Atomic Physics 2024

High-order harmonic generation (HHG) in solids is strongly affected by the dephasing of the coherent electron-hole motion driven by the laser field. The physical mechanisms underlying this dephasing, crucial for understanding and modelling HHG spectra, have remained disputable and controversial, often regarded more as an empirical observation than a firmly established principle. In this contribution, we present comprehensive experimental findings on the wavelength-dependency of HHG in both single-atomic-layer and bulk semiconductors. These findings are further supported by numerical simulations, employing ab initio real-time, real-space time-dependent density functional theory and semiconductor Bloch equations. Our experimental observations necessitate the introduction of a novel concept: a momentum-dependent dephasing time in HHG. Our experimental and numerical results allow to pinpoint momentum-dependent electron-phonon scattering as the predominant mechanism driving dephasing. This insight significantly advances the understanding of dephasing phenomena in solids, addressing a long-standing debate in the field. Furthermore, our findings pave the way for a novel, all-optical measurement technique to determine electron-phonon scattering rates and establish fundamental limits to the efficiency of HHG in condensed matter.

Photoionization, or photoelectric effect, is one of the universally acknowledged manifestations of the quantum nature of matter that led to the discovery of energy quanta. Less widely appreciated is the fact that it bears the mark of yet another fundamentally quantum concept – the entanglement. When a quantum system, such as an atom or a molecule, is ionized, it is broken up into a pair of quantum-mechanically entangled sub-systems: the emitted photoelectron and its parent ion [1]. The coherences responsible for photoelectron-ion entanglement arise at the attosecond and persist at the femtosecond time scales, underpinning the few-femtosecond charge dynamics in the parent ion [2]. Yet quantum entanglement in photoionization has never been probed and verified yet, e.g. by the celebrated Bell tests. In this work, we design theoretically and model numerically a direct probe of quantum entanglement in attosecond photoionization in the form of a Bell test [3]. We simulate from first principles a Bell test protocol for the case of noble gas atoms photoionized by ultrashort, circularly polarized infrared laser pulses in the strong-field regime, predicting robust violation of the Bell inequality. The complete photoionized state is obtained by ab initio simulations based on the advanced time-dependent B-spline ADC method [1] with spin-orbit coupling. The Bell test developed in our work [3] detects entanglement between the internal states of the Ar$^{+}$ atomic ion and the photoelectron’s spin states by exploiting the spin polarization of the photoelectron. This theoretical result paves the way for the direct observation of entanglement in the context of ultrafast photoionization of many-electron systems. Our work provides a novel perspective on attosecond physics directed toward the detection of quantum correlations between systems born during attosecond photoionization and unraveling the signatures of entanglement in ultrafast coherent molecular dynamics, including in the chemical decomposition pathways of molecular ions. References. [1] M. Ruberti, Phys. Chem. Chem. Phys. \textbf {21}, 17584 (2019). [2] D. Schwickert, M. Ruberti, P. Kolorenč, et al, Science Advances \textbf {8} (22), eabn6848 (2022). [3] M. Ruberti, V. Averbukh, F. Mintert, Phys. Rev. X, in production (2024).

Photon pairs generated through spontaneous parametric down-conversion constitute a well-established approach for creating entangled bipartite systems. Laguerre-Gaussian modes, which carry orbital angular momentum (OAM), are commonly used to engineer high-dimensional entangled quantum states within the spatial domain. For Hilbert spaces with dimension $d>2$, maximally entangled states (MESs) enhance the capacity and security of quantum communication protocols and increase the efficiency of quantum-computational tasks. However, directly generating MESs within well-defined high-dimensional subspaces of the infinite OAM basis remains challenging. In this work, we formalize how the spatial distribution of the pump beam and phase-matching conditions within the nonlinear crystal can be utilized to generate MESs without additional spatial filtering of OAM modes in a given subspace. We demonstrate our method with maximally entangled qutrits ($d=3$) and ququints ($d=5$).

