Atomic Physics 2022

Generic closed quantum many-body systems (QMS) equilibrate, and as a consequence, expectation value of observables become constant after the relaxation time. Recently, it was shown that a class of dissipations can be engineered such that decoherence-free subspaces (DFSs) exist [Buca et al., Nature Communications 10, 1730 (2019)]. As a result, observables can exhibit persistent oscillations on timescales much longer than the relaxation timescale. Those oscillations and DFSs may play a central role in storage and retrieval processes of quantum information by diminishing decoherence and loss of information of the QMS. We will present general conditions under which DFSs occurs. In the first part, we show how we can take advantage of symmetries of the QMS for constructing dissipations leading to DFSs. We develop an efficient method based on classical canonical transformations and provide an intuitive picture of the DFS and this class of dissipations. In the second part, we show that there is another class of dissipations, which plays a much more active role for DFSs. Hereby, the DFSs represent quantum attractors and the configuration of the QMS, almost independent of the initialization, moves towards the persistent oscillation regime. It behaves as a quantum limit cycle.

We employ a three-dimensional semiclassical model to study triple ionization in Ne driven by infrared laser pulses at intensities where electron-electron correlation prevails. This model fully accounts for the Coulomb interaction of each electron with the core. It employs effective Coulomb potentials to describe the interaction between bound electrons (ECBB). Using the ECBB model, we obtain triple ionization observables, such as distributions of the sum of the final electron momenta along the direction of the electric field. These observables are in very good agreement with experiments. Also, we identify nondipole effects in three-electron escape. To do so, we fully account for the magnetic field component of the Lorentz force on all four moving particles, the three electrons and the core. We show that the magnetic field jointly with a recollision create a gate for triple and double ionization. Hence, we show that nondipole gated ionization underlies multielectron escape. The hallmark of this mechanism is a large average sum of the final electron momenta along the direction of light propagation, while this sum is zero in the dipole approximation. We demonstrate that this final electron momentum offset probes the degree of correlation in multielectron escape.

It is shown that the vibrational energy of a molecule can be transferred to the electronic motion of a distant neighboring atom or molecule. It is discussed whether such a process can be efficient. In this work we investigate the possibility of intermolecular vibrational energy transfer to electronic motion. Energy transfer of all kinds is of central importance for chemical reactivity and has been widely studied both experimentally and theoretically over many years including the transfer between the two kinds of energies, vibrational and electronic. The studies of the latter are, however, carried out in the framework of collisions where the collision complex formed and/or nonadiabatic coupling give rise to the transfer. Here, we concentrate on intermolecular vibrational energy transfer to electronic motion in weakly bound molecules, i.e., at internuclear distances at which they do not have a chemical bond and nonadiabatic coupling is negligible. We shall see that the transfer can be highly efficient. If time is left, intermolecular vibrational energy transfer between weakly bound molecules is also addressed. Here, most of the studies were done for describing resonant vibrational energy transfer in the condensed phase. Very recently, it has been noticed that if the lifetime of the vibrationally excited molecule is much longer than that of its neighbor, efficient non-resonant vibrational energy transfer can take place. References L.S. Cederbaum, PRL 121,223001 (2018); L.S. Cederbaum, Mol. Phy. 117,1950 (2019)

Oscillations in the probability density of quantum transitions of the eigenstates of a chaotic Hamiltonian within classically narrow energy ranges depend on closed compound orbits. These are formed by a pair of orbit segments, one in the energy shell of the original Hamiltonian and the other in the energy shell of the driven Hamiltonian, with endpoints which coincide. Viewed in the time domain, the same pair of trajectory segments arises in the semiclassical evaluation of the trace of a compound propagator: the product of the complex exponentials of the original Hamiltonian and of its driven image. The probability density is the double Fourier transform of this trace, so that the closed compound orbits emulate the role played by periodic orbits in Gutzwiller's trace formula in its semiclassical evaluation. The phase and the amplitude of the oscillations of the contribution of the closed compound orbits, with the energies or evolution parameters, do not dependend of any feature of the Weyl-Wigner representation in which the calculation was carried out.

Molecular chirality -- the fact that a chiral molecule cannot be superimposed with its mirror image by rotations and translations -- is as ubiquitous as it is intriguing. The left-handed and right-handed versions of a chiral molecule share almost all of their physical properties. Yet, the chemical and biological behavior of the two enantiomers typically differs dramatically. Detection of chirality and the ability to separate enantiomers therefore play a central role across the natural sciences. As physicists, we would ideally like to use electromagnetic fields to this end. When exciting chiral molecules with electric fields, chirality can be detected via vector observables. I will discuss how quantum control, i.e., the constructive and destructive interference between different excitation pathways, allows for enhancing chiral vector observables, all the way to complete enanantiomer-selective excitation.

