in solid-state systems. Here we reveal their potential as quantum simulators for molecular physics and propose a technique to image the three-dimensional molecular orbitals with high resolution. The outstanding tunability of ultracold atoms in terms of potential and interaction offer fully-adjustable model systems for gaining deep insight into the electronic structure of molecules. We study the orbitals of an artificial benzene molecule and discuss the effect of tunable interactions in its conjugated pi electron system with special regard to localization and spin order. The dynamical timescale of ultracold atom simulators are on the order milliseconds which allow for the time-resolved monitoring of a broad range of dynamical processes. As an example, we compute the hole dynamics in the conjugated pi system of the artificial benzene molecule.

#### Twisted complex superfluids in optical lattices

*O. Jürgensen, K. Sengstock, D.-S. Lühmann*

We show that correlated pair tunneling drives a phase transition to a twisted superfluid with a complex order parameter. This unconventional superfluid phase spontaneously breaks the time-reversal symmetry and is characterized by a twisting of the complex phase angle between adjacent lattice sites. We discuss the entire phase diagram of the extended Bose--Hubbard model for a honeycomb optical lattice showing a multitude of quantum phases including twisted superfluids, pair superfluids, supersolids and twisted supersolids. Furthermore, we show that the nearest-neighbor interactions breaks the inversion symmetry of the lattice and gives rise to dimerized density-wave insulators, where particles are delocalized on dimers. For two components, we find twisted superfluid phases with strong correlations between the species already for surprisingly small pair-tunneling amplitudes. Interestingly, this ground state shows an infinite degeneracy ranging continuously from a supersolid to a twisted superfluid.

#### Multiphoton interband excitations of quantum gases in driven optical lattices

* M. Weinberg, C. Ölschläger, C. Sträter, S. Prelle, A. Eckardt, K. Sengstock, J. Simonet*

We report on the observation of multiphoton absorption processes for quantum gases in shaken light crystals. Periodic inertial forcing, induced by a spatial motion of the lattice potential, drives multiphoton interband excitations of up to the 9th order. The occurrence of such excitation features is systematically investigated with respect to the potential depth and the driving amplitude. Ab initio calculations of resonance positions as well as numerical evaluation of their strengths exhibit a good agreement with experimental data. In addition our findings set the stage for reaching novel phases of quantum matter by tailoring appropriate driving schemes.

#### Beyond-mean-field study of a binary bosonic mixture in a state-dependent honeycomb lattice

* L. Cao, S. Krönke, J. Stockhofe, J. Simonet, K. Sengstock, D.-S. Lühmann and P. Schmelcher*

We investigate a binary mixture of bosonic atoms loaded into a state-dependent honeycomb lattice. For this system, the emergence of a so-called twisted-superfluid ground state was experimentally observed in Soltan-Panahi et al. [Nat. Phys. 8, 71 (2012)]. Theoretically, the origin of this effect is not understood. We perform numerical simulations of an extended single-band Bose-Hubbard model adapted to the experimental parameters employing the multilayer multiconfiguration time-dependent Hartree method for Bosons. Our results confirm the overall applicability of mean-field theory in the relevant parameter range, within the extended single-band Bose-Hubbard model. Beyond this, we provide a detailed analysis of correlation effects correcting the mean-field result. These have the potential to induce asymmetries in single shot time-of-flight measurements, but we find no indication of the patterns characteristic of the twisted superfluid. We comment on the restrictions of our model and possible extensions.

#### Dimerized Mott insulators in hexagonal optical lattices

*O. Jürgensen, D.-S. Lühmann*

We study bosonic atoms in optical honeycomb lattices with anisotropic tunneling and find dimerized Mott insulator (MI) phases with fractional filling. These incompressible insulating phases are characterized by an interaction-driven localization of particles in respect to the individual dimers and large local particle-number fluctuations within the dimers. We calculate the ground-state phase diagrams and the excitation spectra using an accurate cluster mean-field method. The cluster treatment enables us to probe the fundamental excitations of the dimerized MI where the excitation gap is dominated by the intra-dimer tunneling amplitude. This allows the distinction from normal Mott insulating phases gapped by the on-site interaction. In addition, we present analytical results for the phase diagram derived by a higher-order strong-coupling perturbative expansion approach. By computing finite lattices with large diameters the influence of a harmonic confinement is discussed in detail. It is shown that a large fraction of atoms forms the dimerized MI under experimental conditions. The necessary anisotropic tunneling can be realized either by periodic driving of the optical lattice or by engineering directly a dimerized lattice potential. The dimers can be mapped to their antisymmetric states creating a lattice with coupled p-orbitals.

#### Spin Orbit Coupling in Periodically Driven Optical Lattices

* J. Struck, J. Simonet, K. Sengstock*

We propose a novel experimental scheme for the emulation of spin-orbit coupling for ultracold, neutral atoms trapped in a one-dimensional lattice. This scheme does not involve near-resonant laser fields, avoiding the heating processes connected to the spontaneous emission of photons.

A time dependent magnetic field gradient periodically drives the atoms, which can lead to complex valued tunnel matrix elements, equivalent to a gauge dependent shift of the dispersion relation for a 1D lattice. For opposite spin states, the dispersion relations are shifted in opposite direction due to the inverted drive for both states. An additional radio-frequency coupling between the spin states leads to a mixing of the spin dispersion relations and a spin-orbit gap in the band structure.

Phys. Rev. A 90, 031601(R) (2014)

http://arxiv.org/abs/1407.1953

#### Quantum phases in tunable state-dependent hexagonal optical lattices

* D.-S. Lühmann, O. Jürgensen, M. Weinberg, J. Simonet, P. Soltan-Panahi, K. Sengstock*

We study the ground-state properties of ultracold bosonic atoms in a state-dependent graphene-like honeycomb optical lattice, where the degeneracy between the two triangular sublattices A and B can be lifted. We discuss the various geometries accessible with this lattice setup and present a novel scheme to control the energy offset with external magnetic fields. The competition of the on-site interaction with the offset energy leads to Mott phases characterized by population imbalances between the sublattices. For the definition of an optimal Hubbard model, we demonstrate a scheme that allows for the efficient computation of Wannier functions. Using a cluster mean-field method, we compute the phase diagrams and provide a universal representation for arbitrary energy offsets. We find good agreement with the experimental data for the superfluid to Mott insulator transition.

#### Tunable gauge potential for spinless particles in driven lattices

*J. Simonet, J. Struck, M. Weinberg, C. Ölschläger, P. Hauke, A. Eckardt, M. Lewenstein, K. Sengstock, P. Windpassinger*

We present a universal method to create a tunable, artificial vector gauge potential for neutral particles trapped in an optical lattice. A suitable periodic shaking of the lattice allows to engineer a Peierls phase for the hopping parameters. This scheme thus allows one to address the atomic internal degrees of freedom independently. We experimentally demonstrate the realisation of such artificial potentials in a 1D lattice, which generate ground state superfluids at arbitrary non-zero quasimomentum [4].

This scheme offers fascinating possibilities to emulate synthetic magnetic fields in 2D lattices. In a triangular lattice, continuously tunable staggered fluxes are realised. Spontaneous symmetry breaking has recently been observed for a π-flux [23]. With the presented scheme, we are now able to study the influence of a small symmetry breaking perturbation.

#### Engineering Ising-XY spin models in a triangular lattice using tunable artificial gauge fields

*J. Struck, M. Weinberg, C. Ölschläger, P. Windpassinger, J. Simonet, K. Sengstock, R. Höppner, P. Hauke, A. Eckardt, M. Lewenstein, L. Mathey*

#### Cluster Gutzwiller method for bosonic lattice systems

*D.-S. Lühmann*

A versatile and numerically inexpensive method is presented allowing the accurate calculation of phase diagrams for bosonic lattice models. By treating clusters within the Gutzwiller theory, a surprisingly good description of quantum fluctuations beyond the mean-field theory is achieved approaching quantum Monte Carlo predictions for large clusters. Applying this powerful method to the Bose-Hubbard model, we demonstrate that it yields precise results for the superfluid to Mott-insulator transition in square, honeycomb, and cubic lattices. Due to the exact treatment within a cluster, the method can be effortlessly adapted to more complicated Hamiltonians in the fast progressing field of optical lattice experiments. This includes state- and site-dependent superlattices, large confined atomic systems, and disordered potentials, as well as various types of extended Hubbard models. Furthermore, the approach allows an excellent treatment of systems with arbitrary filling factors. We discuss the perspectives that allow for the computation of large, spatially varying lattices, low-lying excitations, and time evolution.

#### Non-Abelian gauge fields and topological insulators in shaken optical lattices

*P. Hauke, O. Tielemann, A. Celi, C. Ölschläger, J. Simonet, J. Struck, M. Weinberg, P. Windpassinger, K. Sengstock, M. Lewenstein, A. Eckardt*

Time-periodic driving offers a low-demanding method to generate artificial gauge fields in optical lattices. We demonstrate that it is a powerful and versatile tool for engineering two-dimensional lattice systems: We show how to tune frustration and how to create and control band touching points like Dirac cones in the shaken kagom\'e lattice. We propose the realization of a topological or a quantum spin Hall insulator in a shaken spin-dependent hexagonal lattice. We describe how strong artificial magnetic fields can be achieved for example in a square lattice by employing superlattice modulation. Finally, exemplified on a shaken spin-dependent square lattice, we develop a method to create strong non-Abelian gauge fields.

Phys. Rev. Lett. 109, 145301 (2012)

http://www.arxiv.org/abs/1205.1398

#### Tunable gauge potential for neutral and spinless particles in driven lattices

* J. Struck, C. Ölschläger, M. Weinberg, P. Hauke, J. Simonet, A. Eckardt, M. Lewenstein, K. Sengstock, P. Windpassinger*

We present a universal method to create a tunable, artificial vector gauge potential for neutral particles trapped in an optical lattice. The necessary Peierls phase of the hopping parameters between neighboring lattice sites is generated by applying a suitable periodic inertial force such that the method does not rely on any internal structure of the particles. We experimentally demonstrate the realization of such artificial potentials, which generate ground state superfluids at arbitrary non-zero quasi-momentum. We furthermore investigate possible implementations of this scheme to create tuneable magnetic fluxes, going towards model systems for strong-field physics.

#### Quantum phase transition to unconventional multi-orbital superfluidity in optical lattices

* P. Soltan-Panahi, D.-S. Lühmann, J. Struck, P. Windpassinger, K. Sengstock*

Orbital physics plays a significant role for a vast number of important phenomena in complex condensed matter systems such as high-Tc superconductivity and unconventional magnetism. In contrast, phenomena in superfluids - especially in ultracold quantum gases - are commonly well described by the lowest orbital and a real order parameter. Here, we report on the observation of a novel multi-orbital superfluid phase with a complex order parameter in binary spin mixtures. In this unconventional superfluid, the local phase angle of the complex order parameter is continuously twisted between neighboring lattice sites. The nature of this twisted superfluid quantum phase is an interaction-induced admixture of the p-orbital favored by the graphene-like band structure of the hexagonal optical lattice used in the experiment. We observe a second-order quantum phase transition between the normal superfluid (NSF) and the twisted superfluid phase (TSF) which is accompanied by a symmetry breaking in momentum space. The experimental results are consistent with calculated phase diagrams and reveal fundamentally new aspects of orbital superfluidity in quantum gas mixtures. Our studies might bridge the gap between conventional superfluidity and complex phenomena of orbital physics.

Nature Physics 8, 71–75 (2012)

http://arxiv.org/abs/1104.3456v1

### Project C2

#### Bosonic Topological Excitations from the Instability of a Quadratic Band Crossing

*G.-Q. Luo, A. Hemmerich, Z.-F. Xu*

We investigate the interaction-driven instability of a quadratic band crossing arising for ultracold bosonic atoms loaded into a two-dimensional optical lattice. We consider the case when the degenerate point becomes a local minimum of both crossing energy bands such that it can support a stable Bose–Einstein condensate. A repulsive contact interaction among the condensed bosons induces a spontaneously time-reversal-symmetry broken superfluid phase and a topological gap is opened in the excitation spectrum. We propose two concrete realizations of the desired quadratic band crossing in lattices with either fourfold or sixfold rotational symmetries via suitable tuning of the unit cell leading to reduced Brillouin zones and correspondingly folded bands. In either case, topologically protected edge excitations are found for a finite system.

