Future of Ultracold and Ultrafast Dynamics

Electrons emitted from atomic systems in intense light fields are affected on two different time scales. On the one hand, they experience an acceleration dependent on the phase of the light field at the time of ionization, which can lead to a recollision after the sign of the electric field has changed. On the other hand, there is an effective ponderomotive force formed from the cycle-averaged field. This is zero on average for a plane wave, but it is important for short pulses or standing waves. In this talk I will show two different experiments that investigate the influence of this field envelope. The first results, focusing on temporal gradients of the field envelope, are obtained on a transient absorption beamline. Helium is ionized by extreme ultraviolet light, followed by a few-cycle near-infrared pulse with linear or circular polarization. Reconstruction of the temporal dipole moment shows a regime where circularly polarized light leads to more recollisions due to envelope-driven recolliding periodic orbits [1]. The second experiment investigates the influence of spatial field gradients in standing waves. A femtosecond enhancement cavity is used to generate the intense standing waves at 100 MHz repetition rate to ionize xenon. The emitted electrons are analyzed by a velocity map imaging spectrometer [2] to study electron diffraction from the light grating, known as the Kapitza-Dirac effect. [1] T.H. PRL 130, 183201 (2023) [2] J.-H. Oelmann et al., Rev. Sci. Instrum., 93(12), 123303 (2022).

Electrons liberated from atoms through photoionization offer valuable insights into light-atom interaction. Such ionization dynamics have been extensively studied using the plane wave laser pulses. However, ionization under intense few-cycle twisted laser pulses remains largely unexplored. In this paper, we use the strong field approximation together with saddle point method to analytically derive the ionization transition amplitude in such pulses. The derivation allows us to compute the photoelectron momentum distribution (PMD). Given that Bessel beams can be represented as an infinite sum of circularly polarized plane waves with identical helicity, all arranged with wave vectors on a cone, we investigate the PMD generated by these Bessel pulses. Additionally, we demonstrate the impact of opening angle and orbital angular momentum on the PMD.

Strong-field ionization can induce electron motion in both the continuum and valence shell of the parent ion. Here, we report on a joint theoretical and experimental investigation of laser-induced electron diffraction in xenon. We explore the interplay of electron recollision with spin-orbit dynamics in the valence shell of the xenon cation. On the theory side, the electron-hole potentials for two different states are constructed and the quantitative rescattering model is used to calculate the photoelectron momentum distributions (PMD) for high-order above-threshold ionization of xenon. Measurements were carried out using 40-fs laser pulses with a central wavelength of 3100 nm and a peak laser intensity of \(6 \times 10^{13} \, \text{W/cm}^{2}\). The simulated PMDs describe well the features of the measured angular distributions of photoelectrons. Our study reveals a theoretical distinction between the electron signals resulting from rescattering off the \(m=0\) and \(|m|=1\) hole states, particularly noting a distinct change along the backward scattering angles. However, to fully identify the contributions of the hole states, a more accurate agreement between theory and experiment will be needed.

Quantum droplets are self-bound liquid-like states, which form under the impact of quantum fluctuations, commonly accounted, to first order, by the Lee-Huang-Yang (LHY) correction term. Quantum droplet states emerge in atomic systems with various types of inter-atomic interactions, as well as in different geometries and dimensionalities. In particular, two-component atomic mixtures interacting via contact interactions obtain a droplet character when the inter-component attraction becomes comparable to the average intra-component repulsion. Moreover, one-dimensional droplet configurations are of particular interest due to the enhanced impact of correlations and increased lifetimes, which are common in one-dimensional settings. Interestingly, from the theoretical side, one-dimensional settings facilitate a direct comparison between the effective single field description of droplets, stemming from the LHY theory, and the ab-initio many-body treatment of the atomic mixture.

The experimental platform of ultracold gases provides a unique opportunity to study a diverse range of phenomena in physics. In this presentation, I will provide an overview of how ultracold gases can be employed to investigate the physics in the quantum field theoretical limit. As the first example I will present the connection to quark-gluon plasma, a state of matter that emerges following the collision of heavy ions at CERN. This state of matter is known as the hottest state of matter produced on Earth and has a temperature of approximately 1012°K, which is about 20 orders of magnitude higher than that of ultracold gases i.e. ultrahot. Nevertheless, the far equilibrium situation in ultracold gases after a quench exhibits a temporal evolution that is analogous to that predicted for the state of matter directly following a heavy ion collision [1]. The key of these experiments lies in the utilisation of composite quantum fields, rather than the fundamental fields themselves. This approach presents novel avenues for investigating quantum field theoretical settings [2]. Platforms offering this possibility we classify as quantum field simulators. As a second example of exploring ultralarge, I will present our study of the expansion of spacetime in the limit of the cosmological principle, which assumes homogeneity and isotropy of the universe. Assuming this, the metric for large scales is given by the Friedmann-Lemaitre-Robertson-Walker metric, which is fully characterised by the sign of the curvature and a general scale factor, both are under full control in the experiments with ultracold gases. I will discuss how different curvatures can be realised as well as particle production in expanding spacetime can be detected [3]. These are just two examples of how the experimental platform of ultracold gases can be utilised to address fundamental questions; there are many more to come in the future. References [1] M. Prüfer, et al., Nature, 563, 217 (2018) [2] M. Prüfer, et al. Nature Physics, 16, 1012 (2020) [3] C. Viermann, et al. , Nature, 611, 260 (2022)