Ultracold atomic quantum gases possess very many interesting properties and are promising candidates for quantum-technology applications, including atomic clocks, analog quantum simulators, quantum sensors, or even quantum computers. In most cases the experiments are (necessarily) performed using atoms in some trap, may it be a magneto-optical trap, an optical lattice, or an optical tweezer (array). Consequently, the influence of the trap needs to be known very accurately. In fact, besides trap-induced corrections to, e.g., the position of magnetic Feshbach resonances that in turn are the standard tool for manipulating the atom-atom interaction, there are novel resonances that are purely caused by the trap confinement. After an overview of these confinement-induced resonances, very recent results of a mixed experimental and theoretical work will be presented.

Attosecond time-resolved spectroscopy combined with electron-ion coincidence detection is opening many interesting perspectives. I will discuss how this technique has enabled the measurement of photoionization delays of fully size-resolved water clusters [1]. These delays suggest the existence of a linear relationship between the photoionization delays and the effective radius of the electron hole created during photoionization [1]. These results are also consistent with the interpretation of our previous measurements on the photoionization delays of liquid water [2]. Extending this technique from water clusters to van-der-Waals clusters, we have observed the signature of two-center interference in the relative delays of Kr2 vs. Kr, made possible by the simultaneous detection of both types of signals [3]. Finally, I will present some very recent results on the generation of circularly polarized attosecond pulses and their complete characterization. Applied to the two-color photoionization of atoms, circularly polarized attosecond pulses have been found to create photoelectron vortices. These electron-vortex beams display a very strong circular dichroism, both in the amplitude (up to 35%) and in the time delays (up to 250 as) of their continuum-continuum transitions [4]. References [1] X. Gong, S. Heck et al., Nature 609, 507 (2022) [2] I. Jordan et al., Science 369, 974 (2020) [3] S. Heck, M. Han et al., PRL 129, 133002 (2022) [4] M. Han et al., Nature Physics, in press (2022)

Exciton migration in self-assembled supramolecular structures of organic molecules is controlled by the packing arrangement that imprints on the electronic coupling and the delocalization of excitations. In the recent years, we examined the exciton mobility on multiple supramolecular structures consisting of perylene bisimide dyes, ranging from disordered targets with monomeric character to extended 1D systems like a sting of pearls or more complex structures like winded spirals with J-type excitonic coupling. After a brief introduction on the characterization of the supramolecular structures I will focus on the determination of their exciton diffusion properties. Thereto, we monitor exciton diffusion by the annihilation of the excitons, as can be observed in excitation power dependent ultrafast transient absorption measurements. To enter the annihilation regime much higher pump powers are used than in conventional time resolved measurements, we for instance analyze measurements where up to 10% of the molecules are excited, which leads to fast depopulation due to strong exciton-exciton-interactions. We find reduced exciton mobility for disordered monomeric systems, which we understand quantitatively and can trace it back to the amount of inhomogeneous broadening. In case of the supramolecular structures, we identified certain packing motifs that reduce migration. In case these motifs are circumvented the Frenkel excitons can migrate of up to 190 nm in 1D.

Quantum mechanical description of excited state evolution of molecules and their complexes is complex since it involves mixing of electronic and vibrational degrees of freedom. Time dependent variational principle (TDVP) approach allows systematic description of the excited state evolution at a chosen level of complexity. The method then allows including intramolecular vibrations as well as intermolecular phonons, quantum relaxation in excited state manifold. Numerical simulation can be inspected by laser spectroscopy. Application of this theory to spectroscopy of J and H aggregates demonstrates that quite simple so-called D2 theory can be used to describe J aggregate absorption and flourescence spectral lineshapes at high accuracy. Much more complex theory level is required to decribe H aggregates. Additionally, properties, like zero-phonon-line (ZPL) temperature-induced shift and broadening as well as local bath cooling can be introduced by using phonon scattering techniques in conjunction with TDVP.

Neutral atoms trapped in optical lattices are a versatile platform to study many-body physics in and out of equilibrium. Quantum gas microscopes provide an excellent toolbox to prepare, control and detect such systems at the level of individual particles. In our experimental apparatus, we operate a quantum gas microscope for bosonic rubidium atoms. Using a direct mapping between two-component Bose-Hubbard model and the Heisenberg model, we study spin dynamics out of equilibrium. Our microscopic detection sheds light on the nature of transport in one-dimensional spin chains, which we find to fall into the celebrated Kardar-Parisi-Zhang universality class. Furthermore, by controlled coupling to highly excited Rydberg states, we can engineer long-range interactions in our experiment. Employing coupling to molecular bound states between two Rydberg atoms, we realize exotic distance-selective interactions and probe their characteristics using a many-body Ramsey scheme. Our results raise several interesting questions for future research, reaching from the exploration of the impact of different initial states on transport dynamics to the utilization of long-range Rydberg interactions to realize extended Hubbard models.