Epitaxial semiconductor quantum dots (QDs) have long been investigated in the context of quantum physics and quantum information processing (QIP). The solid-state nature of the quantum dots poses many challenges. One such challenge comes from the magnetic moments of the atomic nuclei that make up the crystal lattice of a QD. The dense 3D lattice of the nuclear spins often acts as a source of magnetic noise, limiting quantum coherence of the electron and photon qubits. However, introduction of a new generation of low-strain optically-active GaAs/AlGaAs QDs has shifted the paradigm with recent efforts focused on harnessing nuclear spin magnetism as a testbed for fundamental quantum physics and QIP applications. The advances of the past few years include demonstrations of electron [1] and nuclear [2] spin qubits in a semiconductor quantum dot, as well as reversible transfer of quantum states between electron and nuclear spins [3], offering a pathway to implementation of a solid-state quantum memory. I will discuss recent advanced both in fundamental physics and prospective applications of QD nuclear spins in QIP. Recent findings include an experimental answer to the long-standing dilemma of nuclear spin diffusion in a central-spin model [4]; ferromagnetic ordering of nuclear spin ensembles, with record-high polarisations exceeding 95% [5]; nondemolition measurement of the central electron spin through entanglement with a nuclear spin ensemble [6], which allows for single-shot qubit readout with fidelities exceeding 99.85%. Moreover, we show how strain-engineering of semiconductor lattice can be used to turn the nuclear spin ensemble into an efficient quantum memory, which can store coherent states for very long times, exceeding 100 ms. [1] L. Zaporski et al., Nature Nano 18, 257 (2023) [2] E. A. Chekhovich et al., Nature Nano 15, 999 (2020) [3] M. Appel, et al., arXiv:2404.19680 (2024) [4] P. Millington-Hotze, et al., Nature Comm. 14, 2677 (2023) [5] P. Millington-Hotze, et al., Nature Comm. 15, 985 (2024) [6] H. Dyte et al., Phys. Rev. Lett. 132, 160804 (2024)

Periodic driving of systems of particles can create crystalline structures in time. Such systems can be used to study solid-state physics phenomena in the time domain. In addition, it is possible to engineer the wave-number band structure of optical systems and to realize photonic time crystals by periodic temporal modulation of the material properties of the electromagnetic wave propagation medium. We introduce here a versatile averaged-permittivity approach which empowers emulating various condensed matter phases in the time dimension in a traveling wave resonator. This is achieved by utilizing temporal modulation of permittivity within a small segment of the resonator and the spatial shape of the segment. The required frequency and depth of the modulation are experimentally achievable, opening a pathway for research into the practical realisation of crystalline structures in time utilising microwave and optical systems.

We formulate a general hybrid quantum-classical technique to describe the interaction of diatomic molecules with XUV pulses. We demonstrate the accuracy of our model in the context of the interaction of the O$_2$ molecule with an XUV pulse with photon energy ranging from 20 eV to 42 eV. We account for the electronic structure and electron ionization quantum mechanically employing accurate molecular continuum wavefunctions. We account for the motion of the nuclei using classical equations of motion. However, the force of the nuclei is computed by obtaining accurate potential-energy curves of O$_2$ up to O$_2^{2+}$, relevant to the 20 eV-42 eV photon-energy range, using advanced quantum-chemistry techniques. We find the dissociation limits of these states and the resulting atomic fragments and employ the Velocity Verlet algorithm to compute the velocities of these fragments. We incorporate both electron ionization and nuclear motion in a stochastic Monte-Carlo simulation and identify the ionization and dissociation pathways when O$_2$ interacts with an XUV pulse. Focusing on the O$^+$ + O$^+$ dissociation pathway, we obtain the kinetic-energy release distributions of the atomic fragments and find very good agreement with experimental results. Also, we explain the main features of the KER in terms of ionization sequences consisting of two sequential single-photon absorptions resulting in different O$^+$ and O$^{2+}$ electronic state configurations involved in the two transitions. (see Ref[1]) Moreover, we obtain continuum molecular wavefunctions for open-shell molecules in the Hartree-Fock framework. We do so while accounting for the singlet or triplet total spin symmetry of the molecular ion, that is, of the open-shell orbital and the initial orbital where the electron ionizes from. Using these continuum wavefunctions, we obtain the dipole matrix elements for a core electron that ionizes due to single-photon absorption by a linearly polarized x-ray pulse. Using these time-delays are obtained for core-level photoionization of NO with very good agreement with experimental results. (see Ref[2]) References: [1] M. Mountney et al. arXiv:2403.20098 (2024) [2] T. Driver, M. Mountney, et al., A. Emmanouilidou, A. Marinelli and J. Cryan, Nature 632, 762 (2024).

Electron degrees of freedom offer an appealing tool to better understand and potentially control nuclear states through light. In this work, we measured the photoelectrons produced upon the photo-excitation of the Mössbauer nuclear transition in Fe57. The photoelectron spectrum carries a clear signature of the hyperfine structure of the nuclear state and shows a surprising coupling to multiple phonon modes of the Fe57 lattice. Our work sets a new benchmark for the energy-resolved photoelectron spectroscopy of nuclear transitions, promising a relevant impact on our understanding of the energy exchange between nuclear states and electron states in atoms.