#### Rotation-Symmetry-Enforced Coupling of Spin and Angular Momentum for p-Orbital Bosons

*Y. Li, J. Yuan, A. Hemmerich, X. Li*

Intrinsic spin angular-momentum coupling of an electron has a relativistic quantum origin with the coupling arising from charged orbits, which does not carry over to charge-neutral atoms. Here, we propose a mechanism of spontaneous generation of spin angular-momentum coupling with spinor atomic bosons loaded into ** p**-orbital bands of a two-dimensional optical lattice. This spin angular-momentum coupling originates from many-body correlations and spontaneous symmetry breaking in a superfluid, with the key ingredients attributed to spin-channel quantum fluctuations and an approximate rotation symmetry. The resultant spin angular-momentum intertwined superfluid has Dirac excitations. In the presence of a chemical potential difference for adjacent sites, it provides a bosonic analogue of a symmetry-protected-topological insulator. Through a dynamical mean-field calculation, this novel superfluid is found to be a generic low-temperature phase, and it gives way to Mott localization only at strong interactions and even-integer fillings. We show the temperature to reach this order is accessible with present experiments.

#### Odd-parity topological superfluidity for fermions in a bond-centered square optical lattice

*Zhi-Fang Xu, Andreas Hemmerich, W. Vincent Liu*

We propose a physical scheme for the realization of two-dimensional topological odd-parity superfluidity in a spin-independent bond-centered square optical lattice based upon interband fermion pairing. The *D*_{4} point-group symmetry of the lattice protects a quadratic band crossing, which allows one to prepare a Fermi surface of spin-up fermions with odd parity close to the degeneracy point. In the presence of spin-down fermions with even parity populating a different energetically well-separated band, odd-parity pairing is favored. Strikingly, as a necessary prerequisite for pairing, both Fermi surfaces can be tuned to match well. As a result, topological superfluid phases emerge in the presence of merely *s*-wave interaction. Due to the *Z*_{2} symmetry of these odd-parity superfluids, we infer their topological features simply from the symmetry and the Fermi-surface topology as confirmed numerically.

#### π-Flux Dirac Bosons and Topological Edge Excitations in a Bosonic Chiral p-Wave Superfluid

*Zhi-Fang Xu, Li You, Andreas Hemmerich, and W. Vincent Liu*

We study the topological properties of elementary excitations in a staggered *p _{x}±ip_{y}* Bose-Einstein condensate realized in recent orbital optical lattice experiments. The condensate wave function may be viewed as a configuration space variant of the famous

*p*momentum space order parameter of strontium ruthenate superconductors. We show that its elementary excitation spectrum possesses Dirac bosons with π Berry flux. Remarkably, if we induce a population imbalance between the

_{x}+ip_{y}*p*and

_{x}+ip_{y}*p*condensate components, a gap opens up in the excitation spectrum resulting in a nonzero Chern invariant and topologically protected edge excitation modes. We give a detailed description of how our proposal can be implemented with standard experimental technology.

_{x}−ip_{y}#### Orbital optical lattices with bosons

*T. Kock, C. Hippler, A. Ewerbeck, and A. Hemmerich*

This article provides a synopsis of our recent experimental work exploring Bose-Einstein condensation in metastable higher Bloch bands of optical lattices. Bipartite lattice geometries have allowed us to implement appropriate band structures, which meet three basic requirements: the existence of metastable excited states sufficiently protected from collisional band relaxation, a mechanism to excite the atoms initially prepared in the lowest band with moderate entropy increase, and the possibility of cross-dimensional tunneling dynamics, necessary to establish coherence along all lattice axes. A variety of bands can be selectively populated and a subsequent thermalisation process leads to the formation of a condensate in the lowest energy state of the chosen band. As examples the 2nd, 4th and 7th bands in a bipartite square lattice are discussed. The geometry of the 2nd and 7th band can be tuned such that two inequivalent energetically degenerate energy minima arise at the X±-points at the edge of the 1st Brillouin zone. In this case even a small interaction energy is sufficient to lock the phase between the two condensation points such that a complex-valued chiral superfluid order parameter can emerge, which breaks time reversal symmetry. In the 4th band a condensate can be formed at the Gamma-point in the center of the 1st Brillouin zone, which can be used to explore topologically protected band touching points. The new techniques to access orbital degrees of freedom in higher bands greatly extend the class of many-body scenarios that can be explored with bosons in optical lattices.

J. Phys. B: At. Mol. Opt. Phys. 49, 042001 (2016)

http://arxiv.org/abs/1601.00500

#### Observation of chiral superfluid order by matter wave interference

* T. Kock, M. Ölschläger, A. Ewerbeck, W.-M. Huang, L. Mathey, A. Hemmerich*

The breaking of time reversal symmetry via the spontaneous formation of chiral order is ubiquitous in nature. Here, we present an unambiguous demonstration of this phenomenon for atoms Bose-Einstein condensed in the second Bloch band of an optical lattice. As a key tool we use a matter wave interference technique, which lets us directly observe the phase properties of the superfluid order parameter and allows us to reconstruct the spatial geometry of certain low energy excitations, associated with the formation of domains of different chirality. Our work marks a new era of optical lattices where orbital degrees of freedom play an essential role for the formation of exotic quantum matter, similarly as in electronic systems.

Physical Review Letters 114, 115301 (2015)

http://arxiv.org/abs/1411.3483

#### Controlling coherence via tuning of the population imbalance in a bipartite optical lattice

* M. Di Liberto, T. Comparin , T. Kock, M. Ölschäger, A. Hemmerich, C. Morais Smith*

The control of transport properties is a key tool at the basis of many technologically relevant effects in condensed matter. The clean and precisely controlled environment of ultracold atoms in optical lattices allows one to prepare simplified but instructive models, which can help to better understand the underlying physical mechanisms. We show that by tuning a structural deformation of the unit cell in a bipartite optical lattice, one can induce a phase transition from a superfluid into various Mott insulating phases forming a shell structure in the superimposed harmonic trap. The Mott shells are identified via characteristic features in the visibility of Bragg maxima in momentum spectra. The experimental findings are explained by Gutzwiller mean-field and quantum Monte Carlo calculations. Our system bears similarities with the loss of coherence in cuprate superconductors, known to be associated with the doping induced buckling of the oxygen octahedra surrounding the copper sites.

#### Proposed formation and dynamical signature of a chiral Bose liquid in an optical lattice

* X. Li, A. Paramekanti, A. Hemmerich, W. Vincent Liu*

Recent experiments on p-orbital atomic bosons have suggested the emergence of a spectacular ultracold superfluid with staggered orbital currents in optical lattices. This raises fundamental questions concerning the effects of thermal fluctuations as well as possible ways of directly observing such chiral order. Here we show via Monte Carlo simulations that thermal fluctuations destroy this superfluid in an unexpected two-step process, unveiling an intermediate normal phase with spontaneously broken time-reversal symmetry, dubbed a ‘chiral Bose liquid’. For integer fillings (n≥2) in the chiral Mott regime, thermal fluctuations are captured by an effective orbital Ising model, and Onsager’s powerful exact solution is adopted to determine the transition from this intermediate liquid to the para- orbital normal phase at high temperature. A lattice quench is designed to convert the staggered angular momentum, previously thought by experts difficult to directly probe, into coherent orbital oscillations, providing a time-resolved dynamical signature of chiral order.

Nature Communications 5, 3205 (2014)

http://arxiv.org/abs/1309.0523

#### Interaction-induced chiral px ± i py superfluid order of bosons in an optical lattice

*M. Ölschläger, T. Kock, G. Wirth, A. Ewerbeck, C. Morais Smith, A. Hemmerich*

The study of superconductivity with unconventional order is complicated in condensed matter systems by their immense complexity. Optical lattices with their exceptional precision and control allow one to emulate superfluidity avoiding many of the complications of condensed matter. A promising approach to realize unconventional superfluid order is to employ orbital degrees of freedom in higher Bloch bands. In recent work, indications were found that bosons condensed in the second band of an optical chequerboard lattice might exhibit px ± i py order. Here we present experiments, which provide strong evidence for the emergence of px ± i py order driven by the interaction in the local p-orbitals. We compare our observations with a multi-band Hubbard model and find excellent quantitative agreement.

New Journal of Physics 15, 083041 (2013)

http://arxiv.org/abs/1305.1177

#### Topologically induced avoided band crossing in an optical chequerboard lattice

* M. Ölschläger, G. Wirth, T. Kock, A. Hemmerich*

We report on the condensation of bosons in the 4th band of an optical chequerboard lattice providing a topologically induced avoided band crossing involving the second, third, and fourth bands. When the condensate is slowly tuned through the avoided crossing, accelerated band relaxation arises and the zero momentum approximately C4-invariant condensate wave function acquires finite momentum order and reduced C2 symmetry. For faster tuning Landau-Zener oscillations between different superfluid orders arise, which are used to characterize the avoided crossing.

Physical Review Letters, 108, 075302 (2012)

http://lanl.arxiv.org/abs/1110.3716

#### Topological semimetal in a fermionic optical lattice

* K. Sun, W. V. Liu, A. Hemmerich, S. Das Sarma*

Optical lattices have an important role in advancing our understanding of correlated quantum matter. The recent implementation of orbital degrees of freedom in chequerboard and hexagonal3 optical lattices opens up a new avenue towards discovering novel quantum states of matter that have no prior analogues in solid-state electronic materials. Here, we predict that an exotic topological semimetal emerges as a parity-protected gapless state in the orbital bands of a two-dimensional fermionic optical lattice. This new quantum state is characterized by a parabolic band-degeneracy point with Berry flux 2 Pi, in sharp contrast to the Pi-flux of Dirac points as in graphene.We showthat the appearance of this topological liquid is universal for all latticeswith D4 point-group symmetry, as long as orbitals with opposite parities hybridize strongly with each other and the band degeneracy is protected by odd parity. Turning on inter-particle repulsive interactions, the system undergoes a phase transition to a topological insulator whose experimental signature includes chiral gapless domain-wall modes, reminiscent of quantumHall edge states.

### Project C3

#### Identifying quantum phase transitions using artificial neural networks on experimental data

*B. S. Rem, N. Käming, M. Tarnowski, L. Asteria, N. Fläschner, C. Becker, K. Sengstock, C. Weitenberg*

Machine-learning techniques such as artificial neural networks are currently revolutionizing many technological areas and have also proven successful in quantum physics applications1,2,3,4. Here, we employ an artificial neural network and deep-learning techniques to identify quantum phase transitions from single-shot experimental momentum-space density images of ultracold quantum gases and obtain results that were not feasible with conventional methods. We map out the complete two-dimensional topological phase diagram of the Haldane model5,6,7 and provide an improved characterization of the superfluid-to-Mott-insulator transition in an inhomogeneous Bose–Hubbard system8,9,10. Our work points the way to unravel complex phase diagrams of general experimental systems, where the Hamiltonian and the order parameters might not be known.

#### Dynamics of Ultracold Quantum Gases in the Dissipative Fermi-Hubbard Model

* K. Sponselee, L. Freystatzky, B. Abeln, M. Diem, B. Hundt, A. Kochanke, T. Ponath, B. Santra, L. Mathey, K. Sengstock and C. Becker*

Abstract. We employ metastable ultracold 173-Yb atoms to study dynamics in the 1D dissipative Fermi-Hubbard model experimentally and theoretically, and observe a complete inhibition of two-body losses after initial fast transient dynamics. We attribute the suppression of particle loss to the dynamical generation of a highly entangled Dicke state. For several lattice depths and for two- and six-spin component mixtures we find very similar dynamics, showing that the creation of strongly correlated states is a robust and universal phenomenon. This offers interesting opportunities for precision measurements.

arXiv:1805.11853 (2018)

https://arxiv.org/abs/1805.11853

https://iopscience.iop.org/article/10.1088/2058-9565/aadccd/meta

#### Observation of Topological Bloch-State Defects and Their Merging Transition

*Matthias Tarnowski, Marlon Nuske, Nick Fläschner, Benno Rem, Dominik Vogel, Lukas Freystatzky, Klaus Sengstock, Ludwig Mathey, and Christof Weitenberg*

Topological defects in Bloch bands, such as Dirac points in graphene, and their resulting Berry phases play an important role for the electronic dynamics in solid state crystals. Such defects can arise in systems with a two-atomic basis due to the momentum-dependent coupling of the two sublattice states, which gives rise to a pseudospin texture. The topological defects appear as vortices in the azimuthal phase of this pseudospin texture. Here, we demonstrate a complete measurement of the azimuthal phase in a hexagonal optical lattice employing a versatile method based on time-of-flight imaging after off-resonant lattice modulation. Furthermore, we map out the merging transition of the two Dirac points induced by beam imbalance. Our work paves the way to accessing geometric properties in optical lattices also with spin-orbit coupling and interactions.