It is assumed that Wigner-Smith (WS) time delays, known from scattering theory, can be determined by measuring streaking shifts. Despite their wide use from atoms to solids this has never been proven. Analyzing the underlying process, energy absorption from the streaking light, we show that streaking time delays become independent of the properties of the streaking laser and approach the WS time delay of short-range potentials for sufficiently weak streaking fields and in the limit of small frequencies or long wavelengths. Further, we discuss properly-defined WS time delays for anisotropic potentials as in molecules.

The function of essentially all present and future quantum devices, from quantum computers over quantum sensors to photocatalytic systems or solar cells, relies on the transport of energy, charges and spins on ultrafast time (femtoseconds) and exceedingly short length scales (nanometers). Usually, these dynamics are governed by such a complex interplay between electronic and nuclear motion that is challenging to visualize them. Our understanding is therefore quite limited and we often rely on oversimplified, particle-like transport models for describing dynamics and function on the nanoscale. In my talk, I will introduce and discuss several systems in which this classical, particle-like transport regime breaks down and the wave-like coherent transport of energy and charge becomes dominant, even in disordered nanostructures and at room temperature [1-4]. I will report on an exceptionally powerful, emerging experimental technique, two-dimensional electronic spectroscopy [5], for probing such transport processes. Specifically, I will describe what 2DES can tell us about coherent couplings between excitons and surface plasmon polaritons, the elementary optical excitations of a large class of artificially designed nanostructures comprising metals and semiconductors. By improving the time resolution and sensitivity in 2DES, we resolve coherent energy exchange (strong coupling) and two-particle excitations in such hybrid systems for the first time. The experiments illustrate a conceptually new approach for understanding how nanostructures “talk to each other”. References [1] S. M. Falke et al., Science 344, 1001 (2014). [2] A. De Sio et al., Nature Commun. 7, 13742 (2016). [3] J. H. Zhong et al., Nature Commun. 11, 1 (2020) [4] P. Dombi et al., Reviews of Modern Physics 92, 025003 (2020) [5] A. De Sio et al., Nature Nanotechnology 16, 63 (2021).

Exploration of fundamental photophysical phenomena at the level of individual quantum objects requires highly specialized optical spectroscopy with ultrahigh spatial resolution, and single-photon capabilities. Recent progress achieved with light spectromicroscopy in plasmonic nanocavities opened the path to investigation of individual excited molecules with unprecedented detail. We integrate photon-detection schemes with a 4K STM, AFM instrumentation and establish a dedicated theoretical support, which allows us to precisely control and measure excited states (excitons) in individual dye molecules with well-defined adsorption geometries on solid crystalline surface at nanoscopic level. The photons emitted from the molecules carry information about the energies, charges, vibronics and temporal evolution of the transient states, and could thus reveal fundamental mechanisms affecting the excitons and the single-photon generation processes. We address exciton delocalization over aggregates of charged chromophores, where the exciton coupling mechanism is identified through an accurate determination of the aggregate geometry via AFM and by comparison of photon maps of excitonic eigenmodes with their theoretical models. Finally, tip-enhanced Raman spectroscopy is performed on the well-known molecular junction with PTCDA in which the charge and spin state can be controlled via controlled mechanical manipulation. References 1. Charge carrier injection electroluminescence with CO functionalized tips on single molecular emitters. J Doležal, P Merino, J Redondo, L Ondič, A Cahlík and M Švec, Nano letters 19, 8605-861, 2019 2. Mechano-Optical Switching of a Single Molecule with Doublet Emission. J Doležal, P Mutombo, D Nachtigallová, P Jelínek, P Merino and M Švec, ACS Nano 14, 8931-8938, 2020 3. Exciton-Trion Conversion Dynamics in a Single Molecule. J Doležal, S Canola, P Merino and M Švec, ACS Nano 15, 7694–7699, 2021 4. Evidence of trion-libron coupling in chirally adsorbed single molecules. J Doležal, S Canola, P Hapala, RCC Ferreira, P Merino, M Švec, arXiv preprint arXiv:2203.04077

Similar to ordinary space crystals, crystal structures can also form spontaneously in time. It turns out that the condensed matter phases, such as the Andreson and many-body localization, topological phases, Mott insulator and superfluid phases, can also be observed in the time domain. In the course of the lecture, I will introduce the concept of time crystals and show how various behaviors resembling condensed matter can be realized in time. [1] K. Sacha, "Time Crystals", Springer International Publishing, Cham 2020.