I will discuss cross-sectional nanoscale imaging in the extreme ultraviolet (XUV) spectral region using high-harmonics produced by femtosecond laser radiation. The imaging technique is particularly easy to understand in time-domain: An attosecond pulse incident on a sample is reflected at the internal structures of the sample. As a consequence, a series of attosecond pulse replicas is generated. The delay between these pulse replicas is on the order of 100 to a few 100\,as, corresponding to structures on the order of 10s to 100s nanometer. Naturally, the pulse replicas differ in spectral amplitude and phase, depending through which and how much material they have propagated. In any case, their spectral interference can be measured by an XUV spectrometer and used to reconstruct the internal structure of the sample. In fact, it is possible to retrieve the phase of the XUV radiation reflected by the sample. Accordingly, the \textit{field} of the train of pulse replicas is known. A particularly relevant application of XCT for the spectral range up to 100 eV are silicon-based samples. We have demonstrated depth resolutions of 20 nm and very high sensitivities. Buried oxide layers of a thickness of a few nanometers could be detected as well as buried monolayers of graphene. Thanks to the ability to reconstruct the field, it is even possible to identify the material encapsulated in silicon and to determine also properties like layer roughness without destroying the sample. A unique perspective is ultrafast imaging.

We show that controlling two-photon ionization with a chirp, originally predicted for linearly-polarized pulses [1], applies to circular polarization as well. In this case the underlying mechanism is particular transparent in the rotating frame. Experimental demonstration of this mechanism for the Helium atom has been achieved at FERMI together with the Freiburg group [2]. [1] Saalmann, Giri and Rost, Phys.Rev.Lett. 121 (2018) 153203. [2] Richter, Saalmann, ... Bruder, arxiv.org/2403.01835 (2024).

In our studies, we use attosecond photoelectron interferometry to investigate photoionization dynamics on its natural timescale, employing high harmonic generation (HHG) and seeded free-electron lasers to generate extreme ultraviolet (XUV) attosecond pulse trains. Our lab-based studies using HHG, focus on molecular photoionization examining the influence of nuclear dynamics. Our approach combines two-color interferometric techniques with photoelectron-photoion coincidence spectroscopy, which allows us to record the photoelectron spectra in a mixture of $CH_4$ and $CD_4$. The different nuclear evolutions in the two isotopologues manifest as modifications in the amplitude and contrast of the two-color signal, suggesting that nuclear dynamics affect the coherence properties of the emitted electronic wave packet. Using seeded free-electron lasers, we introduce a novel attosecond timing tool for single-shot characterization of the relative phase between XUV and the infrared field, essential to perform interferometric studies due to the stochastic relative phase between the two fields. Implementing our correlation-based approach, we demonstrate attosecond coherent control of electronic wave packet released in the process of two-color photoionization of helium.

The difference in photoionization delay between electrons ionized from the 2s or 2p orbitals in neon is an attosecond physics success story. Here measurements from Anne L'Huillier's group (Science 358, 893, 2017) isolated the pure 2s delay from that of nearby shake-up states, and several theoretical descriptions were able to reproduce the experimental results. The situation in argon has, although the system should be just slightly more complicated, proven to be much harder to understand. The difference in photoionization delay between electrons ionized from the 3s or 3p orbitals in the vicinity of the so-called Cooper minimum differs even in sign when comparing different approximations, and the isolation of the pure 3s delay from that of the shake-ups has been harder to achieve experimentally. Very recently new experiments have, however, been able to give a definite answer with regard to the sign. It turns out that details in electron correlation can have a significant effect on the phase of the outgoing wave packet, although the amplitude is not much affected. This will discussed, as will the phase change over resonances when studied with the RABBIT technique.

The recent and future developments of laser sources with extremely high peak intensities is driven by various motivations like achieving very high photon fluxes for single-shot molecular structure analysis, studying matter under extreme conditions, or even trying to achieve pure vacuum break-down, i.e. the spontaneous pair creation in the absence of supporting Coulomb fields. These advances need to be supported by a deeper understanding of the microscopic understanding of matter in extremely intense laser fields. Since in most cases it is expected that neutral atoms and molecules will be stripped of most of their electrons already on the rising edge of the laser pulse, it is of interest to study the behaviour of highly charged ions in intense laser fields. Due to the large nuclear charge, the interaction of highly charged ions with very intense laser pulses will occur almost exclusively in the quasi-static regime. Therefore, we have studied the ionization behaviour of highly charged ions in the (quasi-)static limit solving the time-independent Dirac equation. Based on these results, approximate scaling relations (allowing for a laser-pulse calibration or to uniquely identify relativistic effects), the use of a modified Schrödinger equation for emulating the fully relativistic results of the Dirac equation, and non-dipole effects will be discussed.