It is well known that crystallized shells, of Helium atoms, a so called snowball, forms around the ion in the otherwise (super-)fluid Helium droplet [1]. Here, we show that for sufficiently large droplets a third regime appears between the snowball and the liquid one with a supersolid structure where the Helium density exhibits a periodic modulation of the particle density on a spherical shell while remaining superfluid. To identify supersolidity in a geometrically confined scenario of a droplet we combine modified density functional theory (DFT), allowing us to describe large enough droplets, with a Gaussian Imaginary Time Dependent Hartree (G-ITDH)[2] method which traces the emergence of crystallized structures. Our approach works well as a comparison to Quantum Monte Carlo results [3] for smaller droplets reveals. [1] D. E. Galli etal, J. Phys. Chem. A 2011,115, 7300-7309 [2] W. Unn-Toc etal, J. Chem. Phys. 137, 054112 (2012) [3] M. Rastogi etal, Phys. Chem. Chem. Phys. 2018, 20, 25569

We explore periodically driven quantum rotors as a platform for studying topological phenomena in ultracold and ultrafast systems. Our research focuses on the implementation of multi-gap topological phases through non-Abelian braiding of band degeneracies. By precisely controlling periodic kicks applied to a quantum rotor, we observe nodal-line braiding that alters topological charges of band nodes. In the strongly driven regime, we uncover an anomalous Dirac string phase, a unique out-of-equilibrium state characterized by edge states at zero angular momentum. This phase emerges from braiding processes involving all quasienergy gaps, showcasing the rich phasespace accessible in extreme driving conditions. Our findings have immediate relevance to current experiments, particularly those involving linear molecules subjected to far-off-resonant laser pulses and artificial quantum rotors in optical lattices. The stetup allows for precise manipulation and observation of non-Abelian topological properties, which highlights how the interplay between ultrafast driving and ultracold matter can reveal fundamental aspects of light-matter interactions at extreme limits.

Thouless pumping enables the transport of particles in a one-dimensional periodic potential if the potential is slowly and periodically modulated in time. The change in the position of particles after each modulation period is quantized and depends solely on the topology of the pump cycle, making it robust against perturbations. Here, we demonstrate that Thouless pumping also allows for the realization of topologically protected quantized changes of the distance between atoms if the atomic s-wave scattering length is properly modulated in time.

Highly electronically excited atomic impurities within a BEC typically have interactions characterised by a scattering length that may rival or even surpass the average spacing between the surrounding bosons. The significance of these interactions depends on the thermal de Broglie wavelength; for shorter lengths, the system exhibits a rich absorption spectrum which extends typical polaron physics. However, within a dense bath, the absorption spectrum consists only of a broad single Gaussian, indicating an almost classical behaviour. Beyond altering interaction ranges, scattering length and interaction strength, the electronic angular states of the impurity can be manipulated, breaking the spherical symmetry of the interactions. In free space, this manipulation leads to the emergence of l(l+1) degenerate electronic potential energy surfaces, introducing non-additive interactions. Our investigation delves into the impact of these anisotropic and non-additive interactions on the absorption spectrum of a Rydberg impurity within an ideal BEC.

We study the polaron physics of a heavy impurity inside a Fermi sea with dipole interactions in three dimensions using different theoretical methods. In the limit of an infinitely heavy impurity, this corresponds to an anisotropic scattering potential in the Fermi sea, and the many-body problem can be solved exactly using a functional determinant approach (FDA). For a mobile impurity, we use a Chevy variational ansatz for the polaron wave function and calculate the spectral functions. These results are then compared to the non-self-consistent T-matrix approach and the exact FDA results in the infinite mass limit. We compute the spectra and polaron energies for a range of different s-wave and dipolar scattering lengths. This allows us to study the difference between the pure contact interaction and the dipolar long-range potential for the polaron formation. Possible experimental tests could be realized using magnetic atoms or molecules.

The angulon quasiparticle allows for the description of a rotating impurity in the many-body environment. For example, they are formed from molecules in superfluid helium nanodroplets. Theoretical research also predicts that angulon can be formed out of other impurities with angular momenta, such as molecular ions in ultracold gases or in lead halide perovskites. In our study, we focus on the formation and fate of the angulon quasiparticle in the crossover from few- to many-body physics. To this end, we investigate the system of a molecular quantum rotor in a two-dimensional Bose gas. We show that the system starts to feature angulon characteristics when the size of the bosonic cloud is large enough to screen the rotor. More importantly, we demonstrate the departure from the angulon picture for large system sizes or large angular momenta where the properties of the system are determined by collective excitations of the Bose gas. We will briefly discuss the outlook for further research focused on the emergence of collective excitations, such as solitons and vortices in the system after rapid impurity rotation. The talk will be based on arXiv:2407.06046.

The term "false vaccum decay" (FVD) refers to the relaxation process of a quantum field from a metastable state (the false vacuum) to its ground state (the true vacuum), triggered by quantum or thermal fluctuations. It has attracted extensive attention in cosmology, due to its consequences on the stability of the Higgs vacuum and its application to inflationary models describing the early Universe. In this talk, I will discuss the observation of thermally-induced false vacuum decay with a ferromagnetic superfluid, realised with a coherently-coupled two-component Bose-Einstein condensate, comparing the theoretical prediction for the decay rate with numerical and experimental results.