We show that the recently observed class of long-range ion-Rydberg molecules can be divided into two families of states, which are characterised by their unique electronic structures resulting from the ion-induced admixture of quantum defect split Rydberg $nP$ states with different low-field seeking high-$l$ states. We predict that in both cases these diatomic molecular states can bind additional ground state atoms lying within the orbit of the Rydberg electron, forming charged ultralong-range Rydberg molecules (ULRM) with binding energies similar to that of conventional non-polar ULRM. To demonstrate this, we consider a Rydberg atom interacting with a single ground state atom and an ion. The additional atom breaks the system's cylindrical symmetry, which leads to mixing between states that would otherwise be decoupled. The electronic structure is obtained using exact diagonalisation over a finite basis and the vibrational structure is calculated using the Multi-Configuration Time-Dependent Hartree method. Due to the lobe-like structure of the electronic density, bound trimers with both linear and nonlinear geometrical configurations of the three nuclei are possible. The predicted trimer binding energies and excitation series are distinct enough from those of the ion-Rydberg dimer to be observed using current experimental techniques.

We solve the Schrödinger equation for benzene by expanding the wave function in a linear combination of ground-state Kohn-Sham orbitals. Those have been calculated previously via ground-state density functional theory. This method is orders of magnitude faster than comparable full time-dependent density functional theory simulations but neglects the update of the Hartree-exchange-correlation potential during time evolution. Our simulation is able to describe the qualitative properties of the harmonic spectrum. The $n=6N \pm 1$ selection rules stemming from the 6-fold symmetry of the benzene molecule as well as the opposite polarization of each harmonic couple are observed. We evaluate the performance of different density functional theory basis sets and examine how well the continuum is represented in the test case of hydrogen in a linearly polarized laser field.

Knowing the intrinsic aspects of few-body systems, e.g. binding energies, lifetimes etc, it is always desirable since they dictate the macroscopic properties of a gas. On a two-body level there are well-established dynamical protocols addressing their attributes, however, this is not the case for three-body systems. This talk presents a novel way to dynamically probe such systems. In particular, we consider three bosons subjected to a double sequence of magnetic field pulses. This Ramsey-like protocol, i.e. wiggle interferometry, permits the creation of trimers and by varying the dark time between the two pulses an oscillatory pattern emerges in the fraction of formed trimers. The spectra of these interference fringes provide simultaneously the binding energy of trimers as well as their lifetimes, and they are robust against thermal effects that arise from the temperature of the gas. This means that wiggle intereferometry protocol can potentially used to determine the intrinsic characteristics of exotic few-body states, such as the Efimov states, regardless the sign or the magnitude of the scattering length.

The propagation of the electronic wavepacket upon strong-field scattering with a nanosystem can be obstructed by its geometry. This effect becomes particularly pronounced when the size of the nanosystem is larger than the width of the electron wave packet. We demonstrate by means of recently introduced the phase-of-phase spectroscopy $(\mathcal{POP})$, that the small-angle scattering of the electron wave packet in the prototypical nanosystem $\mathrm{C_{60}}$ molecule and propagation of any trajectory which attempt to cross the molecular plane is hampered by the molecular cage. This so-called $(\mathcal{POP})$ \textit{-controversy} has been resolved in the ionization of $\mathrm{C_{60}}$ by $(\mathcal{POP})$ spectroscopy. Furthermore, we observe the transition to the atomic-like limit of the strong-field driven scattering, where the small-angle scattering is activated. This is realized by expanding the vertical size of the electron wave packet beyond the diameter of the $\mathrm{C_{60}}$ cage. Obviously this scenario is valid when the electron wave packet spread in size beyond of the molecular cage by extending the excursion of the electron wave packet. We anticipate that hampering of the small-angle scattering effect holds potential for enhancing the high-harmonic generation radiation in the nanosystems and energetics of the scattering in the strong laser fields. Our results are corroborate by results of the Simple Man's Theory (SMT) modeling. In the second contribution we report on a universal energy dependence governing the rescattering of electrons emitted from small quantum systems in intense laser fields. The empirical power-law, which describes the field-driven electron rescattering probability, is derived by recording photoelectron spectra from rare gas and metal atoms as well as from $\mathrm{C_{60}}$ fullerenes. We find that the ratio between rescattered and direct photoelectrons scales with the ponderomotive energy as $U_{\text{p}}^{-2}$ independently of laser intensity, laser wavelength and target system. This dependence on the cycle-averaged kinetic energy is in close analogy to the fundamental Rutheford scattering law, which also predicts a decreasing scattering probability with kinetic energy of the projectile according to $E_{\text{kin}}^{-2}$ for a fixed detection angle.