#### Split-and-delay unit for FEL interferometry in the XUV spectral range

*S. Usenko, A. Przystawik, L.L. Lazzarino, M.A. Jakob, F. Jacobs, C. Becker, C. Haunhorst, D. Kip, and T. Laarmann*

In this work we present a reflective split-and-delay unit (SDU) developed for interferometric time-resolved experiments utilizing an (extreme ultraviolet) XUV pump–XUV probe scheme with focused free-electron laser beams. The developed SDU overcomes limitations for phase-resolved measurements inherent to conventional two-element split mirrors by a special design using two reflective lamellar gratings. The gratings produce a high-contrast interference signal controlled by the grating displacement in every diffraction order. The orders are separated in the focal plane of the focusing optics, which enables one to avoid phase averaging by spatially selective detection of a single interference state of the two light fields. Interferometry requires a precise relative phase control of the light fields, which presents a challenge at short wavelengths. In our setup the phase delay is determined by an in-vacuum white light interferometer (WLI) that monitors the surface profile of the SDU in real time and thus measures the delay for each laser shot. The precision of the WLI is 1 nm as determined by optical laser interferometry. In the presented experimental geometry it corresponds to a time delay accuracy of 3 as, which enables phase-resolved XUV pump–XUV probe experiments at free-electron laser (FEL) repetition rates up to 60 Hz.

#### Relaxation dynamics of a closed high-spin Fermi system far from equilibrium

* U. Ebling, J. S. Krauser, N. Fläschner, K. Sengstock, C. Becker, M. Lewenstein, A. Eckardt*

A fundamental question in many-body physics is how closed quantum systems reach equilibrium. We address this question experimentally and theoretically in an ultracold high-spin Fermi gas where we find a complex interplay between internal and motional degrees of freedom. The fermions are initially prepared far from equilibrium with only a few spin states occupied. The subsequent dynamics leading to redistribution among all spin states is observed experimentally and simulated theoretically using a kinetic Boltzmann equation with full spin coherence. The latter is derived microscopically and provides good agreement with experimental data without any free parameters. We identify several collisional processes, which occur on different time scales. By varying density and magnetic field, we control the relaxation dynamics and are able to continuously tune the character of a subset of spin states from an open to a closed system.

Phys. Rev. X 4, 021011 (2014)

http://arxiv.org/abs/1312.6704

#### Detecting quadrupole interactions in ultracold Fermi gases

*M. Lahrz, M. Lemeshko, K. Sengstock, C. Becker, L. Mathey*

#### Creation of Quantum-Degenerate Gases of Ytterbium in a Compact 2D-/3D-MOT Setup

*S. Dörscher, A. Thobe, B. Hundt, A. Kochanke, R. Le Targat, P. Windpassinger, C. Becker, K. Sengstock*

*The following article has been accepted by Review of Scientific Instruments. After it is published, it will be found at http://rsi.aip.org*

We report on the first experimental setup based on a 2D-/3D-MOT scheme to create both Bose-Einstein condensates and degenerate Fermi gases of several ytterbium isotopes. Our setup does not require a Zeeman slower and offers the flexibility to simultaneously produce ultracold samples of other atomic species. Furthermore, the extraordinary optical access favors future experiments in optical lattices. A 2D-MOT on the strong 1S0-1P1 transition captures ytterbium directly from a dispenser of atoms and loads a 3D-MOT on the narrow 1S0-3P1 intercombination transition. Subsequently, atoms are transferred to a crossed optical dipole trap and cooled evaporatively to quantum degeneracy.

Review of Scientific Instruments 84, 043109

http://arxiv.org/abs/1303.1105

#### Intrinsic Photoconductivity of Ultracold Fermions in Optical Lattices

* J. Heinze, J. S. Krauser, N. Fläschner, B. Hundt, S. Götze, A. Itin, L. Mathey, K. Sengstock, C. Becker*

We report on the first experimental observation of a persistent alternating photocurrent in an ultracold gas of fermionic atoms in an optical lattice. The dynamics is induced and sustained by an external harmonic confinement. We find a counterintuitively momentum-dependent oscillation frequency for excited particles and a fast decay of holes which we attribute to spatial trapping. Lifetime measurements reveal a significant enhancement of particle-hole recombination with increasing interactions.

Phys. Rev. Lett. 110, 085302 (2013)

http://arxiv.org/abs/1208.4020

### Project C4

#### Detecting Friedel oscillations in ultracold Fermi gases

* Keno Riechers, Klaus Hueck, Niclas Luick, Thomas Lompe, Henning Moritz*

Investigating Friedel oscillations in ultracold gases would complement the studies performed on solid state samples with scanning-tunneling microscopes. In atomic quantum gases interactions and external potentials can be tuned freely and the inherently slower dynamics allow to access non-equilibrium dynamics following a potential or interaction quench. Here, we examine how Friedel oscillations can be observed in current ultracold gas experiments under realistic conditions. To this aim we numerically calculate the amplitude of the Friedel oscillations which a potential barrier provokes in a 1D Fermi gas and compare it to the expected atomic and photonic shot noise in a density measurement. We find that to detect Friedel oscillations the signal from several thousand one-dimensional systems has to be averaged. However, as up to 100 parallel one-dimensional systems can be prepared in a single run with present experiments, averaging over about 100 images is sufficient.

Eur. Phys. J. D 71, 232 (2017)

http://lanl.arxiv.org/abs/1704.06626

#### Two-Dimensional Homogeneous Fermi Gases

* Klaus Hueck, Niclas Luick, Lennart Sobirey, Jonas Siegl, Thomas Lompe, Henning Moritz*

We report on the experimental realization of homogeneous two-dimensional (2D) Fermi gases trapped in a box potential. In contrast to harmonically trapped gases, these homogeneous 2D systems are ideally suited to probe local as well as non-local properties of strongly interacting many-body systems. As a first measurement, we use a local probe to extract the equation of state (EOS) of a non-interacting Fermi gas. We then perform matter wave focusing to extract its momentum distribution and directly observe Pauli blocking in a near unity occupation of momentum states. Finally, we measure the momentum distribution of strongly interacting homogeneous 2D gases in the crossover between attractively interacting fermions and deeply-bound bosonic molecules.

PRL 120, 060402 (2018).

http://lanl.arxiv.org/abs/1704.06315

#### Calibrating High Intensity Absorption Imaging of Ultracold Atoms

* Klaus Hueck, Niclas Luick, Lennart Sobirey, Jonas Siegl, Thomas Lompe, Henning Moritz, Logan W. Clark, Cheng Chin*

Absorption imaging of ultracold atoms is the foundation for quantitative extraction of information from experiments with ultracold atoms. Due to the limited exposure time available in these systems, the signal-to-noise ratio is largest for high intensity absorption imaging where the intensity of the imaging light is on the order of the saturation intensity. In this case, the absolute value of the intensity of the imaging light enters as an additional parameter making it more sensitive to systematic errors. Here, we present a novel and robust technique to determine the imaging intensity in units of the effective saturation intensity to better than 5%. We do this

by measuring the momentum transferred to the atoms by the imaging light while varying its intensity. We further utilize the method to quantify the purity of the polarization of the imaging light and to determine the correct

imaging detuning.

Opt. Express 25, 8670-8679 (2017)

https://arxiv.org/abs/1702.01943

#### Suppression of kHz-Frequency Switching Noise in Digital Micro-Mirror Devices

* Klaus Hueck, Anton Mazurenko, Niclas Luick, Thomas Lompe, Henning Moritz*

igh resolution digital micro-mirror devices (DMD) make it possible to produce nearly arbitrary light fields with high accuracy, reproducibility and low optical aberrations. However, using these devices to trap and manipulate ultracold atomic systems for e.g. quantum simulation is often complicated by the presence of kHz-frequency switching noise. Here we demonstrate a simple hardware extension that solves this problem and makes it possible to produce truly static light fields. This modification leads to a 47 fold increase in the time that we can hold ultracold 6Li atoms in a dipole potential created with the DMD. Finally, we provide reliable and user friendly APIs written in Matlab and Python to control the DMD.

Rev. Sci. Instrum. 88, 016103 (2017)

https://arxiv.org/abs/1611.03397

#### Sudden and slow quenches into the antiferromagnetic phase of ultracold fermions

*M. Ojekhile, R. Höppner, H. Moritz, L. Mathey*

#### Probing superfluidity of Bose-Einstein condensates via laser stirring

*Vijay Pal Singh, Wolf Weimer, Kai Morgener, Jonas Siegl, Klaus Hueck, Niclas Luick, Henning Moritz, Ludwig Mathey*

We investigate the superfluid behavior of a Bose-Einstein condensate of 6Li molecules. In the experiment by Weimer et al., Phys. Rev. Lett. 114, 095301 (2015) a condensate is stirred by a weak, red-detuned laser beam along a circular path around the trap center. The rate of induced heating increases steeply above a velocity vc, which we define as the critical velocity. Below this velocity, the moving beam creates almost no heating. In this paper, we demonstrate a quantitative understanding of the critical velocity. Using both numerical and analytical methods, we identify the non-zero temperature, the circular motion of the stirrer, and the density profile of the cloud as key factors influencing the magnitude of vc. A direct comparison to the experimental data shows excellent agreement.

Phys. Rev. A 93, 023634 (2016)

http://lanl.arxiv.org/abs/1509.02168

#### The critical velocity in the BEC-BCS crossover

* W. Weimer, K. Morgener, V. P. Singh, J. Siegl, K. Hueck, N. Luick, L. Mathey, H. Moritz*

We map out the critical velocity in the crossover from Bose-Einstein condensation (BEC) to Bardeen-Cooper-Schrieffer superfluidity with ultracold 6Li gases. A small attractive potential is dragged along lines of constant column density. The rate of the induced heating increases steeply above a critical velocity vc. In the same samples, we measure the speed of sound vs by exciting density waves and compare the results to the measured values of vc. We perform numerical simulations in the BEC regime and find very good agreement, validating the approach. In the strongly correlated regime, where theoretical predictions only exist for the speed of sound, our measurements of vc provide a testing ground for theoretical approaches.

Phys. Rev. Lett. 114, 095301 (2015)

http://arxiv.org/abs/1408.5239

### Project C5

#### Nonequilibrium quantum phase transition in a hybrid atom-optomechanical system

*N. Mann, M. Reza Bakhtiari, A. Pelster, M. Thorwart*

We consider a hybrid quantum many-body system formed by a vibrational mode of a nanomembrane, which interacts optomechanically with light in a cavity, and an ultracold atom gas in the optical lattice of the out-coupled light. The adiabatic elimination of the light field yields an effective Hamiltonian which reveals a competition between the force localizing the atoms and the membrane displacement. At a critical atom-membrane interaction, we find a nonequilibrium quantum phase transition from a localized symmetric state of the atom cloud to a shifted symmetry-broken state, the energy of the lowest collective excitation vanishes, and a strong atom-membrane entanglement arises. The effect occurs when the atoms and the membrane are nonresonantly coupled.

#### Light-induced coherence in an atom-cavity system

*C. Georges, J. G. Cosme, L. Mathey, A. Hemmerich*

We demonstrate a light-induced formation of coherence in a cold atomic gas system that utilizes the suppression of a competing density wave (DW) order. The condensed atoms are placed in an optical cavity and pumped by an external optical standing wave, which induces a long-range interaction mediated by photon scattering and a resulting DW order above a critical pump strength. We show that the light-induced temporal modulation of the pump wave can suppress this DW order and restore coherence. This establishes a foundational principle of dynamical control of competing orders analogous to a hypothesized mechanism for light-induced superconductivity in high*-T*_{c} cuprates.

#### Bloch oscillations of a Bose-Einstein condensate in a cavity-induced optical lattice

*Ch. Georges, J. Vargas, H. Keßler, J. Klinder, A. Hemmerich*

This article complements previous work on the nondestructive observation of Bloch oscillations of a Bose-Einstein condensate in an optical lattice formed inside a high-finesse optical cavity [H. Keßler et al., New J. Phys. 18, 102001 (2016)]. We present measurements showing that the observed Bloch frequency is independent of the atom number and hence the cooperative coupling strength, the intracavity lattice depth, and the detuning between the external pump light and the effective cavity resonance. We find that in agreement with theoretical predictions, despite the atom-cavity dynamics, the value of the Bloch frequency agrees with that expected in conventional optical lattices, where it solely depends on the sizes of the force and the lattice constant. We also show that Bloch oscillations are observed in a self-organized two-dimensional lattice, which is formed if, instead of axially pumping the cavity through one of its mirrors, the Bose-Einstein condensate is irradiated by an optical standing wave oriented perpendicularly with respect to the cavity axis. For this case, however, excessive decoherence prevents a meaningful quantitative assessment.