In ultracold atomic gases, a unique interplay arises between phenomena known from condensed matter, few-body physics and chemistry. A good example is the Bose polaron problem of an atomic impurity in a Bose-Einstein condensate (BEC). On the one hand the impurity is dressed by excitations from the BEC, similar to an electron in a solid. On the other hand, the Efimov effect known from universal few-body physics can cause the impurity to mediate attractive interactions between the bosons from the BEC. In the first part of my talk I will show how we can use variational approaches to describe the rich phenomena which arise, illustrating the competition between the impurity-mediated attraction and the intrinsic repulsion in the BEC. In the second part, I will discuss the experimental observation of halo trimers in ultracold mixtures and how a background BEC can couple dimer and trimer states. This leads to polaron states with the nature of dimer-trimer superpositions, showing a beautiful example of chemistry in a quantum medium and the interplay between polaron and bound-state physics.

The assumption that physical systems relax to a stationary state in the long-time limit underpins statistical physics and much of our intuitive understanding of scientific phenomena. For isolated systems, this follows from the eigenstate thermalization hypothesis. When an environment is present the expectation is that all of phase space is explored, eventually leading to stationarity. In this talk, I will identify and discuss simple and generic conditions for dissipation to prevent a quantum many-body system from ever reaching a stationary state [1]. These “dynamical symmetries” go beyond dissipative quantum state engineering approaches towards controllable long-time non-stationary dynamics typically associated with macroscopic complex systems. The resulting coherent and oscillatory evolution constitutes a dissipative version of a quantum time-crystal. I will show how such dissipative dynamics can be engineered and studied with ultracold atoms using current technology. I will present setups that enable the study of long-range quantum coherence, complexity, and η-pairing with a potential connection to driving induced superconductivity [2, 3, 4]. Finally, I will expand these ideas to more general graph geometries that are within reach to being realizable with near future technology [5,6]. References [1] B. Buča, J. Tindall, and D. Jaksch, Complex coherent quantum many-body dynamics through dissipation, Nature Communications 10 1730 (2019). [2] J. Tindall, B. Buča, J. R. Coulthard, and D. Jaksch, Heating-Induced Long-Range η-Pairing in the Hubbard Model, Physical Review Letters 123,  030603 (2019). [3] J. Tindall, F. Schlawin, M. Buzzi, D. Nicoletti, J. R. Coulthard, H. Gao, A. Cavalleri, M. Sentef and D. Jaksch, Dynamical Superconductivity in a Frustrated Many-Body System, Physical Review Letters 125,  137001 (2020). [4] B. Buca, C. Booker and D. Jaksch, Algebraic Theory of Quantum Synchronization and Limit Cycles under Dissipation, SciPost Phys. 12, 097 (2022). [5] J. Tindall, A. Searle, A. Alhajri, D. Jaksch, Quantum physics in connected worlds, Nature Communications volume 13, 7445 (2022). [6] T. Hashizume, F. Herbort, J. Tindall, D. Jaksch, Emergent quantum dynamics on complex networks, in preparation.

During recent years interest has been rising for applications of vector light beams towards magnetic field sensing. In particular, a series of experiments were performed to extract information about properties of static magnetic fields from absorption profiles of light passing through an atomic gas target. In the present work, we propose an extension to this method for oscillating magnetic fields. To investigate this scenario, we carried out theoretical analysis based on the time-dependent density matrix theory. We found that absorption profiles, even when averaged over typical observation times, are indeed sensitive to both strength and frequency of the time-dependent field, thus opening the prospect for a powerful diagnostic technique. To illustrate this sensitivity, we performed detailed calculations for the $5s \;\, {}^2S_{1/2}$ ($F=1$) $-$ $5p \;\, {}^2 P_{3/2}$ ($F=0$) transition in rubidium atoms, subject to a superposition of an oscillating (test) and a static (reference) magnetic field.

Coherent control drew a lot of interest in recent years spanning over various fields of research regarding the promising abilities for quantum computing and precision measurements. Coherent control extended to the strong-field regime is particularly promising for the manipulation of matter and the control of photochemical reactions. In this work, we develop a scheme to extend strong-field coherent control to the XUV domain. With intense XUV pulses, we induce Rabi oscillations in atoms, leading to Autler-Townes level splittings in the photoelectron spectra [1]. In the near infrared domain, the feasibility to coherently control the population of the Autler-Townes doublet has been shown, based on chirp manipulation of the laser pulses [2,3]. To establish comparable schemes in the XUV domain, we implement chirp control of the XUV pulses from the free electron laser FERMI. By manipulating the chirp of the XUV pulses in a controlled way, we demonstrate strong-field coherent control of Autler-Townes states in the XUV domain. [1] S. Nandi et al. Nature 608, 488–493 (2022). [2] M. Wollenhaupt et al., Appl. Phys. B 82, 183–188 (2006). [3] U. Saalmann et al., Phys. Rev. Lett. 121, 153203 (2018).

Rydberg atoms interact strongly over large distances leading to effects such as Rydberg blockade or facilitation. In the facilitation regime the dynamics of the system closely resembles those of epidemics, manifesting a non-equilibrium phase transition between large-scale spreading of excitations and an inactive system. Using Monte-Carlo simulations of an optically driven Rydberg many body gas in the facilitation regime, we analyze the effects of thermal motion on the universality class of the phase transition. In the low temperature regime, we show that this phase transition falls into the universality class of directed percolation. With increasing temperature however, we show that the existence of power-law distributed Levy flights leads the system to display signatures of anomalous directed percolation. For high temperatures the system displays mean field dynamics.