The discovery of Rydberg matter empowers prospects in ultracold science. Recently, scientists took another step forward by measuring the Rydberg series of highly magnetic lanthanide – Er. In our work, we examine the complex entity of the ultralong-range Rydberg molecule and search for intriguing energy structure, novel transitions, and unusual magnetic properties. We use the perturbation theory due to the lack of sufficient experimental data for a general model. We discuss the limited capabilities of this approach in the case of complex Er molecules and prospect precise calculations. A step towards developing a proper model is understanding molecules with a two-valence electron Rydberg atom. Here, the Hg*Rb molecule serves as a platform. We present promising energy spectra with easily accessible trilobite states and approach homonuclear Hg molecules calculations.

We report on results of systematic experimental-theoretical investigation of high-order harmonic generation (HHG) in layers of CdSe semiconductor quantum dots of different sizes and a reference thin film of bulk CdSe. We observe a strong decrease in the efficiency, or even complete suppression of harmonic generation for harmonics with energies of quanta above the bandgap for the smallest dots, whereas the intensity of below bandgap harmonics remains almost unaffected by the dot size. This becomes even more pronounced for longer laser driving wavelength. These systematic investigations allow us to develop a simple physical picture explaining the observed suppression of the highest harmonics: the discretization of electronic energy levels seems to be not the predominant contribution to the observed suppression but rather the confined dot size itself, causing field-driven electrons to scatter off the dot’s walls. The reduction in the dot size below the classical electron oscillatory radius and the corresponding scattering limits the maximum acceleration by the laser field. Moreover, this scattering leads to a chaotization of motion, causing dephasing and a loss of coherence, therefore suppressing the efficiency the emission of highest-order harmonics. Our results demonstrate a new regime of intense laser-nanoscale solid interaction, intermediate between the bulk and single molecule response.

The time evolution of an atomic ensemble under the influence of twisted light has been investigated within the framework of the density-matrix theory based on the Liouville–von Neumann equation. Special attention has been paid to the effect of the external homogeneous magnetic field orientation on the atomic absorption profile. While the derived expressions can be employed to study the photoabsorption by any atomic system, detailed calculations have been performed for the $5s {}^2 S_{1/2} \, (F=1) \rightarrow 5p {}^2 P_{3/2} \, (F=0)$ transition in $^{87}$Rb. Our calculations indicate how the evolution of the atomic absorption profile is governed by the initial conditions, the relaxation, the spatial structure of the light field, as well as by the applied magnetic field. This study contributes to a better understanding of the potential of twisted light and atomic clouds for magnetic sensing as has been proposed by Castellucci et al. [Phys. Rev. Lett. 127, 233202 (2021)].

Intense laser-matter interactions are at the center of interest in research and technology since the development of high power lasers. They have been widely used for fundamental studies in atomic, molecular, and optical physics, and they are at the core of attosecond physics and ultrafast opto-electronics. Although the majority of these studies have been successfully described using classical electromagnetic fields, recent investigations based on fully quantized approaches have shown that intense laser-atom interactions can be used for the generation of controllable high-photon-number entangled coherent states and coherent state superposition. We provide a comprehensive fully quantized description of intense laser-atom interactions. We elaborate on the processes of high-harmonic generation, above-threshold-ionization, and we discuss new phenomena that cannot be revealed within the context of semi-classical theories. We provide the description for conditioning the light field on different electronic processes, and their consequences for quantum state engineering of light. Finally, we discuss the extension of the approach to more complex materials, and the impact to quantum technologies for a new photonic platform composed by the symbiosis of attosecond physics and quantum information science.

Ultrashort XUV pulses allow to investigate physical processes down to the attosecond timescale. Here we present recent progresses made in the investigation of "large" spatially extended systems using ultrashort XUV pulses. We study how the spatial distribution of atoms in a complex molecule influences processes such as attosecond ionization delays or proton dynamics. The goal of this work is to be able to apply ultrafast XUV technology to extremely complex molecular systems.

Recent results of pump-probe measurements with small molecules will be presented. Using a 50-kHz laser amplifier and high-harmonic generation we performed RABBIT-like experiments on ionization and fragmentation of H2 molecules with a reaction microscope. Emphasis is given to signatures of possible quantum entanglement after break-up. This includes the creation, observation and modification of two-particle entanglement in the final state. In the second part of the presentation XUV pump-probe experiments with Di-Iodo-Methane molecules at the XUV-FEL in Hamburg will be discussed. Here, clear signatures of inter-molecular dynamics and rearrangement processes after the first ionization step could be resolved.

This talk reports on a joint experimental-theoretical study of xenon ionized by combined infrared and terahertz pulses. A femtosecond laser pulse is used to create a temporally-localized electron wave packet through multiphoton absorption at a well defined phase of the time-synchronized near-single-cycle terahertz field. We focus specifically on the low-energy electrons close to the continuum threshold, which are particularly sensitive to the electron-core Coulomb interaction. By recording the photoelectron momentum distributions as a function of the time delay, we observe signatures of various regimes of dynamics, ranging from recollision-free acceleration to coherent electron-ion scattering induced by the terahertz field. The measurements are confirmed by three-dimensional time-dependent Schrödinger equation simulations. A classical trajectory model allows us to identify scattering phenomena analogous to strong-field photoelectron holography and high-order above-threshold ionization.