#### Driven Bose-Hubbard Model with a Parametrically Modulated Harmonic Trap

*N. Mann, M. Reza Bakhtiari, F. Massel, A. Pelster, M. Thorwart*

We investigate a one-dimensional Bose–Hubbard model in a parametrically driven global harmonic trap. The delicate interplay of both the local interaction of the atoms in the lattice and the driving of the global trap allows us to control the dynamical stability of the trapped quantum many-body state. The impact of the atomic interaction on the dynamical stability of the driven quantum many-body state is revealed in the regime of weak interaction by analyzing a discretized Gross–Pitaevskii equation within a Gaussian variational ansatz, yielding a Mathieu equation for the condensate width. The parametric resonance condition is shown to be modified by the atom interaction strength. In particular, the effective eigenfrequency is reduced for growing interaction in the mean-field regime. For a stronger interaction, the impact of the global parametric drive is determined by the numerically exact time-evolving block decimation scheme. When the trapped bosons in the lattice are in a Mott insulating state, the absorption of energy from the driving field is suppressed due to the strongly reduced local compressibility of the quantum many-body state. In particular, we find that the width of the local Mott region shows a breathing dynamics. Finally, we observe that the global modulation also induces an effective time-independent inhomogeneous hopping strength for the atoms.

#### Topological Varma superfluid in optical lattices

* M. Di Liberto, A. Hemmerich, and C. Morais Smith*

Topological states of matter are peculiar quantum phases showing different edge and bulk transport properties connected by the bulk-boundary correspondence. While non-interacting fermionic topological insulators are well established by now and have been classified according to a ten-fold scheme, the possible realisation of topological states for bosons has not been much explored yet. Furthermore, the role of interactions is far from being understood. Here, we show that a topological state of matter exclusively driven by interactions may occur in the p-band of a Lieb optical lattice filled with ultracold bosons. The single-particle spectrum of the system displays a remarkable parabolic band-touching point, with both bands exhibiting non-negative curvature. Although the system is neither topological at the single-particle level, nor for the interacting ground state, on-site interactions induce an anomalous Hall effect for the excitations, carrying a non-zero Chern number. Our work introduces an experimentally realistic strategy for the formation of interaction-driven topological states of bosons.

Physical Review Letters 117, 163001 (2016)

https://arxiv.org/abs/1604.06055

#### In-situ observation of optomechanical Bloch oscillations in an optical cavity

*H. Keßler, J. Klinder, B. Prasanna Venkatesh, Ch. Georges, A. Hemmerich*

It is shown experimentally that a Bose-Einstein condensate inside an optical cavity, operating in the regime of strong cooperative coupling, responds to an external force by an optomechanical Bloch oscillation, which can be directly observed in the light leaking out of the cavity. Previous theoretical work predicts that the frequency of this oscillation matches with that of conventional Bloch oscillations such that its in-situ monitoring may help to increase the data acquisition speed in precision force measurements.

New Journal of Physics 18, 102001 (2016)

https://arxiv.org/abs/1606.08386

#### Dynamical phase transition in the open Dicke model

*J. Klinder, H. Keßler, M. Wolke, L. Mathey, A. Hemmerich*

The Dicke model with a weak dissipation channel is realized by coupling a Bose–Einstein condensate to an optical cavity with ultranarrow bandwidth. We explore the dynamical critical properties of the Hepp–Lieb–Dicke phase transition by performing quenches across the phase boundary. We observe hysteresis in the transition between a homogeneous phase and a self-organized collective phase with an enclosed loop area showing power-law scaling with respect to the quench time, which suggests an interpretation within a general framework introduced by Kibble and Zurek. The observed hysteretic dynamics is well reproduced by numerically solving the mean-field equation derived from a generalized Dicke Hamiltonian. Our work promotes the understanding of nonequilibrium physics in open many-body systems with infinite range interactions.

#### Observation of a superradiant Mott insulator in the Dicke-Hubbard model

* J. Klinder, H. Keßler, M. Reza Bakhtiari, M. Thorwart, and A. Hemmerich*

It is well known that the bosonic Hubbard model possesses a Mott insulator phase. Likewise, it is known that the Dicke model exhibits a self-organized superradiant phase. By implementing an optical lattice inside of a high finesse optical cavity both models are merged such that an extended Hubbard model with cavity-mediated infinite range interactions arises. In addition to a normal superfluid phase, two superradiant phases are found, one of them coherent and hence superfluid and one incoherent Mott insulating.

Physical Review Letters 115, 230403 (2015)

http://arxiv.org/abs/1511.00850

#### Nonequilibrium phase transition of interacting bosons in an intra-cavity optical lattice

* M. R. Bakhtiari, A. Hemmerich, H. Ritsch, M. Thorwart*

We investigate the nonlinear light-matter interaction of a Bose-Einstein condensate trapped in an external periodic potential inside an optical cavity, which is weakly coupled to the vacuum radiation modes and driven by a transverse pump field. Based on a generalized Bose-Hubbard model, which incorporates a single cavity mode, we include the collective back action of the atoms on the cavity light field and determine the nonequilibrium quantum phases within the non-perturbative bosonic dynamical mean-field theory. With the system parameters adapted to recent experiments, we find a quantum phase transition from a normal phase to a self-organized superfluid phase, which is related to the Hepp-Lieb-Dicke phase transition. For even stronger pumping, a self-organized Mott insulator phase arises.

Physical Review Letters 114, 123601 (2015)

http://arxiv.org/abs/1410.5735

#### Steering matter wave superradiance with an ultra-narrowband optical cavity

* H. Keßler, J. Klinder, M. Wolke, A. Hemmerich*

A superfluid atomic gas is prepared inside an optical resonator with an ultra-narrow band width on the order of the single photon recoil energy. When a monochromatic off-resonant laser beam irradiates the atoms, above a critical intensity the cavity emits superradiant light pulses with a duration on the order of its photon storage time. The atoms are collectively scattered into coherent superpositions of discrete momentum states, which can be precisely controlled by adjusting the cavity resonance frequency. With appropriate pulse sequences the entire atomic sample can be collectively accelerated or decelerated by multiples of two recoil momenta. The instability boundary for the onset of matter wave superradiance is recorded and its main features are explained by a mean field model.

Physical Review Letters 113, 070404 (2014)

http://arxiv.org/abs/1407.4954

#### Optomechanical atom-cavity interaction in the sub-recoil regime

* H. Keßler, J. Klinder, M. Wolke, A. Hemmerich*

We study the optomechanical interaction of a Bose-Einstein condensate with a single longitudinal mode of an ultra-high finesse standing wave optical resonator. As a unique feature the resonator combines three extreme regimes, previously not realized together, i.e., strong cooperative coupling, cavity dominated scattering with a Purcell factor far above unity, and sub-recoil resolution provided by a cavity damping rate smaller than four times the single photon recoil frequency. We present experimental observations in good agreement with a two-mode model predicting highly non-linear dynamics with signatures as bistability, hysteresis, persistent oscillations, and superradiant back-scattering instabilities.

New Journal of Physics 16, 053008 (2014)

http://arxiv.org/abs/1403.3545

#### Cavity cooling below the recoil limit

* M. Wolke, J. Klinner, H. Keßler, A. Hemmerich*

Conventional laser cooling relies on repeated electronic excitations by near-resonant light, which constrains its area of application to a selected number of atomic species prepared at moderate particle densities. Optical cavities with sufficiently large Purcell factors allow for laser cooling schemes avoiding these limitations. Here, we report on an atom-cavity system, combining a Purcell factor above 40 with a cavity bandwidth below the recoil frequency associated with the kinetic energy transfer in a single photon scattering event. This lets us access a yet unexplored regime of atom-cavity interactions, in which the atomic motion can be manipulated by targeted dissipation with sub-recoil resolution. We demonstrate cavity-induced heating of a Bose-Einstein condensate and subsequent cooling at particle densities and temperatures incompatible with conventional laser cooling.

### Project C6

#### Symmetry effects on the spin switching of adatoms

* C. Hübner, B. Baxevanis, A. A. Khajetoorians, D. Pfannkuche*

Highly symmetric magnetic environments have been suggested to stabilize the magnetic information stored in magnetic adatoms on a surface. Utilized as memory devices such systems are subjected to electron tunneling and external magnetic fields. We analyze theoretically how such perturbations affect the switching probability of a single quantum spin for two characteristic symmetries encountered in recent experiments and suggest a third one that exhibits robust protection against surface-induced spin flips. Further we illuminate how the switching of an adatom spin exhibits characteristic behavior with respect to low energy excitations from which the symmetry of the system can be inferred.

#### Isospin correlations in two-partite hexagonal optical lattices

* M. Prada, E.-M. Richter, D. Pfannkuche*

Two-component mixtures in optical lattices reveal a rich variety of different phases. We employ an exact diagonalization method to obtain the relevant correlation functions in hexagonal optical lattices which characterize those phases. We relate the occupation difference of the two species to the magnetic polarization. “Iso” -magnetic correlations disclose the nature of the system, which can be of easy-axis type, bearing phase segregation, or of easy-plane type, corresponding to super-counter-fluidity. In the latter case, the correlations reveal easy-plane segregation, involving a highly entangled state. We identify striking correlated supersolid phases appearing within the superfluid limit.

#### Doublon Relaxation in the Bose-Hubbard Model

*A. L. Chudnovskiy, D. M. Gangardt, A. Kamenev*

### Project C7

#### Quantum point spread function for imaging trapped few-body systems with a quantum gas microscope

*S. Krönke, M. Pyzh, C. Weitenberg, P. Schmelcher*

Quantum gas microscopes, which image the atomic occupations in an optical lattice, have opened a new avenue to the exploration of many-body lattice systems. Imaging trapped systems after freezing the density distribution by ramping up a pinning lattice leads, however, to a distortion of the original density distribution, especially when its structures are on the scale of the pinning lattice spacing. We show that this dynamics can be described by a filter, which we call in analogy to classical optics a quantum point spread function. Using a machine learning approach, we demonstrate via several experimentally relevant setups that a suitable deconvolution allows for the reconstruction of the original density distribution. These findings are both of fundamental interest for the theory of imaging and of immediate importance for current quantum gas experiments.

#### Spectral properties and breathing dynamics of a few-body Bose–Bose mixture in a 1D harmonic trap

*M. Pyzh, S. Krönke, C. Weitenberg, P. Schmelcher*

We investigate a few-body mixture of two bosonic components, each consisting of two particles confined in a quasi one-dimensional harmonic trap. By means of exact diagonalization with a correlated basis approach we obtain the low-energy spectrum and eigenstates for the whole range of repulsive intra- and inter-component interaction strengths. We analyse the eigenvalues as a function of the inter-component coupling, covering hereby all the limiting regimes, and characterize the behaviour in-between these regimes by exploiting the symmetries of the Hamiltonian. Provided with this knowledge we study the breathing dynamics in the linear-response regime by slightly quenching the trap frequency symmetrically for both components. Depending on the choice of interactions strengths, we identify 1 to 3 monopole modes besides the breathing mode of the centre of mass coordinate. For the uncoupled mixture each monopole mode corresponds to the breathing oscillation of a specific relative coordinate. Increasing the inter-component coupling first leads to multi-mode oscillations in each relative coordinate, which turn into single-mode oscillations of the same frequency in the composite-fermionization regime.

#### Entanglement Induced Interactions in Binary Mixtures

*J. Chen, J.M. Schurer and P. Schmelcher*

We establish a conceptual framework for the identification and the characterization of induced interactions in binary mixtures and reveal their intricate relation to entanglement between the components or species of the mixture. Exploiting an expansion in terms of the strength of the entanglement among the two species enables us to deduce an effective single-species description. In this way, we naturally incorporate the mutual feedback of the species and obtain induced interactions for both species which are effectively present among the particles of same type. Importantly, our approach incorporates few-body and inhomogeneous systems extending the scope of induced interactions where two particles interact via a bosonic bath-type environment. Employing the example of a one-dimensional ultracold Bose-Fermi mixture, we obtain induced Bose-Bose and Fermi-Fermi interactions with short-range attraction and long-range repulsion. With this, we show how beyond species mean-field physics visible in the two-body correlation functions can be understood via the induced interactions.