By using a high-resolution ion microscope we can image ion and Rydberg systems with a spatial resolution of at least 200nm and a temporal resolution of less than 50ns. This allows to study various dynamic processes that arise from Rydberg-ion interactions. In the first part of the talk we will report on a recent study of collisional onset dynamics between an ion and a Rydberg atom. At sufficiently small distances, the charge-induced Stark shift leads to a large number of avoided crossings between an atomic Rydberg S-state and the adjacent hydrogenic manifold. These crossings offer fast and slow collisional channels. For a certain energy regime this results in an interesting counter-intuitive behavior, where initially slow (cold) particles predominantly occupy faster collisional channels, which leads to a more rapid overall collision than for initially faster (hotter) systems. In the second part, we will discuss a bound state between an ion and a Rydberg atom arising from a flipping dipole mechanism. The resulting charged ultralong-range Rydberg molecule can be studied experimentally by means of high-resolution spectroscopy, mass spectrometry and in situ imaging. Furthermore, due to the huge bond length, the vibrational motion takes place in the microsecond range and can therefore be observed directly. These studies pave the way for experimental investigations of more complex ion-Rydberg systems such as trimer states, which feature a much richer structure of the molecular potential landscape.

We shall present a variational method for extracting the effective mass of an ion moving through a dense cold gas of neutral atoms, and compare it with a classical hydrodynamic approach.

Supersolids are exotic states of matter that spontaneously break two symmetries: gauge invariance through the phase-locking of the wavefunction, and translational symmetry owing to the emergence of a crystalline structure. First predicted in solid helium, they have recently been observed in ultracold atoms, with particular success coming from dipolar atoms [1, 2, 3, 4]. The crystalline structure is naturally observable as a modulation of the integrated in situ density profile. Phase coherence has instead been probed by studying the self-interference pattern of an expanding supersolid [1, 2, 3] and the emergence of Goldstone modes [5]. What had not yet been observed are quantized vortices, a hallmark of superfluidity. Here, we report on the theoretical study and experimental observation of vortices in a dipolar supersolid of Dysprosium [6]. When rotated, the supersolid phase shows a mixture of rigid-body and irrotational behavior, highlighting a fundamental difference between modulated and unmodulated superfluids. Our observations open the way to study the peculiar properties of vortices in supersolids: the reduced angular momentum, the influence of the crystal structure on the vortex dynamics and further applications to the study of other systems with multiple spontaneously broken symmetries, such as neutron stars [7]. References [1] F. B¨ottcher et al., Phys. Rev. X 9 011051 (2019) [2] L. Tanzi et al., Phys. Rev. Lett. 122 130405 (2019) [3] L. Chomaz et al., Phys. Rev. X 9 021012 (2019) [4] L. Chomaz et al., Rep. Prog. Phys. 86 026401 (2022) [5] M. Guo et al., Nature 564 386 (2019) [6] E. Casotti∗, E. Poli∗ et al., arXiv:2403.18510 (2024) [7] E. Poli et al., Phys. Rev. Lett. 131 223401 (2023)

Since the first observation of a Bose-Einstein condensate (BEC) made from strongly magnetic atoms, these systems have proven to be a rich source of new and fascinating phenomena arising from the long-range and anisotropic dipole-dipole interaction. Recently, these dipolar quantum gases have proven to be a versatile platform in order to observe the long-sought after supersolid phase—a state that simultaneously manifests a crystalline order and superfluid properties. Here, I will present the latest results from our research on ultracold dipolar quantum gas in Innsbruck, with a particular focus on the combined theoretical and experimental effort to characterize the rotational properties of these systems. The presence of quantized vortices—topological defects of the wavefunction characterized by a 2π phase winding—consists of one of the most distinctive manifestations of their superfluid nature. I will report on the theoretical study and experimental observation of quantized vortices in a strongly magnetic gas of dysprosium atoms in the supersolid phase [1]. Finally, I will show an application of rotating dipolar supersolids, i.e. the possibility to simulate “glitches”, instantaneous jumps of the rotation frequency occurring due to the internal vortex dynamics, akin to observations in neutron stars [2]. [1] E. Casotti*, E. Poli* et al., arXiv:2403.18510 (2024). [2] E. Poli et al., Phys. Rev. Lett. 131, 223401 (2023).

Driven systems are of fundamental scientific interest, as they can display properties that are radically different from similar systems at equilibrium. However, systems out of equilibrium are difficult to describe theoretically, as they are inherently time-dependent and deeply nonlinear. This makes the study of such systems an ideal task for quantum field simulators, in which complex dynamics emerge naturally and can be probed experimentally. Here, we demonstrate two distinct branches of Supersolid sound in a driven, two-dimensional superfluid that only has contact interactions. The self-stabilized patterned state emerges as a result of large occupations of phononic modes due to driving and can be described theoretically using an out-of-equilibrium fixed point of amplitude equations. To demonstrate supersolid excitations, we induce collective modes of the lattice, and show that the system supports lattice phonon propagation. We also show that the state maintains phase rigidity, a key property of superfluidity.