A light wave can be diffracted by a grating made by usual material, resulting in equally spaced interference fringes. On the contrary, an electron can also be diffracted by a standing wave of light, which is called Kapitza-Dirac (KD) effect. Although it was already predicted at the early ages of quantum mechanism [1], experimental realization was only possible 20 years before [2]. Very recently, the Frankfurt group observed the time evolution of electron phase with KD and referred it as ultrafast Kapitsa-Dirac effect (UKD) [3]. In this talk, I will show that both KD and UKD can be well understood whether regarding electron as a quantum or classical object. The saddle point integral of the path integral bridges the quantum and classical aspects, and also provides the criteria for the feasibility of classical pictures. Meanwhile, I will also show that one can reconstruct the classical trajectory of electron in coulombic field, or the phase of coulomb wave function using UKD. [1] P. L. Kapitza and P. A. M. Dirac, The reflection of electrons from standing light waves, Proc. Camb. Phil. Soc. 29, 297 (1933). [2] D. L. Freimund, K. Aflatooni, and H. Batelaan, Observation of the Kapitza–Dirac effect, Nature 413, 142 (2001). [3] K. Lin et al., Ultrafast Kapitza-Dirac effect, Science 383, 1467 (2024).

Free electron laser facilities have sprout all over the world. These light sources can produce ultrashort pulses, already in the sub-femtosecond regime, with enough intensity to induce non-linear phenomena in gas phase atoms and molecules. One of the most fundamental non-linear processes, two-photon ionization has been object of recent experiments, exploring and exploiting new aspects of well-known light-induced physical problems such as Rabi oscillations [1] or light-induced interferences leading to asymmetric photoelectron emission from simple atoms [2,3]. The present work proposes new schemes to employ these light sources to access information on dynamical electron correlation effects in double photoionization problems. This theoretical study first explores the electron dynamics of hydrogen using strong fields that alter the molecular potential, with relatively long wavelengths, and then investigate the double ionization of helium using a two-color scheme. In the first scenario, we examine the strong variation of the ionization yield, as well as the depletion of the ground state of the H atom with the laser intensity and compare with existing data [4]. In the second scenario, although the laser intensities are large, we employ much shorter wavelengths, thus keeping the problem within a perturbative regime. We then demonstrate how the double ionization yield can be manipulated by employing a given time-delay between these pulses of different color. In both cases, we employ a numerical approach based on the numerical solution of the time-dependent Schrödinger equation (TDSE) in full dimensionality. The wave function is described using a Finite Element Method with a Discrete Variable Representation (FM-DVR), which greatly simplifies the numerical implementation. The TDSE is the solved employing a Cranck-Nicholson [5] or Lanczos propagator [6]. The scattering function, corresponding to a specific single or double ionization channel, is then extracted by an implicit propagation to infinite time using an Exterior Complex Scaling (ECS) of the electronic coordinates, followed by a Fourier transform [5,7] [1] S. Nandi et al, Nature 608, 488 (2022) [2] M. Di Fraia et al., Phys. Rev. Lett. 123, 213904 (2019) [3] D. You et al., Phys. Rev. X 10, 031070 (2020) [4] J. Rowan et al., Phys. Rev. E 101, 023313 (2020) [5] A. Palacios, T. N. Rescigno and C. W. McCurdy, Phys. Rev. A 77, 032716 (2008) [6] A. Palacios, T. N. Rescigno and C. W. McCurdy, Phys. Rev. A 79, 033402 (2009) [7] J. Feist et al., Phys. Rev. A 77, 043420 (2008)