#### Bosonic quantum dynamics following a linear interaction quench in finite optical lattices of unit filling

*S.I. Mistakidis, G.M. Koutentakis and P. Schmelcher*

The nonequilibrium ultracold bosonic quantum dynamics in finite optical lattices of unit filling following a linear interaction quench from a superfluid to a Mott insulator state and vice versa is investigated. The resulting dynamical response consists of various inter and intraband tunneling modes. We find that the competition between the quench rate and the interparticle repulsion leads to a resonant dynamical response, at moderate ramp times, being related to avoided crossings in the many-body eigenspectrum with varying interaction strength. Crossing the regime of weak to strong interactions several transport pathways are excited. The higher-band excitation dynamics is shown to obey an exponential decay possessing two distinct time scales with varying ramp time. Studying the crossover from shallow to deep lattices we find that for a diabatic quench the excited band fraction decreases, while approaching the adiabatic limit it exhibits a non-linear behavior for increasing height of the potential barrier. The inverse ramping process from strong to weak interactions leads to a melting of the Mott insulator and possesses negligible higher-band excitations which follow an exponential decay for decreasing quench rate. Finally, independently of the direction that the phase boundary is crossed, we observe a significant enhancement of the excited to higher-band fraction for increasing system size.

#### Many-body expansion dynamics of a Bose-Fermi mixture confined in an optical lattice

*P. Siegl, S.I. Mistakidis and P. Schmelcher*

We unravel the correlated nonequilibrium dynamics of a mass balanced Bose-Fermi mixture in a one-dimensional optical lattice upon quenching an imposed harmonic trap from strong to weak confinement. Regarding the system's ground state, the competition between the inter- and intraspecies interaction strength gives rise to the immiscible and miscible phases characterized by negligible and complete overlap of the constituting atomic clouds, respectively. The resulting dynamical response depends strongly on the initial phase and consists of an expansion of each cloud and an interwell tunneling dynamics. For varying quench amplitude and referring to a fixed phase, a multitude of response regimes is unveiled, being richer within the immiscible phase, which are described by distinct expansion strengths and tunneling channels.

#### Correlation effects in the quench-induced phase separation dynamics of a two species ultracold quantum gas

*S.I. Mistakidis, G.C. Katsimiga, P.G. Kevrekidis and P. Schmelcher*

We explore the quench dynamics of a binary Bose–Einstein condensate crossing the miscibility–immiscibility threshold and vice versa, both within and in particular beyond the mean-field approximation. Increasing the interspecies repulsion leads to the filamentation of the density of each species, involving shorter wavenumbers and longer spatial scales in the many-body (MB) approach. These filaments appear to be strongly correlated and exhibit domain-wall structures. Following the reverse quench process multiple dark–antidark solitary waves are spontaneously generated and subsequently found to decay in the MB scenario. We simulate single-shot images to connect our findings to possible experimental realizations. Finally, the growth rate of the variance of a sample of single-shots probes the degree of entanglement inherent in the system.

#### Correlation induced localization of lattice trapped bosons coupled to a Bose–Einstein condensate

*K. Keiler, S. Krönke and P. Schmelcher*

We investigate the ground state properties of a lattice trapped bosonic system coupled to a Lieb–Liniger type gas. Our main goal is the description and in depth exploration and analysis of the two-species many-body quantum system including all relevant correlations beyond the standard mean-field approach. To achieve this, we use the multi-configuration time-dependent Hartree method for mixtures (ML-MCTDHX). Increasing the lattice depth and the interspecies interaction strength, the wave function undergoes a transition from an uncorrelated to a highly correlated state, which manifests itself in the localization of the lattice atoms in the latter regime. For small interspecies couplings, we identify the process responsible for this cross-over in a single-particle-like picture. Moreover, we give a full characterization of the wave function's structure in both regimes, using Bloch and Wannier states of the lowest band, and we find an order parameter, which can be exploited as a corresponding experimental signature. To deepen the understanding, we use an effective Hamiltonian approach, which introduces an induced interaction and is valid for small interspecies interaction. We finally compare the ansatz of the effective Hamiltonian with the results of the ML-MCTDHX simulations.

#### Quantum dynamics of two trapped bosons following infinite interaction quenches

*L.M.A. Kehrberger, V.J. Bolsinger and P. Schmelcher*

We investigate the quantum dynamics of two identical bosons in a one-dimensional harmonic trap following an interaction quench from zero to infinite interaction strength and vice versa. For both quench scenarios, closed analytical expressions for the temporal evolution of the wave function as well as the Loschmidt echo are found and the dynamics of the momentum density as well as the reduced single-particle density matrix are analyzed. We observe a crossover of these quantities between bosonic, “symmetrized” fermionic, and fermionic properties. Furthermore, several combined quenches are analyzed as well.

#### Quantum dynamical response of ultracold few-boson ensembles in finite optical lattices to multiple interaction quenches

*J. Neuhaus-Steinmetz, S. Mistakidis and P. Schmelcher*

The correlated nonequilibrium quantum dynamics following a multiple interaction quench protocol for few-bosonic ensembles confined in finite optical lattices is investigated. The quenches give rise to an interwell tunneling and excite the cradle and a breathing mode. Several tunneling pathways open during the time interval of increased interactions, while only a few occur when the system is quenched back to its original interaction strength. The cradle mode, however, persists during and in between the quenches, while the breathing mode possesses distinct frequencies. The occupation of excited bands is explored in detail revealing a monotonic behavior with increasing quench amplitude and a nonlinear dependence on the duration of the application of the quenched interaction strength. Finally, a periodic population transfer between momenta for quenches of increasing interaction is observed, with a power-law frequency dependence on the quench amplitude. Our results open the possibility to dynamically manipulate various excited modes of the bosonic system.

#### Collective excitations of dipolar gases based on local tunneling in superlattices

*L. Cao, S.I. Mistakidis, X. Deng and P. Schmelcher*

The collective dynamics of a dipolar fermionic quantum gas confined in a one-dimensional double-well superlattice is explored. The fermionic gas resides in a paramagnetic-like ground state in the weak interaction regime, upon which a new type of collective dynamics is found when applying a local perturbation. This dynamics is composed of the local tunneling of fermions in separate supercells, and is a pure quantum effect, with no classical counterpart. Due to the presence of the dipolar interactions the local tunneling transports through the entire superlattice, giving rise to a collective dynamics. A well-defined momentum-energy dispersion relation is identified in the ab-initio simulations demonstrating the phonon-like behavior. The phonon-like characteristic is also confirmed by an analytical description of the dynamics within a semiclassical picture.

#### Mode coupling of interaction quenched ultracold few-boson ensembles in periodically driven lattices

*S.I. Mistakidis and P. Schmelcher*

The out-of-equilibrium dynamics of interaction quenched finite ultracold bosonic ensembles in periodically driven one-dimensional optical lattices is investigated. It is shown that periodic driving enforces the bosons in the outer wells of the finite lattice to exhibit out-of-phase dipolelike modes, while in the central well the atomic cloud experiences a local breathing mode. The dynamical behavior is investigated with varying driving frequencies, revealing resonantlike behavior of the intrawell dynamics. An interaction quench in the periodically driven lattice gives rise to admixtures of different excitations in the outer wells, enhanced breathing in the center, and amplification of the tunneling dynamics. We then observe multiple resonances between the inter- and the intrawell dynamics at different quench amplitudes, with the position of the resonances being tunable via the driving frequency. Our results pave the way for future investigations of the use of combined driving protocols in order to excite different inter- and intrawell modes and to subsequently control them.

#### Quench-induced resonant tunneling mechanisms of bosons in an optical lattice with harmonic confinement

*G.M. Koutentakis, S.I. Mistakidis and P. Schmelcher*

The nonequilibrium dynamics of small boson ensembles in a one-dimensional optical lattice is explored upon a sudden quench of an additional harmonic trap from strong to weak confinement. We find that the competition between the initial localization and the repulsive interaction leads to a resonant response of the system for intermediate quench amplitudes, corresponding to avoided crossings in the many-body eigenspectrum with varying final trap frequency. In particular, we show that these avoided crossings can be utilized to prepare the system in a desired state. The dynamical response is shown to depend on both the interaction strength as well as the number of atoms manifesting the many-body nature of the tunneling dynamics.

#### Resonant quantum dynamics of few ultracold bosons in periodically driven finite lattices

* S.I. Mistakidis, T. Wulf, A. Negretti and P. Schmelcher*

The out-of-equilibrium dynamics of finite ultracold bosonic ensembles in periodically driven one-dimensional optical lattices is investigated. Our study reveals that the driving enforces the bosons in different wells to oscillate in-phase and to exhibit a dipole-like mode. A wide range from weak-to-strong driving frequencies is covered and a resonance-like behavior of the intra-well dynamics is discussed. In the proximity of the resonance a rich intraband excitation spectrum is observed. The single particle excitation mechanisms are studied in the framework of Floquet theory elucidating the role of the driving frequency. The impact of the interatomic repulsive interactions is examined in detail yielding a strong influence on the tunneling period and the excitation probabilities. Finally, the dependence of the resonance upon a variation of the tunable parameters of the optical lattice is examined. Our analysis is based on the ab initio multi-configuration time-dependent Hartree method for bosons.

#### Two-body correlations and natural-orbital tomography in ultracold bosonic systems of definite parity

* S. Krönke and P. Schmelcher*

The relationship between natural orbitals, one-body coherences, and two-body correlations is explored for bosonic many-body systems of definite parity with two occupied single-particle states. We show that the strength of local two-body correlations at the parity-symmetry center characterizes the number-state distribution and controls the structure of nonlocal two-body correlations. A recipe for the experimental reconstruction of the natural-orbital densities and quantum depletion is derived. These insights into the structure of the many-body wave function are applied to the predicted quantum-fluctuation-induced decay of dark solitons.

#### Magnetic Kink States Emulated with Dipolar Superlattice Gases

* X. Yin, L. Cao. P. Schmelcher*

We propose an effective Ising spin chain constructed with dipolar quantum gases confined in a one-dimensional optical superlattice. Mapping the motional degree of freedom of a single particle in the lattice onto a pseudo-spin results in an effective Ising type chain dressed with transverse and longitudinal magnetic fields. The ground state of this effective Ising chain changes from a paramagnetic to a single-kink state as the dipolar interaction increases. Particularly in the single-kink state this effective chain permits emulations of magnetic kink effects. Being realizable with current experimental techniques, this effective Ising chain presents a unique platform for emulations of Ising physics and enriches the toolbox for quantum emulation of spin models by ultracold quantum gases.

#### Correlated quantum dynamics of a single atom collisionally coupled to an ultracold finite bosonic ensemble

* S. Krönke, J. Knörzer and P. Schmelcher*

We explore the correlated quantum dynamics of a single atom, regarded as an open system, with a spatio-temporally localized coupling to a finite bosonic environment. The single atom, initially prepared in a coherent state of low energy, oscillates in a one-dimensional harmonic trap and thereby periodically penetrates an interacting ensemble of NA bosons held in a displaced trap. We show that the inter-species energy transfer accelerates with increasing NA and becomes less complete at the same time. System-environment correlations prove to be significant except for times when the excess energy distribution among the subsystems is highly imbalanced. These correlations result in incoherent energy transfer processes, which accelerate the early energy donation of the single atom and stochastically favour certain energy transfer channels, depending on the instantaneous direction of transfer. Concerning the subsystem states, the energy transfer is mediated by non-coherent states of the single atom and manifests itself in singlet and doublet excitations in the finite bosonic environment. These comprehensive insights into the non-equilibrium quantum dynamics of an open system are gained by ab initio simulations of the total system with the recently developed multi-layer multi-configuration time-dependent Hartree method for bosons.

#### Beyond-mean-field study of a binary bosonic mixture in a state-dependent honeycomb lattice

* L. Cao, S. Krönke, J. Stockhofe, J. Simonet, K. Sengstock, D.-S. Lühmann and P. Schmelcher*

We investigate a binary mixture of bosonic atoms loaded into a state-dependent honeycomb lattice. For this system, the emergence of a so-called twisted-superfluid ground state was experimentally observed in Soltan-Panahi et al. [Nat. Phys. 8, 71 (2012)]. Theoretically, the origin of this effect is not understood. We perform numerical simulations of an extended single-band Bose-Hubbard model adapted to the experimental parameters employing the multilayer multiconfiguration time-dependent Hartree method for Bosons. Our results confirm the overall applicability of mean-field theory in the relevant parameter range, within the extended single-band Bose-Hubbard model. Beyond this, we provide a detailed analysis of correlation effects correcting the mean-field result. These have the potential to induce asymmetries in single shot time-of-flight measurements, but we find no indication of the patterns characteristic of the twisted superfluid. We comment on the restrictions of our model and possible extensions.