Dipolar molecules have been identified for many years as a platform to extend the achievements of ultracold atoms in quantum sensing, metrology and computing. They offer a richer spectrum and significantly stronger interactions, making them perfect candidates for theorized phases of matter such as the defect-induced supersolid. Despite these promises, significant practical challenges have so far obstructed the feasibility of bosonic ultracold molecules. Recent advancements in experimental techniques over the last year have overcome many of the obstacles, culminating in the creation of the first molecular Bose-Einstein condensate earlier this year. In recent work, we have explored the feasibility of Path Integral Monte Carlo applied to a realistic model of dipolar molecules. Sophisticated techniques such as PIMC are necessary to provide reliable simulation results, since mean-field approaches, routinely used for dilute and weakly-interacting ultracold gases, break down in the presence of stronger interactions. In this talk, I will present our findings on cluster formation for a model of dipolar molecules in quasi-1D geometry. I will discuss the advantages and limitations of current QMC approaches, and outlooks towards realizing a single-particle crystal with ultracold molecules.

In 2022, Rabi oscillations were observed at extreme ultraviolet (XUV) wavelengths using the seeded Free-Electron Laser (FEL) at FERMI [1]. This opens up a new domain of coherent control experiments in atoms and molecules. Here [2], we deepen our theoretical investigation of quantum entanglement in the photoelectric effect, generated between a photoelectron and a light-dressed atomic ion, that we recently proposed with Nandi et al. in Ref. [3]. A high-intensity XUV pulse ionizes a helium atom and dresses the resulting ion, see Fig. 1A. The ion-dressing modifies the kinetic energy of the electron to yield a “new” doublet in the photoelectron spectra, in agreement with the seminal work of Grobe and Eberly [4] and more recent works [5, 6]. The appearance of the GE doublet is a manifestation of quantum entanglement generated between the photoelectron and the dressed ion that the von Neumann entropy can characterize. Direct detection of such entanglement is however not possible by coincidence schemes due to the dressing having a cloaking effect on the ion. Our theoretical methodology is expanded by utilizing time symetry through the use of odd pulses, which therefore have zero pulse area. It is shown that these odd envelopes fundamentally alter the entanglement, such that unique channel-resolved photoelectron distributions are formed: Electrons from different channels are uncloaked. This constitutes a first usage of the parity of time symmetry in strong-field interactions. [1] S. Nandi et al. Nature 608, 488-493 (2022) https://doi.org/10.1038/s41586-022-04948-y [2] A. Stenquist and J. M. Dahlström arXiv:2405.03339v2 [quant-ph] https://doi.org/10.48550/arXiv.2405.03339 [3] S. Nandi, A. Stenquist et al. Sci. Adv. 10, eado0668 (2024) https://doi.org/10.1126/sciadv.ado0668 [4] R. Grobe and J. H. Eberly, Phys. Rev. A 48, 623-627 (1993) [5] S. B. Zhang and N. Rohringer, Phys. Rev. A 89, 013407 (2014) [6] C. Yu and L. B. Madsen, Phys. Rev. A 98, 033404 (2018).

Superfluorescene is a prominent example of quantum many-body effects, where a group of initially uncorrelated atoms emits radiation coherently in a short, bright burst of light. This phenomenon can occur when a free-electron laser excites a solid or gaseous target, creating a population inversion within the atomic system. The excited atoms then exchange spontaneously emitted photons, leading to the synchronization of their dipole moments. Through this correlation mechanism, the atoms emit coherently, resulting in a photon avalanche known as superfluorescence. Observing superfluorescence typically requires a macroscopic number of atoms, making conventional quantum-mechanical approaches intractable. A common method to overcome this challenge is through semi-phenomenological approaches, which recognize the stochastic nature of spontaneous emission and model it as a noise process. Inspired by these approaches, we develop a formalism based on the positive P representation. In this formalism, the atomic and field variables are described by stochastic differential equations. The deterministic terms of these equations represent semi-classical behavior, while the noise-induced correlations capture quantum effects, such as spontaneous emission. Our approach is applicable to a wide range of problems. In this talk, we specifically apply it to multi-color superfluorescence, where multiple pulses with different carrier frequencies are involved. In these schemes, superfluorescence exhibits complex correlation properties. We show that our formalism can accurately reproduce key features of spontaneous emission and is capable of efficiently simulating realistic macroscopic systems. reproduce key features of spontaneous emission and is capable of efficiently simulating realistic macroscopic systems. Observing superfluorescence typically requires a macroscopic number of atoms, making conventional quantum-mechanical approaches intractable. A common method to overcome this challenge is through semi-phenomenological approaches, which recognize the stochastic nature of spontaneous emission and model it as a noise process. Inspired by these approaches, we develop a formalism based on the positive P representation. In this formalism, the atomic and field variables are described by stochastic differential equations. The deterministic terms of these equations represent semi-classical behavior, while the noise-induced correlations capture quantum effects, such as spontaneous emission. Our approach is applicable to a wide range of problems. In this poster, we specifically apply it to multi-color superfluorescence, where multiple pulses with different carrier frequencies are involved. In these schemes, superfluorescence exhibits complex correlation properties. We show that our formalism can accurately reproduce key features of spontaneous emission and is capable of efficiently simulating realistic macroscopic systems. reproduce key features of spontaneous emission and is capable of efficiently simulating realistic macroscopic systems.