High-harmonic generation (HHG) has become an essential method for investigating ultrafast electron dynamics. While HHG processes in gases and solids are fairly well understood [1,2], limitations in earlier knowledge restricted the use of high-harmonic spectroscopy (HHS) for studying light-driven electron behavior in bulk liquids. However, recent discoveries indicate that electron trajectories limited by scattering serve as the central mechanism for HHG in liquids [3]. Experiments across diverse laser parameters have demonstrated that in liquids such as H$_2$O, D$_2$O, and alcohols, the cutoff energy (E$_c$) remains fixed due to the limited mean free path (MFP) of electrons, resulting in an E$_c$ that does not vary with laser wavelength, intensity, or pulse duration [3,4]. Simulations on H$_2$O clusters and bulk water confirm this fixed cutoff, linking it to the scattering-restricted nature of electron motion in liquids. This insight has opened new possibilities for in-situ measurements of the time scales linked with light-induced electron dynamics in liquids. In this work, we use two interferometric techniques to examine the temporal dynamics of recolliding electron wave packets in liquids and aqueous solutions. First, by using a two-color light field to actively modulate electron trajectories [5,6], we measure the atto-chirp of liquid harmonics. Interestingly, we observe a large, linear chirp in liquids, which is significantly more pronounced than in gases. Comparisons with strong-field approximation (SFA) calculations suggest that this chirp reflects an effective band gap that is several electron volts lower than the field-free band gap, a reduction linked to the impact of the intense driving field as predicted by Floquet theory calculations. This atto-chirp, detected through active interferometry, reveals details of the recombination times of recolliding electron wave packets. In a complementary approach, we use passive interferometry with aqueous salt solutions (NaCl, NaBr, NaI) and find that modulating salt concentrations and the anions selectively dampen certain harmonics. This observation aligns with a two-emitter model (solvent + anion), where differences in ionization energies introduce ionization delays that produce phase shifts ($\Delta \phi (\omega)$) in high-harmonic emissions consistent with the reduced band gap seen in pure liquids. By utilizing the effective ionization energy difference $\Delta I_p$, we derive electron excursion times for various harmonics. These techniques collectively enable the measurement and modulation of effective band gaps in liquids, achieved either dynamically through a light field or passively via the introduction of dopant ions. References: [1] P. B. Corkum, Phys. Rev. Lett. 71, 1994-1997 (1993), DOI: https://doi.org/10.1103/PhysRevLett.71.1994 [2] S. Ghimire S and D. A. Reis, Nature Physics 15, 10-16 (2019), DOI: https://doi.org/10.1038/s41567-018-0315-5 [3] A. Mondal et al. Nature Physics 19, 1813–1820 (2023), DOI: https://doi.org/10.1038/s41567-023-02214-0 [4] A. Mondal et al. Optics Express 31, 34348–343461 (2023), DOI: https://doi.org/10.1364/OE.496686 [5] N. Dudovich et al. Nature Physics 2, 781–786 (2006), DOI: https://doi.org/10.1038/nphys434 [6] G. Vampa et al. Nature 522, 462–464 (2015), DOI: https://doi.org/10.1038/nature14517

Femtosecond time-resolved studies of molecular bond-breaking has been the subject of a vast number of studies since the pioneering work by Zewail and coworkers in the late 1980s and it remains a very active research area. Due to its unimolecular nature, bond breaking is fairly straightforward to explore experimentally. By contrast, time-resolved studies of bond making between two molecules or atoms is experimentally much more challenging. The key difficulty is to clock the bimolecular reaction, i.e. measure when the two reactants meet because this is determined by diffusion – a process that is not controllable on ultrafast time scales. Therefore, the few previous works that explored bimolecular reactions used weakly bonded van der Waals complexes as starting points to eliminate diffusion. In this talk, I will show recent experimental findings that allowed us to measure, in real time, the formation of a Li$^+$--benzene complex stating from a Li$^+$ ion and a benzene molecule initially separated by 35 Å. Our experimental scheme employs nanometer-sized droplets of liquid helium to ensure a well-defined starting geometry for the diffusion process and ensuing bond formation, and to serve as a solvent into which the \$sim$1.5 eV binding energy of the cation-molecule complex can be dissipated.

It is well known that solvation shells, of Helium atoms, cage the ion giving rise to the formation of solid-like structures, i.e. snowballs, in the otherwise superfluid Helium droplet[1]. Here, we demonstrate that for sufficiently large droplets a third regime appears between the snowball and the liquid one with a supersolid structure. Namely, the Helium density exhibits a periodic modulation on a spherical shell. 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) method [2] 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

Resonances are crucial in a variety of systems and reactions. Recent studies have highlighted the potential and effectiveness of intense IR pulses in inducing and controlling atomic resonance spectra. However, light-induced vibrational resonances in photodissociation spectra have not been thoroughly studied and controlled, partly due to the complex interaction between vibrational dynamics and intense IR pulses. To address this issue, we propose incorporating the bound potential into a dissociative continuum using a UV pulse. Notably, this UV pulse does not initiate photo-excitation from the ground state but effectively couples the vibrational continuum with an excited bound state. By modulating the frequency of the embedding pulse, we gain the ability to tailor the asymmetric profiles of UV pulse-induced vibrational resonances, which in turn significantly affects the photodissociation process. This is demonstrated in our simulations of kinetic energy release spectra in diatomic and polyatomic molecules. These proof-of-principle examples offer new opportunities for controlling photo-induced fragmentation and photo-chemical reaction pathways in various molecular systems.