#### Negative-quench-induced excitation dynamics for ultracold bosons in one-dimensional lattices

* S.I. Mistakidis, L. Cao and P. Schmelcher*

The nonequilibrium dynamics following a quench of strongly repulsive bosonic ensembles in one-dimensional finite lattices is investigated by employing interaction quenches and/or a ramp of the lattice potential. Both sudden and time-dependent quenches are analyzed in detail. For the case of interaction quenches we address the transition from the strong repulsive to the weakly interacting regime, suppressing in this manner the heating of the system. The excitation modes such as the cradle process and the local breathing mode are examined via local density observables. In particular, the cradle mode is inherently related to the initial delocalization and, following a negative interaction quench, can be excited only for incommensurate setups with filling larger than unity. Alternatively, a negative quench of the lattice depth which favors the spatial delocalization is used to access the cradle mode for setups with filling smaller than unity. Our results shed light on possible schemes to control the cradle and the breathing modes. Finally, employing the notion of fidelity we study the dynamical response of the system after a diabatic or adiabatic parameter modulation for short and long evolution times. The evolution of the system is obtained numerically using the ab initio multilayer multiconfiguration time-dependent Hartree method for bosons, which permits us to follow nonequilibrium dynamics including the corresponding investigation of higher-band effects.

#### Interaction quench induced multimode dynamics of finite atomic ensembles

*S. Mistakidis, L. Cao, P. Schmelcher*

The correlated non-equilibrium dynamics of few-boson systems in one-dimensional finite lattices is investigated. Starting from weak interactions we perform a sudden interaction quench and employ the numerically exact multi-layer multi-configuration time-dependent Hartree method for bosons to obtain the resulting quantum dynamics. Focusing on the low-lying modes of the finite lattice we observe the emergence of density-wave tunneling, breathing and cradle-like processes. In particular, the tunneling induced by the quench leads to a 'global' density-wave oscillation. The resulting breathing and cradle modes are inherent to the local intrawell dynamics and connected to excited-band states. Moreover, the interaction quenches couple the density-wave and the cradle modes allowing for resonance phenomena. These are associated with an avoided-crossing in the respective frequency spectrum and lead to a beating dynamics for the cradle. Finally, complementing the numerical studies, an effective Hamiltonian in terms of the relevant Fock states is derived for the description of the spectral properties and the related resonant dynamics.

#### Quantum breathing dynamics of ultracold bosons in one-dimensional harmonic traps: Unraveling the pathway from few- to many-body systems

* R. Schmitz, S. Krönke, L. Cao, P. Schmelcher*

Following a “bottom-up approach” in understanding many-particle effects and dynamics we provide a systematic ab initio study of the dependence of the breathing dynamics of ultracold bosons in a one-dimensional (1D) harmonic trap on the number of bosons ranging from few to many. To this end, we employ the multilayer multiconfiguration time-dependent Hartree method for bosons (ML-MCTDHB) which has been developed very recently [ Krönke, Cao, Vendrell and Schmelcher New J. Phys. 15 063018 (2013)]. The beating behavior for two bosons is found numerically and consequently explained by an analytical approach. Drawing on this, we show how to compute the complete breathing mode spectrum in this case. We examine how the two-mode breathing behavior of two bosons evolves to the single-frequency behavior of the many-particle limit when adding more particles. In the limit of many particles, we numerically study the dependence of the breathing mode frequency on both the interaction strength as well as on the particle number. We provide an estimate for the parameter region where the mean-field description provides a valid approximation.

#### The multi-layer multi-configuration time-dependent Hartree method for bosons: Theory, implementation, and applications

* L. Cao, S. Krönke, O. Vendrell, P. Schmelcher*

We develop the multi-layer multi-configuration time-dependent Hartree method for bosons (ML-MCTDHB), a variational numerically exact ab initio method for studying the quantum dynamics and stationary properties of general bosonic systems. ML-MCTDHB takes advantage of the permutation symmetry of identical bosons, which allows for investigations of the quantum dynamics from few to many-body systems. Moreover, the multi-layer feature enables ML-MCTDHB to describe mixed bosonic systems consisting of arbitrary many species. Multi-dimensional as well as mixed-dimensional systems can be accurately and efficiently simulated via the multi-layer expansion scheme. We provide a detailed account of the underlying theory and the corresponding implementation. We also demonstrate the superior performance by applying the method to the tunneling dynamics of bosonic ensembles in a one-dimensional double well potential, where a single-species bosonic ensemble of various correlation strengths and a weakly interacting two-species bosonic ensemble are considered.

#### Non-equilibrium quantum dynamics of ultra-cold atomic mixtures: the multi-layer multi-configuration time-dependent Hartree method for bosons

* S. Krönke, L. Cao, O. Vendrell, P. Schmelcher*

We develop and apply the multi-layer multi-configuration time-dependent Hartree method for bosons, which represents an ab initio method for investigating the non-equilibrium quantum dynamics of multi-species bosonic systems. Its multi-layer feature allows for tailoring the wave function ansatz to describe intra- and inter-species correlations accurately and efficiently. To demonstrate the beneficial scaling and efficiency of the method, we explored the correlated tunneling dynamics of two species with repulsive intra- and inter-species interactions, to which a third species with vanishing intra-species interaction was weakly coupled. The population imbalances of the first two species can feature a temporal equilibration and their time evolution significantly depends on the coupling to the third species. Bosons of the first and second species exhibit a bunching tendency, whose strength can be influenced by their coupling to the third species.

#### Two-component few-fermion mixtures in a one-dimensional trap: Numerical versus analytical approach

*I. Brouzos, P. Schmelcher*

We explore a few-fermion mixture consisting of two components that are repulsively interacting and confined in a one-dimensional harmonic trap. Different scenarios of population imbalance ranging from the completely imbalanced case where the physics of a single impurity in the Fermi sea is discussed to the partially imbalanced and equal population configurations are investigated. For the numerical calculations the multiconfigurational time-dependent Hartree method is employed, extending its application to few-fermion systems. Apart from numerical calculations we generalize our ansatz for a correlated pair wave function proposed recently [ I. Brouzos and P. Schmelcher Phys. Rev. Lett. 108 045301 (2012)] for bosons to mixtures of fermions. From weak to strong coupling between the components the energies, the densities and the correlation properties of one-dimensional systems change vastly with an upper limit set by fermionization where for infinite repulsion all fermions can be mapped to identical ones. The numerical and analytical treatments are in good agreement with respect to the description of this crossover. We show that for equal populations each pair of different component atoms splits into two single peaks in the density while for partial imbalance additional peaks and plateaus arise for very strong interaction strengths. The case of a single-impurity atom shows rich behavior of the energy and density as we approach fermionization and is directly connected to recent experiments [ G. Zürn et al. Phys. Rev. Lett. 108 075303 (2012)].

#### Controlled Excitation and Resonant Acceleration of Ultracold Few-Boson Systems by Driven Interactions in a Harmonic Trap

*I. Brouzos, P. Schmelcher*

### Project C8

#### Hydration shell effects in the relaxation dynamics of photoexcited Fe-II complexes in water

*P. Nalbach, A. J. A. Achner, M. Frey, M. Grosser, C. Bressler, M. Thorwart*

We study the relaxation dynamics of photoexcited Fe-II complexes dissolved in water and identify the relaxation pathway which the molecular complex follows in presence of a hydration shell of bound water at the interface between the complex and the solvent. Starting from a low-spin state, the photoexcited complex can reach the high-spin state via a cascade of different possible transitions involving electronic as well as vibrational relaxation processes. By numerically exact path integral calculations for the relaxational dynamics of a continuous solvent model, we find that the vibrational life times of the intermittent states are of the order of a few ps. Since the electronic rearrangement in the complex occurs on the time scale of about 100 fs, we find that the complex first rearranges itself in a high-spin and highly excited vibrational state, before it relaxes its energy to the solvent via vibrational relaxation transitions. By this, the relaxation pathway can be clearly identified. We find that the life time of the vibrational states increases with the size of the complex (within a spherical model), but decreases with the thickness of the hydration shell, indicating that the hydration shell acts as an additional source of fluctuations.

#### Photon-assisted confinement-induced resonances for ultracold atoms

*V. Leyton, M. Roghani, V. Peano, M. Thorwart*

We solve the two-particle s-wave scattering for an ultracold-atom gas confined in a quasi-one-dimensional trapping potential which is periodically modulated. The interaction between the atoms is included via Fermi’s pseudopotential. For a modulated isotropic transverse harmonic confinement, the atomic center of mass and relative degrees of freedom decouple and an exact solution is possible. The modulation opens additional photon-assisted resonant scattering channels. Applying the Bethe-Peierls boundary condition, we obtain the general scattering solution of the time-dependent Floquet-Schrödinger equation which is universal at low energies. The effective one-dimensional scattering length can be controlled by the external driving.

#### Quantification of non-Markovian effects in the Fenna-Matthews-Olson complex

*C. Mujica-Martinez, P. Nalbach, M. Thorwart*

The excitation energy transfer dynamics in the Fenna-Matthews-Olson complex is quantified in terms of a non-Markovianity measure based on the time evolution of the trace distance of two quantum states. We use a system description derived from experiments and different environmental fluctuation spectral functions, which are obtained either from experimental data or from molecular dynamics simulations. These exhibit, in all cases, a nontrivial structure with several peaks attributed to vibrational modes of the pigment-protein complex. Such a structured environmental spectrum can, in principle, give rise to strong non-Markovian effects. We present numerically exact real-time path-integral calculations for the transfer dynamics and find, in all cases, a monotonic decrease of the trace distance with increasing time which renders a Markovian description valid.

#### Nonequilibrium quantum fluctuation relations for harmonic systems in nonthermal environments

*D. Pagel, P. Nalbach, A. Alvermann, H. Fehske, M. Thorwart*

We formulate exact generalized nonequilibrium fluctuation relations for the quantum mechanical harmonic oscillator coupled to multiple harmonic baths. Each of the different baths is prepared in its own individual (in general nonthermal) state. Starting from the exact solution for the oscillator dynamics we study fluctuations of the oscillator position as well as of the energy current through the oscillator under general nonequilibrium conditions. In particular, we formulate a fluctuation–dissipation relation for the oscillator position autocorrelation function that generalizes the standard result for the case of a single bath at thermal equilibrium. Moreover, we show that the generating function for the position operator fulfils a generalized Gallavotti–Cohen-like relation. For the energy transfer through the oscillator, we determine the average energy current together with the current fluctuations. Finally, we discuss the generalization of the cumulant generating function for the energy transfer to nonthermal bath preparations.

#### Crossover from coherent to incoherent quantum dynamics due to sub-Ohmic dephasing

*P. Nalbach, M. Thorwart*

We report exact results for the influence of purely sub-Ohmic dephasing on the dynamics of a quantum two-level system. From response functions, we determine a crossover coupling strength between oscillatory coherent and overdamped dynamics. Surprisingly, we find no overdamping even at arbitrary large dephasing for spectra with spectral exponent.

#### Organic pi-conjugated copolymers as molecular charge qubits

*C. A. Mujica-Martinez, P. Nalbach, M. Thorwart*

We propose a design for molecular charge qubits based on π-conjugated block copolymers and determine their electronic structure as well as their vibrational active modes. By tuning the length of the oligomers, the tunnel coupling in the charge qubit and its decoherence properties due to molecular vibrations can be chemically engineered. Coherent oscillations result with quality factors of up to 104 at room temperature. In turn, the molecular vibrational spectrum induces strong non-Markovian electronic effects which support the survival of quantum coherence.

#### Noise-Induced Förster Resonant Energy Transfer between Orthogonal Dipoles in Photoexcited Molecules

* P. Nalbach, I. Pugliesi, H. Langhals, M. Thorwart*

#### Quantum noise properties of multiphoton transitions in driven nonlinear resonators

*V. Leyton, V. Peano, M. Thorwart*

We investigate the quantum noise properties of a weakly nonlinear Duffing resonator in the deep quantum regime, where only a few quanta are excited. This regime is dominated by the appearance of coherent multiphoton resonances in the nonlinear response of the resonator to the modulation. We determine simple expressions for the photon noise spectrum and find that the multiphoton resonances also induce a multiple peak structure in that spectrum. When the corresponding multiphoton Rabi oscillations are underdamped, zero-temperature quantum fluctuations determine comparable populations of all quasienergy states which belong to a resonant multiphoton doublet. Most interestingly, the quantum fluctuations probe the multiphoton transitions by inducing several peaks in the noise spectrum of the resonator observables. In particular, the noise of the photon number contains complete information about the multiphoton states and their stationary populations via pairs of nearly symmetric peaks at opposite frequencies. Their widths are determined by the damping of the Rabi oscillations and their heights are proportional to the stationary nonequilibrium populations. A finite detuning from a multiphoton resonance generates a quasielastic noise peak at zero frequency. In addition, we relate the stationary populations of the quasienergy states with an effective quantum temperature and discuss the role of a finite temperature.