I will present a rigorous definition of the high-harmonic cutoff which is applicable to arbitrary driver waveforms. This new definition provides a natural meaning for the imaginary part of the cutoff energy, which controls the strength of quantum-path interference in the plateau. This construction radically simplifies quantum-orbit calculations. Using this definition, we build the Harmonic-Cutoff Approximation to calculate the exact location and brightness of the cutoff at a fraction of the cost of the state of the art — giving access to a much wider class of optimization tasks. The harmonic cutoff is one of the key concepts in high-harmonic generation, but it is also an elusive object which has long escaped a precise definition. In this talk I will present and demonstrate the first natural definition for the harmonic cutoff; I will show how to find it, in a simple and computationally effective way; and I will show how it can be used. The construction is built based on a new type of quantum orbit, which recollides at the harmonic-cutoff times $t_\mathsf{hc}$ defined by a second-order saddle-point equation for the usual action $S$, $$ \frac{\mathrm d^2 S}{\mathrm dt^2}(t_\mathsf{hc}) = 0. $$ The cutoff energy is then given by the real part of $\Omega_\mathsf{hc} = \frac{\mathrm dS}{dt}(t_\mathsf{hc})$. This provides a natural value for $\mathrm{Im}(\Omega_\mathsf{hc})$, which controls the strength of quantum-path interference in the plateau. The quantum orbits emerge as different branches of a unified Riemann surface, which are united at branch points — the harmonic-cutoff times $t_\mathsf{hc}$. More practically, the times $t_\mathsf{hc}$ can be used to classify the solutions of saddle-point equations into quantum orbits in a simple and efficient way, making calculations more flexible and effective. Last (but not least), the information at the times $t_\mathsf{hc}$ is enough to fully characterize the harmonic spectrum at the cutoff. This allows us to build a new approach — the Harmonic-Cutoff Approximation (HCA) — which gives a quantitatively accurate estimate of the location and brightness of the cutoff, and a qualitative estimate of the spectrum in the upper plateau. This requires solving a single saddle-point equation — as opposed to dozens or hundreds of equations, as in previous approaches. Reference: E Pisanty et al, J. Phys.: Photon. 2, 034013 (2020)

Nonlinear frequency conversion processes are broadly explored and applied in the visible spectral region. Extending these effects into the x-ray spectral domain is challenging due to their inherently low cross section [1]. Yet, these processes are accessible at high-brilliance storage-ring based x-ray sources and x-ray free electron lasers. The process of x-ray parametric down conversion (XPDC) of x-ray photons in a pair of x-ray (signal) and visible (idler) photons is predominantly mediated by the valence electron density and provides a valence sensitive probe of electronic structure. Recently, we developed a quantitative theory [1,3] that linked the measured nonlinear scattering signal to an electronic current-density density correlation function. We identified a characteristic signature, that allows for an unequivocal experimental identification of this extremely weak process – the XPDC emission cone [1]. In a recent experiment, we successfully measured the XPDC cone resulting of nonlinear x-ray scattering of photons of 10 keV from diamond, for idler energies in the range of 100 eV. The XPDC scattering cone clearly shows the contribution of two distinct branches, manifested by a positive and negative signal with respect to the Compton scattering background. We interpret this finding as inelastic x-ray scattering from a XUV polaritonic excitation in diamond. A simple polariton model of two coupled electronic and photonic excited states concurrent with energy and momentum conservation of the nonlinear scattering process agrees with the data and corroborates our interpretation. Momentum-resolved nonlinear x-ray scattering thus provides a means to determine the microscopic structure of EUV polaritons on the length scale of the x-ray wavelength. [1] C. Boemer, D. Krebs, A. Benediktovitch, E. Rossi, S. Huotari & N. Rohringer, Faraday Discuss. 228, 451 (2021). [3] D. Krebs and N. Rohringer, Phys. Rev. X (under review), arXiv:2104.05838