Attosecond-pump attosecond-probe spectroscopy (APAPS) has often been regarded as the most straightforward way to investigate and understand electron dynamics on extremely short timescales. Here I will report on our efforts to perform APAPS using high-harmonic generation (HHG). Recently, we have demonstrated table-top all-attosecond transient absorption spectroscopy (AATAS) for the first time. Results on electron dynamics obtained in atoms, molecules and solids will be presented. Furthermore, I will shortly summarize our activities on increasing the repetition rate at which APAPS can be performed. To this end, first results on APAPS using a 40 kHz ytterbium-based driving laser will be presented. This setup is ideally suited to perform electron spectroscopy in low-density samples and will be used to study charge migration in biologically relevant molecules.

The fluctuating electromagnetic field leads to a variety of mesoscopic phenomena, including the famous Casimir or van der Waals effects. Recent interest and work has gone far beyond these original considerations in many aspects, for example, by including non-equilibrium scenarios, investigation of nanoscopic geometries, or by studying modern materials, both in theory as well as in experiments. In this contribution, I will introduce scattering theory as a tool for analysis and investigation of phenomena induced by the fluctuating electromagnetic field in the mentioned situations. Specific examples include recent work on fluctuation induced forces acting between non-reciprocal media [1][2] as well as thermal conductivity from electromagnetic fluctuations [3]. References [1] D. Gelbwaser-Klimovsky, N. Graham, M. Kardar, M. Krüger, Phys. Rev. Lett. 126, 170401 (2021) [2] D. Gelbwaser-Klimovsky, N. Graham, M. Kardar, M. Krüger, Phys. Rev. B 106, 115106 (2022) [3] M. Krüger, K. Asheichyk, M. Kardar, R. Golestanian, Phys. Rev. Lett. 132, 106903 (2024)

Atom surface Casimir-Polder potential is intrinsically difficult to measure due to distances between atom and surface smaller than few 100 nm. To conceive an experiment devoted to an accurate measurement in such a range of distance is subbtle. We have chosen to build an hybrid system using nanotechnology facilities and cold atoms potentiality. We realised transmission nano-gratings crossed by an adjustable low velocity atomic beam of metastable Argon. A meticulous approach using the 1D Schrödinger equation solution with a reasonable Casimir-Polder potential approximation leads us to carefully estimate the model validity. Consequently, the statistical and systematic error bars on the potential are investigated and appear to be promising.

Highly excited (Rydberg) atoms in vapour cells have recently attracted significant attention as sensitive sensors of electromagnetic fields and as single photon sources for quantum technology applications. Rydberg atoms also present a fundamental interest for studying atom-surface interactions, because they expose limitations in the traditional approach of Casimir-Polder (CP) theory. Indeed, when Rydberg atoms interact with surfaces in the extreme near-field, the dipole approximation breaks down and higher-order terms need to be considered. This is because the diameter of Rydberg atoms compares to the probing depth of spectroscopic experiments in nanocells filled with atomic vapours. Here I will present our recent calculations of the dipole-dipole and the combined quadrupole-quadrupole and dipole-octupole CP coefficients for alkali Rydberg atoms. I also examine the effects of higher-order interactions in nanocell transmission spectroscopy. Finally, I will present the results of an ongoing experiment probing atoms in a nanocell whose thickness varies from 50-800nm. The recorded transmission spectra show a clear shift of the atomic resonance due to strong CP interactions allowing us to extract the CP dipole-dipole coefficient of Rydbergs atoms by fitting our theoretical model to the experimental curves. Quantifying systematic effects due to the interactions with parasitic electric fields from charge build-up on the windows is an important challenge on the road towards measuring CP quandrupole interactions .

In the constant race towards miniaturization, the technological relevance of fluctuation-induced phenomena is rapidly increasing. Indeed many of these effects, which are often negligible at the macroscopic scale, can become crucial for microscopic systems. Paradigmatic examples are van der Waals / Casimir-Polder forces between atoms and/or molecules as well as the Casimir effect between larger objects. These phenomena can be both useful and disruptive and have to be taken into account in the designing microscopic devices, especially if atomic systems are involved. The investigation and understanding of these interactions are therefore important for the challenges and opportunities that they offer to modern quantum technologies. In this talk I will present some recent results in this field of research. I will focus on electromagnetic fluctuation-induced interactions, devoting particular attention to the role that material properties and geometry play in characterizing their behavior.