### Project C9

#### Squeezed-field path-integral description of second sound in Bose-Einstein condensates

*Ilias M. H. Seifie, Vijay Pal Singh, and L. Mathey*

We propose a generalization of the Feynman path integral using squeezed coherent states. We apply thisapproach to the dynamics of Bose-Einstein condensates, which gives an effective low-energy descriptionthat contains both a coherent field and a squeezing field. We derive the classical trajectory of this action,which constitutes a generalization of the Gross-Pitaevskii equation, at linear order. We derive the low-energyexcitations, which provides a description of second sound in weakly interacting condensates as a squeezingoscillation of the order parameter. This interpretation is also supported by a comparison to a numerical c-fieldmethod.

#### Critical behavior of a chiral superfluid in a bipartite square lattice

*J. Okamoto, W.-M. Huang, R. Höppner and L. Mathey*

We study the critical behavior of Bose–Einstein condensation in the second band of a bipartite optical square lattice in a renormalization group framework at one-loop order. Within our field theoretical representation of the system, we approximate the system as a two-component Bose gas in three dimensions. We demonstrate that the system is in a different universality class than the previously studied condensation in a frustrated triangular lattice due to an additional Umklapp scattering term, which stabilizes the chiral superfluid order at low temperatures. We derive the renormalization group flow of the system and show that this order persists in the low energy limit. Furthermore, the renormalization flow suggests that the phase transition from the thermal phase to the chiral superfluid state is first order.

#### Influence of electron-phonon coupling on the low-temperature phases of metallic single-wall carbon nanotubes

*J. Okamoto, L. Mathey and W.-M. Huang*

We investigate the effect of electron-phonon coupling on low-temperature phases in metallic single-wall carbon nanotubes. We obtain low-temperature phase diagrams of armchair and zigzag type nanotubes with screened interactions with a weak-coupling renormalization group approach. In the absence of electron-phonon coupling, two types of nanotubes have similar phase diagrams. A D-Mott phase or d-wave superconductivity appears when the on-site interaction is dominant, while a charge-density wave or an excitonic insulator phase emerges when the nearest neighbor interaction becomes comparable to the on-site interaction. The electron-phonon coupling, treated by a two-cutoff scaling scheme, leads to different behavior in two types of nanotubes. For strong electron-phonon interactions, phonon softening is induced and a Peierls insulator phase appears in armchair nanotubes. We find that this softening of phonons may occur for any intraband scattering phonon mode. On the other hand, the effect of electron-phonon coupling is negligible for zigzag nanotubes. The distinct behavior of armchair and zigzag nanotubes against lattice distortion is explained by analysis of the renormalization group equations.

#### Light-induced coherence in an atom-cavity system

*C. Georges, J. G. Cosme, L. Mathey, A. Hemmerich*

We demonstrate a light-induced formation of coherence in a cold atomic gas system that utilizes the suppression of a competing density wave (DW) order. The condensed atoms are placed in an optical cavity and pumped by an external optical standing wave, which induces a long-range interaction mediated by photon scattering and a resulting DW order above a critical pump strength. We show that the light-induced temporal modulation of the pump wave can suppress this DW order and restore coherence. This establishes a foundational principle of dynamical control of competing orders analogous to a hypothesized mechanism for light-induced superconductivity in high*-T*_{c} cuprates.

#### Dynamics of Ultracold Quantum Gases in the Dissipative Fermi-Hubbard Model

* K. Sponselee, L. Freystatzky, B. Abeln, M. Diem, B. Hundt, A. Kochanke, T. Ponath, B. Santra, L. Mathey, K. Sengstock and C. Becker*

Abstract. We employ metastable ultracold 173-Yb atoms to study dynamics in the 1D dissipative Fermi-Hubbard model experimentally and theoretically, and observe a complete inhibition of two-body losses after initial fast transient dynamics. We attribute the suppression of particle loss to the dynamical generation of a highly entangled Dicke state. For several lattice depths and for two- and six-spin component mixtures we find very similar dynamics, showing that the creation of strongly correlated states is a robust and universal phenomenon. This offers interesting opportunities for precision measurements.

arXiv:1805.11853 (2018)

https://arxiv.org/abs/1805.11853

https://iopscience.iop.org/article/10.1088/2058-9565/aadccd/meta

#### Fermion pairing in mixed-dimensional atomic mixtures

*Junichi Okamoto,1,2 Ludwig Mathey,1,2 and Wen-Min Huang*

We investigate the quantum phases of mixed-dimensional cold atom mixtures. In particular, we consider a mixture of a Fermi gas in a two-dimensional lattice, interacting with a bulk Fermi gas or a Bose-Einstein condensate in a three-dimensional lattice. The effective interaction of the two-dimensional system mediated by the bulk system is determined. We perform a functional renormalization group analysis, and demonstrate that by tuning the properties of the bulk system, a subtle competition of several superconducting orders can be controlled among *s*−wave, *p*−wave, *d _{x2−y2}*−wave, and

*g*−wave pairing symmetries. Other instabilities such as a charge-density-wave order are also demonstrated to occur. In particular, we find that the critical temperature of the

_{xy(x2−y2)}*d*−wave pairing induced by the next-nearest-neighbor interactions can be an order of magnitude larger than that of the same pairing induced by doping in the simple Hubbard model. We expect that by combining the nearest-neighbor interaction with the next-nearest-neighbor hopping (known to enhance

*d*−wave pairing), an even higher critical temperature may be achieved

#### Dynamic Kosterlitz-Thouless transition in two-dimensional Bose mixtures of ultracold atoms

*L. Mathey, Kenneth J. Günter, Jean Dalibard, and A. Polkovnikov*

We propose a realistic experiment to demonstrate a dynamic Kosterlitz-Thouless transition in ultracold atomic gases in two dimensions. With a numerical implementation of the truncated Wigner approximation we simulate the time evolution of several correlation functions, which can be measured via matter wave interference. We demonstrate that the relaxational dynamics is well described by a real-time renormalization-group approach and argue that these experiments can guide the development of a theoretical framework for the understanding of critical dynamics.

#### Observation of Topological Bloch-State Defects and Their Merging Transition

*Matthias Tarnowski, Marlon Nuske, Nick Fläschner, Benno Rem, Dominik Vogel, Lukas Freystatzky, Klaus Sengstock, Ludwig Mathey, and Christof Weitenberg*

Topological defects in Bloch bands, such as Dirac points in graphene, and their resulting Berry phases play an important role for the electronic dynamics in solid state crystals. Such defects can arise in systems with a two-atomic basis due to the momentum-dependent coupling of the two sublattice states, which gives rise to a pseudospin texture. The topological defects appear as vortices in the azimuthal phase of this pseudospin texture. Here, we demonstrate a complete measurement of the azimuthal phase in a hexagonal optical lattice employing a versatile method based on time-of-flight imaging after off-resonant lattice modulation. Furthermore, we map out the merging transition of the two Dirac points induced by beam imbalance. Our work paves the way to accessing geometric properties in optical lattices also with spin-orbit coupling and interactions.

#### Implementing supersymmetric dynamics in ultracold-atom systems

*M. Lahrz, C. Weitenberg, L. Mathey*

Supersymmetric systems derive their properties from conserved supercharges which form a supersymmetric algebra. These systems naturally factorize into two subsystems, which, when considered as individual systems, have essentially the same eigenenergies, and their eigenstates can be mapped onto each other. We propose a Mach-Zehnder interference experiment to detect supersymmetry in quantum-mechanical systems, which can be realized with current technology. To demonstrate this interferometric technique, we first propose a one-dimensional ultracold-atom setup to realize a pair of supersymmetric systems. Here, a single-atom wave packet evolves in a superposition of the subsystems and gives an interference contrast that is sharply peaked if the subsystems form a supersymmetric pair. Second, we propose a two-dimensional setup that implements supersymmetric dynamics in a synthetic gauge field.

#### Emergence in Driven Solid-State and Cold-Atom Systems

*L. Mathey, J. Okamoto*

While phase transitions in equilibrium systems have been studied extensively, the emergence of order in non-equilibrium systems, such as periodically driven systems, continues to pose conceptual questions as well as offer intriguing possibilities. In particular, two recent experimental developments emphasise the urgency of further exploration. A new direction of research is taking place in the field of ultra-cold atoms. In a recent set of experiments, atoms in an optical lattice were subjected to a lattice shaking protocol. With this new feature of ultra-cold atom systems, it has been possible to create effective, renormalised Hamiltonians. In particular, the lattice shaking could be performed in such a manner to create frustrated systems and synthetic gauge fields, see e.g. [1]. A parallel development is taking place in solid state physics. A new research direction was established by using ultrafast light pulses to stabilise superconducting order. Here, the periodic driving was used to achieve a remarkable, counterintuitive result: to enhance superconductivity with high frequency and high intensity driving, see e.g

#### Sudden and slow quenches into the antiferromagnetic phase of ultracold fermions

*M. Ojekhile, R. Höppner, H. Moritz, L. Mathey*

We propose a method to reach the antiferromagnetic state of two-dimensional Fermi gases trapped in optical lattices: Independent subsystems are prepared in suitable initial states and then connected by a sudden or slow quench of the tunneling between the subsystems. Examples of suitable low-entropy subsystems are double wells or plaquettes, which can be experimentally realised in Mott insulating shells using optical super-lattices. We estimate the effective temperature T* of the system after the quench by calculating the distribution of excitations created using the spin wave approximation in a Heisenberg model. We investigate the effect of an initial staggered magnetic field and find that for an optimal polarisation of the initial state the effective temperature can be significantly reduced from T*≈1.7 Tc at zero polarisation to T*<0.65Tc, where Tc is the crossover temperature to the antiferromagnetic state. The temperature can be further reduced using a finite quench time. We also show that T* decreases logarithmically with the linear size of the subsystem.

#### Hierarchical equations of motion approach to transport through an Anderson impurity coupled to interacting Luttinger liquid leads

*Jun-ichi Okamoto, Ludwig Mathey, and Rainer Härtle*

We generalize the hierarchical equations of motion method to study electron transport through a quantum dot or molecule coupled to one-dimensional interacting leads that can be described as Luttinger liquids. Such leads can be realized, for example, by quantum wires or fractional quantum Hall edge states. In comparison to noninteracting metallic leads, Luttinger liquid leads involve many-body correlations and the single-particle tunneling density of states shows a power-law singularity at the chemical potential. Using the generalized hierarchical equations of motion method, we assess the importance of the singularity and the next-to-leading order many-body correlations. To this end, we compare numerically converged results with second- and first-order results of the hybridization expansion that is inherent to our method. As a test case, we study transport through a single-level quantum dot or molecule that can be described by an Anderson impurity model. Cotunneling effects turn out to be most pronounced for attractive interactions in the leads or repulsive ones if an excitonic coupling between the dot and the leads is realized. We also find that an interaction-induced negative differential conductance near the Coulomb blockade thresholds is slightly suppressed as compared to a first-order and/or rate equation result. Moreover, we find that the two-particle (*n*-particle) correlations enter as a second-order (*n*-order) effect and are, thus, not very pronounced at the high temperatures and parameters that we consider.

#### Bose-Einstein condensation in a frustrated triangular optical lattice

*Peter Janzen, Wen-Min Huang, and L. Mathey*

The recent experimental condensation of ultracold atoms in a triangular optical lattice with a negative effective tunneling parameter paves the way for the study of frustrated systems in a controlled environment. Here, we explore the critical behavior of the chiral phase transition in such a frustrated lattice in three dimensions. We represent the low-energy action of the lattice system as a two-component Bose gas corresponding to the two minima of the dispersion. The contact repulsion between the bosons separates into intra- and intercomponent interactions, referred to as V0 and V12, respectively. We first employ a Huang-Yang-Luttinger approximation of the free energy. For V12/V0=2, which corresponds to the bare interaction, this approach suggests a first-order phase transition, at which both the U(1) symmetry of condensation and the Z2 symmetry of the emergent chiral order are broken simultaneously. Furthermore, we perform a renormalization-group calculation at one-loop order. We demonstrate that the coupling regime 0<V12/V0≤1 shares the critical behavior of the Heisenberg fixed point at V12/V0=1. For V12/V0>1 we show that V0 flows to a negative value, while V12 increases and remains positive. This results in a breakdown of the effective quartic-field theory due to a cubic anisotropy and, again, suggests a discontinuous phase transition.