We present a universal methodology for deriving quantum master equations for the reduced density matrix of a molecular system embedded in its environment. The method allows us to overcome the limitation of the standard perturbation theory, and it is flexible enough to accommodate various memory effects found in the non-linear optical response functions. We can not only thoroughly analyze and overcome approximations pertaining to the standard results of the perturbation theory, such as Redfield equations and the Förster energy transfer rates, but we can also complete all these theories with novel expressions for the evolution of the coherence elements of the density matrix. Correspondingly, we can always provide a rigorous theory for all elements of the non-linear response necessary for calculating optical signals. We can relax all approximations which effectively forbid application (i.e., make it inconsistent with their assumptions) of these theories to calculate the time-resolved spectroscopic responses. For instance, we can formulate short time Förster theory and show its agreement with exact calculations of dynamics within important regions of system parameters. Not only that, but we can also show some pieces of common theoretical wisdom to be invalid. For instance, the assumption that the corresponding dephasing always accompanies incoherent energy transfer is shown not to apply in the region of validity of the Förster theory. Such insight is enabled by the fact that master equations do not act as black boxes and instead provide rates, or their equivalents, for the processes in terms of which we are used to discuss the time evolution of systems interacting with their environments. Carefully designed master equations validated by exact (black box) propagation methods may provide better insight into the observations made by advanced time- and frequency-resolved non-linear spectroscopic methods than the exact black boxes alone.

Conical intersections between electronic potential energy surfaces are paradigmatic for the study of nonadiabatic processes in the excited states of large molecules. However, since the corresponding dynamics occurs on a femtosecond timescale, their investigation remains challenging and requires ultrafast spectroscopy techniques. We demonstrate that trapped Rydberg ions are a platform to engineer conical intersections and to simulate their ensuing dynamics on larger length scales and timescales of the order of nanometers and microseconds, respectively; all this in a highly controllable system. Here, the shape of the potential energy surfaces and the position of the conical intersection can be tuned thanks to the interplay between the high polarizability and the strong dipolar exchange interactions of Rydberg ions. We study how the presence of a conical intersection affects both the nuclear and electronic dynamics demonstrating, in particular, how it results in the inhibition of the nuclear motion. These effects can be monitored in real time via a direct spectroscopic measurement of the electronic populations in a state-of-the-art experimental setup.

Using two-colour measurements and a combined experimental-theoretical analysis, we were able to measure the duration of electron strong-field emission from nanoscale needle tips to 710 ± 30 as, representing precisions attosecond physics from a solid (currently under review). In graphene and at the graphene-gold transition, we could identify different field-driven mechanisms: real vs. imaginary charge carrier excitations, also in a combined exp.-theor. study. Based on these insights, we could demonstrate a potentially light-fast logic gate (Boolakee et al., Nature 2022). If time permits, I will also show recent results on electron correlations and electron coincidence detection of surprisingly strong two electron Coulomb repulsion effects (arXiv:2209.11806).

Rydberg excitons in semiconductors provide a promising solid-state realization of Rydberg states, for which orbital sizes of up to a micrometer have been observed in cuprous oxide crystals. In this talk, I will discuss recent experiments demonstrating the generation and control of strong exciton interactions by optically generating --- via a pump-probe scheme --- two types of Rydberg excitons with different principal quantum numbers. The experimental results provide clear evidence for long-range interactions between semiconductor excitons. I will argue that these results can be explained by the process of Rydberg facilitation in which a nonresonant excitation of a probe exciton can become resonant by virtue of the van der Waals potential provided by the sea of pump excitons.

Rydberg atoms and molecules are explored using laser and microwave pulses for quantum control, spectroscopy and cold-ion-plasma sourcing. In this presentation, I will provide an overview over our studies of Rydberg molecules and interacting Rydberg atoms, which includes spectroscopic work as well as time-domain investigations in ion-imaging devices. Analysis of the experimental data is supported by Rydberg-molecule modeling. On similar experimental platforms, we investigate the Coulomb-expansion dynamics of pulsed, dense ion clouds, which exhibit disorder-induced heating, adiabatic and ballistic cooling, and time-dependent Coulomb coupling. The ion clouds are probed using ion imaging and electric-field measurement based on the Stark effect of Rydberg atoms. The Stark spectra reveal ion-cloud regimes that cover a continuous range from micro-field- to macro-field-dominated. In the last part of the talk, time-dependent manipulation methods applicable to spectroscopy and quantum control of Rydberg atoms trapped in modulated optical lattices are discussed.

Long-range Rydberg molecules are molecules in highly-excited electronic states where the binding results from the scattering of an almost free electron from neutral atoms within its orbit. The existence of such bound states was first predicted by Greene and coworkers in 2000 [1] and confirmed experimentally by Bendkowsky and coworkers in 2009. Since then, numerous experimental and theoretical studies have resulted in a solid understanding of the exotic properties of these molecules. In recent work we have investigated the properties of homonuclear Cs$_2$, K$_2$, and heteronuclear KCs long-range Rydberg molecules and introduced millimeter-wave photodissociation as a new tool to probe the properties of long-range Rydberg molecules. In this talk I will briefly review these studies and then focus on our experimental progress towards the formation of an ultracold plasma of equal-mass charges starting from a gas of long-range Rydberg molecules.