The fundamental ingredient for fermionic superconductivity and superfluidity is the energetically favorable formation of Cooper pairs. In continuous systems, this was established by Bardeen, Cooper and Schriefer [1], leading to the well-known BCS regime, where Cooper pairs form between fermions of opposite momentum near the Fermi surface. However, in systems with broken translational symmetry, such as dirty superconductors and atomic nuclei, the standard BCS theory does not directly apply. Anderson extended this framework by postulating pairing between time-reversed states [2], offering a more general explanation for superconductivity in these complex systems. In our cold atom experiment, we leverage precise control over atom number and interaction strength to explore the transition from pairing between time-reversed harmonic oscillator states to BCS-like pairing, and ultimately to molecular pairing at very strong interactions. These distinct regimes are characterized by their pair densities in both real and momentum space, which we experimentally probe using our single-atom and spin-resolved imaging techniques. Future objectives include studying the thermalization of few fermionic atoms, exploring open shell configurations akin to nuclear physics, and observing interference among identical few-body systems. [1] J. Bardeen, L. N. Cooper, and J. R. Schrieffer, Physical Review 108, 1175 (1957). [2] P. Anderson, Journal of Physics and Chemistry of Solids 11, 26–30 (1959).

Since the discovery of high-Tc superconductors around four decades ago, the search for materials with increasing critical temperatures has lead to the discovery of unconventional superconductivity in a number of compounds, among them copper- and nickel based superconductors. However, a complete microscopic understanding of these phenomena remains elusive, as both numerical simulations and experimental studies of these materials pose significant challenges. In my talk, I will present the setting of mixed dimensional (mixD) bilayers, where the interlayer hopping is entirely suppressed. I will explain how mixD bilayers can provide valuable insights into the mechanisms of superconductivity in cuprate and bilayer nickelate systems. Specifically, I will discuss the experimental realization of these bilayers using optical lattices, enabling the exploration of key features of superconductivity, such as pair-pair correlations. Finally, I will explore how such experimental platforms can be harnessed to enhance machine learning techniques, particularly in improving neural quantum state methods.

High-harmonic generation (HHG) is a process by which ultrashort (10−18−10−15 s) laser pulses can be generated. This is of immense interest as it opens up the possibility of time-resolved measurements at this time scale. Furthermore, HHG has potential as a spectroscopic due to various symmetry considerations. However, in 2018 Silva et. al. published HHG spectra from a study of a Mott insulator which showed signal at noninteger harmonics [1]. This was in stark contrast to more common solids where the odd-integer harmonics have been observed repeatedly. FIG. 1. HHG spectra for a 10-site long chain of atoms with relatively low correlation. Ncyc is the number of cycles in the pulse used. Each spectrum is scaled by the value in the associated textbox, with the exception of the Ncyc = 16 spectrum. Mott insulators are a class of materials which act as insulators due to significant beyond mean-field electronelectron interaction. Such solids are commonly referred to as correlated solids. Correlated solids are an interesting set of materials as the beyond mean-field electronelectron interaction results in significantly different dynamics than traditional solids, probably most notably the high-tc superconductivity of cuprates. Such solids are often simulated using the Fermi-Hubbard model, which is also the model we use to study the appearance of the noninteger harmonics. The Fermi-Hubbard model allows us to study systems both with and without correlation by varying the so-called Hubbard U-parameter. This feature makes it an ideal model to study the appearance of the non-integer harmonics, as the non-integer harmonics were only observed in the correlated solids. Using Floquet theory one can show that any timeperiodic system described by a single Floquet state can only generate integer harmonics. Furtermore, inversion symmetric targets only generate odd-integer harmonics. Here we utilized Floquet theory to explain how the noninteger harmonics appear as a result of the nonadiabaticity of the laser pulse. This is illustrated in Fig. 1 where HHG spectra for a variety of pulse lengths are shown. As the pulse length increases the high-harmonic spectra show increasingly clear peaks at odd-integer harmonics. We utilize the picture of Floquet states and Floquet quasi-energies to explain the appearence of non-integer harmonics, and where in the various HHG spectra they appear. Furthermore, we demonstrate how the generation of non-integer harmonics scale with the degree of correlation and relate this to the typical exitation mechanisms of such solids [2].

Light-matter interactions within the strong-field regime, such as high-harmonic generation, typically give rise to highly-oscillatory integrals, which are often solved using saddle-point methods. Not only do these methods promise a much faster computation, but they also inform a more intuitive understanding of the process in terms of quantum orbits, as the saddle points correspond to interfering quantum trajectories (think Feynman's path integral formalism). Despite these advantages, a sound understanding of how to apply saddle-point methods to highly-oscillatory integrals in a rigorous way, and with algorithms which work uniformly for arbitrary configurations and laser drivers, remains lacking. This hinders our ability to keep up with state-of-the-art experimental setups which increasingly rely on tightly-controlled laser waveforms. In this talk, I will introduce the key ideas of Picard-Lefschetz theory – the foundation of all saddle-point methods – and their implementation. Using high-harmonic generation and above-threshold ionisation as examples, I will show how those ideas provide a robust framework for the fast computation of integrals, as well as a widely-applicable algorithm to derive the relevant semiclassical quantum orbits that underlie the physical processes.