#### Realizing and optimizing an atomtronic SQUID

*A. C. Mathey, L. Mathey*

We demonstrate how a toroidal Bose–Einstein condensate with a movable barrier can be used to realize an atomtronic SQUID. The magnitude of the barrier height, which creates the analogue of an SNS junction, is of crucial importance, as well as its ramp-up and -down protocol. For too low of a barrier, the relaxation of the system is dynamically suppressed, due to the small rate of phase slips at the barrier. For a higher barrier, the phase coherence across the barrier is suppressed due to thermal fluctuations, which are included in our Truncated Wigner approach. Furthermore, we show that the ramp-up protocol of the barrier can be improved by ramping up its height first, and its velocity after that. This protocol can be further improved by optimizing the ramp-up and ramp-down time scales, which is of direct practical relevance for on-going experimental realizations.

#### Probing superfluidity of Bose-Einstein condensates via laser stirring

*Vijay Pal Singh, Wolf Weimer, Kai Morgener, Jonas Siegl, Klaus Hueck, Niclas Luick, Henning Moritz, Ludwig Mathey*

We investigate the superfluid behavior of a Bose-Einstein condensate of 6Li molecules. In the experiment by Weimer et al., Phys. Rev. Lett. 114, 095301 (2015) a condensate is stirred by a weak, red-detuned laser beam along a circular path around the trap center. The rate of induced heating increases steeply above a velocity vc, which we define as the critical velocity. Below this velocity, the moving beam creates almost no heating. In this paper, we demonstrate a quantitative understanding of the critical velocity. Using both numerical and analytical methods, we identify the non-zero temperature, the circular motion of the stirrer, and the density profile of the cloud as key factors influencing the magnitude of vc. A direct comparison to the experimental data shows excellent agreement.

Phys. Rev. A 93, 023634 (2016)

http://lanl.arxiv.org/abs/1509.02168

#### Theory of enhanced interlayer tunneling in optically driven high Tc superconductors

*J. Okamoto, A. Cavalleri, L. Mathey*

Motivated by recent pump-probe experiments indicating enhanced coherent c-axis transport in underdoped YBCO, we study Josephson junctions periodically driven by optical pulses. We propose a mechanism for this observation by demonstrating that a parametrically driven Josephson junction shows an enhanced imaginary part of the low-frequency conductivity when the driving frequency is above the plasma frequency, implying an effectively enhanced Josephson coupling. We generalize this analysis to a bilayer system of Josephson junctions modeling YBCO. Again, the Josephson coupling is enhanced when the pump frequency is blue-detuned to either of the two plasma frequencies of the material. We show that the emergent driven state is a genuine, non-equilibrium superconducting state, in which equilibrium relations between the Josephson coupling, current fluctuations, and the critical current no longer hold.

#### Magnus expansion approach to parametric oscillator systems in a thermal bath

*B. Zhu, T. Rexin, L. Mathey*

We develop a Magnus formalism for periodically driven systems which provides an expansion both in the driving term and the inverse driving frequency, applicable to isolated and dissipative systems. We derive explicit formulas for a driving term with a cosine dependence on time, up to fourth order. We apply these to the steady state of a classical parametric oscillator coupled to a thermal bath, which we solve numerically for comparison. Beyond dynamical stabilization at second order, we find that the higher orders further renormalize the oscillator frequency, and additionally create a weakly renormalized effective temperature. The renormalized oscillator frequency is quantitatively accurate almost up to the parametric instability, as we confirm numerically. Additionally, a cut-off dependent term is generated, which indicates the break-down of the hierarchy of time scales of the system, as a precursor to the instability. Finally, we apply this formalism to a parametrically driven chain, as an example for the control of the dispersion of a many-body system.

arXiv:1604.01010

http://arxiv.org/abs/1604.01010

* *

#### Sudden-quench dynamics of Bardeen-Cooper-Schrieffer states in deep optical lattices

*Marlon Nuske, L. Mathey, Eite Tiesinga*

We determine the exact dynamics of an initial Bardeen-Cooper-Schrieffer (BCS) state of ultracold atoms in a deep hexagonal optical lattice. The dynamical evolution is triggered by a quench of the lattice potential such that the interaction strength Uf is much larger than the hopping amplitude Jf. The quench initiates collective oscillations with frequency ∣∣Uf|/2π in the momentum occupation numbers and imprints an oscillating phase with the same frequency on the BCS order parameter Δ. The oscillation frequency of Δ is not reproduced by treating the time evolution in mean-field theory. In our theory, the momentum noise (i.e., density-density) correlation functions oscillate at frequency ∣∣Uf|/2π as well as at its second harmonic. For a very deep lattice, with zero tunneling energy, the oscillations of momentum occupation numbers are undamped. Nonzero tunneling after the quench leads to dephasing of the different momentum modes and a subsequent damping of the oscillations. The damping occurs even for a finite-temperature initial BCS state, but not for a noninteracting Fermi gas. Furthermore, damping is stronger for larger order parameter and may therefore be used as a signature of the BCS state. Finally, our theory shows that the noise correlation functions in a honeycomb lattice will develop strong anticorrelations near the Dirac point.

#### Dynamical phase transition in the open Dicke model

*J. Klinder, H. Keßler, M. Wolke, L. Mathey, A. Hemmerich*

The Dicke model with a weak dissipation channel is realized by coupling a Bose–Einstein condensate to an optical cavity with ultranarrow bandwidth. We explore the dynamical critical properties of the Hepp–Lieb–Dicke phase transition by performing quenches across the phase boundary. We observe hysteresis in the transition between a homogeneous phase and a self-organized collective phase with an enclosed loop area showing power-law scaling with respect to the quench time, which suggests an interpretation within a general framework introduced by Kibble and Zurek. The observed hysteretic dynamics is well reproduced by numerically solving the mean-field equation derived from a generalized Dicke Hamiltonian. Our work promotes the understanding of nonequilibrium physics in open many-body systems with infinite range interactions.

#### The critical velocity in the BEC-BCS crossover

* W. Weimer, K. Morgener, V. P. Singh, J. Siegl, K. Hueck, N. Luick, L. Mathey, H. Moritz*

We map out the critical velocity in the crossover from Bose-Einstein condensation (BEC) to Bardeen-Cooper-Schrieffer superfluidity with ultracold 6Li gases. A small attractive potential is dragged along lines of constant column density. The rate of the induced heating increases steeply above a critical velocity vc. In the same samples, we measure the speed of sound vs by exciting density waves and compare the results to the measured values of vc. We perform numerical simulations in the BEC regime and find very good agreement, validating the approach. In the strongly correlated regime, where theoretical predictions only exist for the speed of sound, our measurements of vc provide a testing ground for theoretical approaches.

Phys. Rev. Lett. 114, 095301 (2015)

http://arxiv.org/abs/1408.5239

#### Observation of chiral superfluid order by matter wave interference

* T. Kock, M. Ölschläger, A. Ewerbeck, W.-M. Huang, L. Mathey, A. Hemmerich*

The breaking of time reversal symmetry via the spontaneous formation of chiral order is ubiquitous in nature. Here, we present an unambiguous demonstration of this phenomenon for atoms Bose-Einstein condensed in the second Bloch band of an optical lattice. As a key tool we use a matter wave interference technique, which lets us directly observe the phase properties of the superfluid order parameter and allows us to reconstruct the spatial geometry of certain low energy excitations, associated with the formation of domains of different chirality. Our work marks a new era of optical lattices where orbital degrees of freedom play an essential role for the formation of exotic quantum matter, similarly as in electronic systems.

Physical Review Letters 114, 115301 (2015)

http://arxiv.org/abs/1411.3483

#### Redistribution of phase fluctuations in a periodically driven cuprate superconductor

*R. Höppner, B. Zhu, T. Rexin, A. Cavalleri, and L. Mathey*

We study the thermally fluctuating state of a bilayer cuprate superconductor under the periodic action of a staggered field oscillating at optical frequencies. This analysis distills essential elements of the recently discovered phenomenon of light-enhanced coherence in YBa_{2}Cu_{3}O_{6+x}, which was achieved by periodically driving infrared active apical oxygen distortions. The effect of a staggered periodic perturbation is studied using a Langevin and Fokker-Planck description of driven, coupled Josephson junctions, which represent two neighboring pairs of layers and their two plasmons. In a toy model including only two junctions, we demonstrate that the external driving leads to a suppression of phase fluctuations of the low-energy plasmon, an effect which is amplified via the resonance of the high-energy plasmon. When extending the modeling to the full layers, we find that this reduction becomes far more pronounced, with a striking suppression of the low-energy fluctuations, as visible in the power spectrum. We also find that this effect acts on the in-plane fluctuations, which are reduced on long length scales. All these findings provide a physical framework to describe light control in cuprates.

#### Noise correlations of two-dimensional Bose gases

*V. P. Singh, L. Mathey*

We analyze density-density correlations of expanding clouds of weakly interacting two-dimensional Bose gases below and above the Berezinskii-Kosterlitz-Thouless transition, with particular focus on short-time expansions. During time-of-flight expansion, phase fluctuations of the trapped system translate into density fluctuations, in addition to the density fluctuations that exist in situ. We calculate the correlations of these fluctuations both in real space and in momentum space and derive analytic expressions in momentum space. Below the transition, the correlation functions show an oscillatory behavior, controlled by the scaling exponent of the quasicondensed phase, due to constructive interference. We argue that this can be used to extract the scaling exponent of the quasicondensate experimentally. Above the transition, the interference is rapidly suppressed when the atoms travel an average distance beyond the correlation length. This can be used to distinguish the two phases qualitatively.

#### Quantum Phases of quadrupolar Fermi gases in optical lattices

*S. G. Bhongale, L. Mathey, E. Zhao, S. F. Yelin, M. Lemeshko*

We introduce a new platform for quantum simulation of many-body systems based on non-spherical particles with zero dipole moment but possessing a significant value of the electric quadrupole moment. Considering a quadrupolar quantum gas trapped in a 2D optical lattice, we show that the peculiar symmetry and broad tunability of the quadrupole-quadrupole interactions results in a rich phase diagram encompassing unconventional BCS and charge density wave phases, and paves the way to create topological superfluid ground states of px + i py symmetry. Quadrupolar species, such as metastable alkaline-earth atoms and homonuclear molecules, are stable against chemical reactions and collapse and are readily available in experiment at high densities.

Phys. Rev. Lett. 110, 155301 (2013)

http://arxiv.org/abs/1211.3317

#### Unconventional Spin Density Waves in Dipolar Fermi Gases

*S. G. Bhongale, L. Mathey, S. Tsai, C. W. Clark, E. Zhao*

The conventional spin density wave (SDW) phase (Overhauser, 1962), as found in antiferromagnetic metal for example (Fawcett 1988), can be described as a condensate of particle-hole pairs with zero angular momentum, $\ell=0$, analogous to a condensate of particle-particle pairs in conventional superconductors. While many unconventional superconductors with Cooper pairs of finite $\ell$ have been discovered, their counterparts, density waves with non-zero angular momenta, have only been hypothesized in two-dimensional electron systems (Nayak, 2000). Using an unbiased functional renormalization group analysis, we here show that spin-triplet particle-hole condensates with $\ell=1$ emerge generically in dipolar Fermi gases of atoms (Lu, Burdick, and Lev, 2012) or molecules (Ospelkaus et al., 2008; Wu et al.) on optical lattice. The order parameter of these exotic SDWs is a vector quantity in spin space, and, moreover, is defined on lattice bonds rather than on lattice sites. We determine the rich quantum phase diagram of dipolar fermions at half-filling as a function of the dipolar orientation, and discuss how these SDWs arise amidst competition with superfluid and charge density wave phases.

Phys. Rev. A 87, 043604 (2012)

http://arxiv.org/abs/1209.2671

#### Decay of a superfluid current of ultra-cold atoms in a toroidal trap

*Amy C. Mathey, Charles W. Clark, L. Mathey*

Using a numerical implementation of the truncated Wigner approximation, we simulate the experiment reported by Ramanathan et al. in Phys. Rev. Lett. 106, 130401 (2011), in which a Bose-Einstein condensate is created in a toroidal trap and set into rotation via a Gauss-Laguerre beam. A potential barrier is then placed in the trap to study the decay of the superflow. We find that the current decays via thermally activated phase slips, which can also be visualized as vortices crossing the barrier region in radial direction. Adopting the notion of critical velocity used in the experiment, we determine it to be lower than the local speed of sound at the barrier. This result is in agreement with the experimental findings, but in contradiction to the predictions of the Gross-Pitaevskii equation. This emphasizes the importance of thermal fluctuations in the experiment.