Typically, ultrafast phenomena are studied by pump-probe techniques providing the dynamics of averaged system properties after excitation. Recent advances enable a time-domain access also to their elementary fluctuations both in and out of equilibrium. Examples will be featured concerning the quantum noise of the mid-infrared electromagnetic field, statistics of electron transport at the atomic spatio-temporal scale and magnonic correlations in antiferromagnets.

I will review recent theoretical results on the role of quantum fluctuations in backreaction phenomena induced by the dynamical Casimir emission [1,2] and (analogue) early universe preheating [3]. In both cases, I will show that the backreaction affects the dynamics of the background system by inducing dissipation, fluctuations and decoherence. I will finally discuss implications of these results on the validity of the usual semiclassical description of backreaction, and assess experimental observability of the predicted effects in realistic analog model systems based on superconducting circuits and on ultracold atomic systems. [1] S. Butera and I. Carusotto, Phys. Rev. A 99, 053815 (2019). [2] S. Butera and I. Carusotto, Europhys. Lett. 128, 24002 (2019). [3] S. Butera and I. Carusotto, Phys. Rev. Lett. 130, 241501 (2023).

T. Schoger$^{1,2}$, B. Spreng$^3$, G.-L. Ingold$^1$, P. A. Maia Neto$^4$ and S. Reynaud$^2$ $^1$ Universität Augsburg, Augsburg, Germany $^2$ Laboratoire Kastler Brossel, Sorbonne Université, CNRS, ENS-Université PSL, Collège de France, Paris, France $^3$ University of California, Davis, USA $^4$ Universidade Federal do Rio de Janeiro, Rio de Janeiro, Brazil We investigated the Casimir interaction between two spherical objects at arbitrary temperatures and for different media. Our study includes analytical solutions for the Casimir force between two Drude spheres in vacuum, two dielectric spheres immersed in an electrolytic solution and two perfect electromagnetic conductor (PEMC) spheres. The sphere-sphere geometry is particularly important because it is used in experiments that measure the Casimir force (e.g. [1,2]). It is also one of the few non-trivial geometries in which the Casimir interaction can be calculated analytically. For the system of two Drude spheres, we were particularly interested in the classical Casimir interaction, the force arising from thermal fluctuations of the electromagnetic field. It was previously found that an analytical expression can be derived for the sphere-plane geometry [3]. We showed that this also holds for two non-equally sized spheres by relating the scattering problem between the spheres to a combinatorial problem of bi-coloured integer partitions [4]. In a recent experiment [1] involving two dielectric spheres in salted water, it was found that the Casimir force is not screened for the part induced by low-frequency transverse magnetic fluctuations. The Casimir force is thus expected to contribute to a long-range interaction, which should be relevant for biophysical interfaces and colloidal systems. We derived a semi-analytical expression for the two dielectric spheres which is accurate enough for most practical applications, with no need to go through numerical computations [5]. While the Casimir force in the two aforementioned setups is attractive, systems where a repulsive Casimir force occurs, have been also of interest for a long time. The possibility of switching the sign of the Casimir force by external control parameters like the temperature is of particular importance and has possible practical applications in nano- and microelectromechanical systems. One idealized system which leads to Casimir repulsion involves PEMC materials. PEMCs interpolate between perfect electric and perfect magnetic conductors. Previous research involving two dissimilar PEMC plates at zero temperature demonstrated a vanishing Casimir force [6]. We build upon this discussion by analyzing two PEMC spheres at finite temperatures in order to explore how the interplay between geometry, temperature, and material properties influences the sign of the Casimir force [7]. References [1] L. B. Pires, et al., Phys. Rev. Res. 3, 033037 (2021) [2] J. L. Garrett, D. A. T. Somers and J. N. Munday, Phys. Rev. Lett. 120, 040401 (2018) [3] G. Bimonte and T. Emig, Phys. Rev. Lett. 109, 160403 (2012) [4] T. Schoger and G.-L. Ingold, SciPost Phys. Core 4, 011 (2021) [5] T. Schoger, B. Spreng, G.-L. Ingold, P. A. Maia Neto, and S. Reynaud, Phys. Rev. Lett. 128, 230602 (2022) [6] S. Rode, R. Bennett and S.Y. Buhmann, New J. Phys. 20, 043024 (2018) [7] T. Schoger and G.-L. Ingold, Phys. Rev. A 109, 052815 (2024)