Understanding and controlling the electron dynamics in atoms and molecules is essential for studying material properties, chemical reactions, and ultrafast processes. In the past decade, there have been significant advances in developing table-top sources able to generate few-cycle pulses at high energies, and eventually obtain the attosecond time resolution necessary to access the electron motions. A key technique in this field is time-resolved X-ray absorption spectroscopy, which provides element-specific information [1,2]. So far, the method of choice for generating the few-cycle driving pulses has been the spectral broadening of laser pulses in a gas-filled hollow-core fiber (HCF) followed by a temporal compression stage via chirped mirrors or material dispersion. However, this method has typically remained limited to $\sim$2-cycle pulses. Here, we demonstrate the first application of soliton self-compression to create single-cycle pulses as drivers for soft-X-ray (SXR) high-harmonic generation (HHG). In this method, the fiber dispersion is inherently compensated by the gas nonlinearity, which avoids the need for post-compression stages. We present the first results from a beamline developed for attosecond transient absorption experiments using a mid-IR pump and attosecond SXR probe pulses. The experimental setup consists of a cryogenically cooled 1 kHz Ti:Sa laser that pumps an optical parametric amplifier to produce passively CEP-stable 2.4 mJ, 35 fs pulses centered at 1800 nm. The pulses are broadened in a 2.6-m, gas-filled hollow-core fiber (HCF), where the delicate interplay between the nonlinearity and fiber anomalous dispersion yields pulses with multi-octave supercontinuum spectrum and temporal self-compression. Although the soliton self-compression scheme at 1.8 $\mu$m has already been demonstrated [4], we apply such pulses both as a pump and a driver for generating the soft X-ray probe. Due to the broad spectrum and the short pulse duration, temporal characterization with common techniques as FROG or SPIDER, is challenging. Therefore, the TIPTOE method [3] has been implemented for a direct in situ measurement of the pulses directly at the sample position and to completely determine their electric-field profile. We control the time delay between the pump and probe using an interferometric split-toroidal mirror, which ensures stability between the two arms of $\sim$9 as. To find the best compression parameters and to explore the soliton regime, we have performed systematic pressure-dependent scans in HCFs with diameters of 530 $\mu$m, 500 $\mu$m, and 450 $\mu$m, filled with Ar, Ne, He. The shortest pulse of 2.9 fs (FWHM) has been obtained in the 530 $\mu$m HCF filled with 2 bar of Ne. Nevertheless, in this configuration, no HHG was observed. Our flux improved by a factor of $\sim$4 by using 450 $\mu$m HCF. In this configuration, the pulses are cleaner and the broadening is more symmetric around 1800 nm. With this scheme, the highest flux is generated in a pre-soliton regime (3 bar), with pulses of 11.6 fs (FWHM). In the soliton regime (3.5 bar) the flux slightly decreases. After this regime, the HH flux benefits from the presence of 1 mm fused silica (FS) on the beam after the HCF. We found that for a pump and probe experiment, the best configuration is at 3.5 bar with 1 mm FS, where the flux is very good and the mid-IR pulse is 5.15 fs, corresponding to a single-cycle pulse. Since quasi-single-cycle pulses have been obtained, strong-field ionization can be confined to a single half cycle, which will ensure sub-femtosecond resolution in water-window transient-absorption experiments. Our apparatus is an ideal tool for studying sub-femtosecond electron dynamics prepared by strong-field pump pulses such as charge migration at C and N K-edges in small organic molecules. Due to the pulse duration of the pump pulse, the same technique could be employed also for investigating ultrafast dynamics on thin film materials such as fullerene. References 1. K. S. Zinchenko et al, Science 371, 489–494 (2021). 2. Y. Pertot et al, Science 355, 264-267 (2017). 3. C. Brahms et al, Physical Review Research 2, 043037 (2020). 4. W. Cho et al, Scientific Reports, 9, 402–408 (2019).

Preparing single-mode photonic states with non-classical properties has long been a promising area of research connecting the fields of quantum optics and quantum computations. An intriguing path toward achieving these states has been proposed recently by means of high-order harmonic generation and post-selection. Yet, a quantum optical description of a strongly-driven emitter entangled with a selection of electromagnetic modes, which is crucial for shaping the resulting non-trivial states, has remained elusive. Here we demonstrate that this gap in understanding is bridged by considering the joint evolution of the emitter and the vacuum modes beyond the commonly used Markov approximation. By employing a novel stochastic method for describing the quantum field states, we demonstrate in numerical simulation how quantum harmonic emission can arise in an extremely trivial setup.

Sub-wavelength arrays of quantum emitters offer an interesting approach to coherent light-matter interfacing, using ultracold atoms or two-dimensional solid-state quantum materials. The combination of collectively suppressed photon-losses and emerging optical nonlinearities due to strong photon-coupling to mesoscopic numbers of emitters holds promise for generating nonclassical light and engineering effective interactions between freely propagating photons. In my talk I will describe the interaction between photons and a specific configuration of two-level atoms, namely two parallel 2D arrays individually acting like mirrors and together forming a cavity-like system. The long confinement of photons in this system results in an accumulation of correlation between the photons, revealing their strong effective interaction mediated by the atoms. While most studies have thus far relied on numerical simulations, I will furthermore describe a Green's function approach that permits analytical investigations of the nonlinear processes of the system. The approach yields intuitive insights into the nonlinear response of the system and offers a promising framework for a systematic development of a many-body theory for interacting photons and many-body effects on collective radiance in two-dimensional arrays of quantum emitters.

High-harmonic generation (HHG) is a process where a high-intensity driving  eld is up-converted into its harmonic orders. In atomic systems, HHG involves electron ionization, subsequent propagation in the continuum driven by the  eld, and recombination with the parent ion, during which harmonic radiation is generated. Therefore, as noted in this brief description, the electron dynamics underlying HHG in atomic systems are generally well understood. In this presentation, I will provide a description on how these electron dynamics can in uence the quantum optical state, leading to quantum correlations between the di erent modes of light, and the possibility of generating non-classical states of light through heralding operations. I will also discuss the potential for reproducing the strong- eld-driven electron dynamics using analog quantum simulators based on trapped ultracold atoms. Finally, if the time permits, I will brie y present recent results on driving HHG with non-classical light. This presentation is primarily based on [J. Rivera-Dean, arXiv:2409.15556 (2024)] and [J. Arguello-Luengo et al, PRX Quantum 5, 010328 (2024)].