Extending nonlinear optical effects to level of single photons is an important research area, with applications in optical quantum technologies. A promising approach maps the strong, long-range dipole-dipole interactions between atoms, excited to high-lying energy levels known as Rydberg states, onto photons. Using this method in cold atoms, researchers have created single photon sources, gates and transistors for single photons. In this talk I will explain how such states also exist in some semiconductors such as cuprous oxide (see figure), where the atoms are replaced by excitons – bound states of electrons and holes. I will discuss how such states can be probed via coherent second harmonic generation spectroscopy [1]. I will also describe our recent work that shows that the presence of strong electric dipole transitions between excitonic states give rise to a huge microwave-optical cross-Kerr nonlinearity that could be exploited for microwave to optical conversion at low temperatures, for example as an optical interface to a superconducting quantum device. [2] [1] Gallagher et al., Phys. Rev. Research 4, 013031 (2022) [2] Rogers et al., Phys. Rev. B 105, 115206 (2022)

I will present our results on the properties and non-equilibrium dynamics of few-body quantum systems based on ultracold polar molecules, Rydberg atoms, or their mixtures. On the one hand, we investigated interacting ultracold molecules in a one-dimensional harmonic trap as a fundamental building block of molecular quantum simulators, where we observed an interesting interplay of intermolecular interactions, external fields, and trapping potentials. On the other hand, we studied the non-equilibrium properties of a Rydberg electron interacting with a gas of spin-1/2 fermionic atoms and found the dynamical emergence of the Kondo screening cloud. Finally, we explored the quantum simulation of the central spin model with a Rydberg atom surrounded by polar molecules in optical tweezers.

We present a novel method that allows to non-destructively image structures inside bulk samples with nano-scale resolution and a very sensitivity. The method uses XUV radiation from high-harmonic generation. Thus, also ultrafast transient phenomena inside solid state material can be recorded.

We report on two different approaches that use highly intense tailored light fields to study position-space-related properties of small molecules. Both experimental approaches are realized using cold-target recoil-ion momentum spectroscopy (COLTRIMS) reaction microscopes and femtosecond laser pulses with tailored intense fields. In the first part of the talk, the technique of Holographic Angular Streaking of Electrons (HASE) is presented. HASE enables the retrieval of Wigner time delays in strong-field ionization. We find that for the strong-field ionization of molecular hydrogen, which is among the smallest extended systems, the Wigner time delays vary on an attosecond time scale as a function of the electron's emission direction with respect to the molecular axis. The second part of the talk is about spatially separated entangled atoms that can have distances on the order of dozens of nanometers. To prepare this diatomic, spatially extended state, we trigger dissociation of oxygen molecules using femtosecond laser pulses. This prepares spatially separated entangled atoms on femtosecond time scales. A time-delayed probe pulse is used to prove that the prepared atoms are entangled in an internal degree of freedom (the magnetic quantum number of the electrons), and not only classically correlated.

Carotenoids are an integral part of natural photosynthetic complexes, with tasks ranging from light harvesting to photoprotection. Their underlying energy deactivation network of optically dark and bright excited states is extremely efficient: after excitation of light with up to 2.5 eV of photon energy, the system relaxes back to ground state on a timescale of a few picoseconds. In my talk, I will give a brief overview of the current status of carotenoid photophysics with emphasis on the so-called S*-state. I will present a model based on the vibrational energy relaxation approach (VERA) to explain the main characteristics of relaxation dynamics after one-photon excitation. Lineshapes after two-photon excitation are beyond the current model of VERA, which presents a future line of research I will outline briefly. As an outlook, I will outline experimental techniques needed to better describe energy dissipation effects in carotenoids and within the first solvation shell.

Boson sampling in its standard form rests on the scrambling of an input state of photons by a passive linear optical setup [1]. We first review that an initial Fock state of standard boson sampling can be represented by an application of Kan's summation formula for monomials [2]. Due to the close analogy of this formula to the representation of generalized coherent states (GCS) [3] in terms of Fock states, an exact analytic representation of a {\it single} Fock state in terms of GCS is established. The unitary evolution (the scrambling) of the initial state can thus be performed exactly analytically by the multiplication of two finite-size matrices. In the present talk, we will discuss the complexity scaling of the approach as well as its relation to the calculation of permanents [4]. By dividing the full system into two halves, the generation of entanglement in the subsystems by the unitary will be investigated [5]. [1] S. Aaronsson and A. Arkhipov, Proceedings of the 43rd annual ACM symposium on Theory of computing - STOC '11, 333 (2013) [2] R. Kan, J. Multivar. Anal. {\bf 99}, 542 (2008) [3] A. Perelomov, {\it Generalized coherent states and their applications}, Springer (2004) [4] S. Scheel, arXiv:quant-ph/0406127 (2004) [5] Y. Qiao, J. Huh, and F. Grossmann, preprint