Atoms confined in optical tweezer arrays constitute a platform for the implementation of quantum computers and simulators. State-dependent operations are realized by exploiting electrostatic dipolar interactions that emerge, when two atoms are simultaneously excited to high-lying electronic states, so-called Rydberg states. These interactions also lead to state-dependent mechanical forces, which couple the electronic dynamics of the atoms to their vibrational motion. We explore these vibronic couplings within an artificial molecular system in which Rydberg states are excited under so-called facilitation conditions. This system, which is not necessarily self-bound, undergoes a structural transition between an equilateral triangle and an equal-weighted superposition of distorted triangular states (Jahn-Teller regime) exhibiting spin-phonon entanglement on a micrometer distance. This highlights the potential of Rydberg tweezer arrays for the study of molecular phenomena at exaggerated length scales.

We formulate a temporal Clauser-Horne inequality by considering two parties choosing two observables to measure at different consecutive times. For two entangled antipodal spins joined by a spin chain, we show that the inequality is violated during a small finite time interval between the measurements. This fact contrasts with the time evolution in vacuum, which is describable in terms of a hidden-variable theory. Our result demonstrates that the finite velocity for quantum information spreading in the chain prevents signaling and therefore the immediate vanishing of quantumness.

I will present our work on a novel Rydberg qubit encoded in circular states of strontium atoms trapped in optical tweezers. Circular Rydberg states promise orders of magnitude longer lifetimes compared to their low-L counterparts, which allows for overcoming fundamental limitations in the coherence properties of Rydberg atom based quantum simulators. We have recently demonstrated efficient transfer into high-n circular Rydberg atoms with n≈80 via rapid adiabatic passage, which exhibit lifetimes of several milliseconds in our room-temperature setup. Furthermore, we realized a qubit between circular states of closeby hydrogenic manifolds coupled by a two-photon microwave transition and studied its coherence properties. Enabled by the second available valence electron of the Sr atom, we demonstrated trapping of the Rydberg atoms in standard Gaussian beams. In addition, we used the long coherence time of our qubit to probe the small quadrupole interaction between the electric field gradient of the circular Rydberg electron at the core position and the inner electron excited to a metastable D state. These results open exciting prospects for exploiting the unique properties of long-lived circular states of two-valence electron atoms for quantum technologies, comprising coherent ionic core manipulation.

Rydberg atoms provide tunable, long-range interactions which are applicable for a range of applications in quantum science. Incorporating with single-site control and readout of a quantum gas microscope, it allows us to explore many-body systems under long-range interactions. In the first set of experiments, we utilized a single Rydberg atom to switch strong light-matter interfaces of subwavelength atomic arrays via the "Rydberg blockade". The optical properties of the array can be rendered from transmissive to reflective, allowing control of the optical photons to be directionally transmited or reflected. These experiments demonstrate the building block towards creating deterministic atom-photon entanglement or realizing quantum-controlled metamaterials. In the second set of experiments, we off-resonantly couple to the Rydberg states, so called "Rydberg dressing". We improve the lifetime of Rydberg dressed states by operating with stroboscopically pulsed interactions to avoid facilitation losses. We then realize 1D extended Bose-Hubbard model (eBHM) and observe key features of repulsively-bound pairs, stabilization of charge density wave state, and density ordering of low-energy ensembles. The results pave the way for studying complex phase transitions under long-range interactions.

We report on the observation of two vibrational series of pure trilobite rubidium Rydberg molecules. These kinds of molecules consist of a Rydberg atom and a ground state atom. The binding mechanism is based on the scattering interaction between the Rydberg electron and the ground state atom. The trilobite molecules are created via three- photon photoassociation and lie energetically more than 15 GHz below the atomic 22F state. In agreement with theoretical calculations, we find an almost perfect harmonic oscillator behavior of six vibrational states. We show that these states can be used to measure electron- atom scattering lengths for low energies in order to benchmark current theoretical calculations. The molecules have extreme properties: their dipole moments are in the range of kilo-Debye and the electronic wave function is made up of high angular momentum states with only little admixture from the nearby 22F state. This high-l character of the trilobite molecules leads to an enlarged lifetime as compared to the 22F atomic state. Furthermore, our ion pulse spectrometer provides insights into the decay processes.

Trilobite molecules are ultralong-range Rydberg molecules formed when a high angular momentum Rydberg electron scatters off of a ground-state atom. Their unique electronic structure and highly oscillatory potential energy curves support a rich variety of dynamical effects yet to be explored. We analyze the vibrational motion of these molecules using a framework of adiabatic wavepacket propagation dynamics and observe that for appropriate initial states, the trilobite potential acts as molecular diffraction grating. Hence, we propose a time resolved pump-probe scheme designed for the realization of the diffraction effect in question, and advertise the utilization of a single diatomic Rydberg molecule as a testbed for the study of exaggerated quantum dynamical phenomena. Furthermore, we discuss the possibility of non-adiabatic effects in such systems after a brief introduction to the beyond Born-Oppenheimer physics in these molecules.