The free expansion of a wave packet is one of the simplest problems of classical optics (CO) and quantum mechanics (QM). In CO it provides a clear picture of the wave to beam transition. In QM it does the same for the quantum to classical transition. It will be shown that the approximations leading to the paraxial equation of CO and the 2-d time-dependent Schroedinger equation are identical. In wave packet propagation the Hermite-Gauss modes(CO) and the equivalent Harmonic Oscillator eigenfunctions of QM play a prominent role. A frame transformation is introduced to render these space-dependent functions constant. In this frame, co-moving with the stream lines (CO) or the Bohmian trajectories (QM), the Gouy phase (L.G. Gouy 1890) is dominant and plays the role of the proper time. An expansion of Gauss slit functions in these basis modes gives simple new insight into the interference leading to Young's fringes (T. Young 1801).

In recent years, vacuum-induced modifications of molecular properties have regained considerable attention in the context of cavity QED, where the coupling of matter to individual electromagnetic modes is strongly enhanced by a tight confinement of the field. It has been speculated that under such ultrastrong coupling conditions, the electromagnetic vacuum could change the rate of chemical reactions or modify work functions, phase transitions and (super-)conductivity, even without externally driving the cavity mode. Here we investigate the ground state energy shift of a single dipole due to its coupling to the electromagnetic vacuum in a confined geometry and address the fundamental question of whether or not it is possible to achieve conditions under which the light-matter coupling can result in nonperturbative corrections to the dipole’s ground state. To do so we consider two simplified, but otherwise rather generic cavity QED setups, which allow us to derive analytic expressions for the total ground state energy and to distinguish explicitly between purely electrostatic and genuine vacuum-induced contributions. Importantly, this derivation takes the full electromagnetic spectrum into account while avoiding any ambiguities arising from an ad-hoc mode truncation. Our findings show that while the effect of confinement per se is not enough to result in substantial vacuum-induced corrections, the presence of high-impedance modes, such as plasmons or engineered LC resonances, can drastically increase these effects.

Spontaneous time-translation symmetry breaking had not attracted much attention until Wilczek introduced the concept of time crystals. Despite this particular realization being prohibited by the ,,no-go'' theorem, the idea inspired a new version of time crystals, i.e. the discrete time crystals (DTCs). In general, a DTC is a periodically driven quantum many-body system that spontaneously breaks the discrete time-translation symmetry of the Hamiltonian due to particle interactions and starts evolving with a period s-times, where s is integer, longer than the period of the external driving. One platform for realizing DTC consists of a single ultracold atomic cloud, i.e. weakly interacting bosons, bouncing resonantly on a periodically driven atom mirror. In our work, we extend this concept by considering two distinct ultracold atomic clouds. In our setup, atoms in different clouds interact with infinite repulsive strength, while atoms within each cloud interact attractively. The system is one-dimensional and placed in a gravitational field, with the lower atomic cloud bouncing on an oscillating mirror. Due to the infinite repulsive inter-species interaction, the lower cloud effectively acts as a driving force for the upper cloud. We investigate how sufficiently strong intra-species interactions can induce discrete time-translation symmetry breaking, leading to the formation of a complex DTC.

A convenient method to describe light matter interaction in cavity resonators is to reduce the involved degrees of freedom to the absolute minimum. In the context of a localized quantum emitter in a lossy cavity, the so-called pseudomode approach condenses the effect of the electromagnetic field on the emitter’s dynamics in a discrete set of effective modes. These modes absorb the strongly-coupling field’s degrees of freedom and the weakly-coupling ones are usually represented as an external “environment”, allowing one to efficiently describe the emitter’s dynamics, e.g. by Markovian Lindblad master equations. This system-environment separation becomes ever more difficult, though, as the system’s complexity and/or the number of strongly coupled degrees of freedom increase. Here, we construct a fully analytical and non-perturbative pseudomode model for open cavities by “reverse-engineering” from the exact, position-resolved spectral density within the cavity. This subsequently guarantees the construction of an optimal set of modes that efficiently captures the emitter’s dynamics. Our method thus generalizes the application of the standard pseudomodes to more complex targets such as condensed matter or extended atomic systems and even to very leaky open cavities.

We analyse the dispersion force between an atom and a (semi)conducting surface, using tools of fluctuation electrodynamics. The electromagnetic response of the surface is described with the help of diffusive or hydrodynamic charge transport models. As a function of distance $d$ and (equilibrium) temperature, we find cross-overs between non-retarded ($\sim 1/d^3$) and retarded ($\sim 1/d^4$) power laws. The dependence on the bulk conductivity is analysed in detail in order to elucidate the behaviour of the van der Waals entropy associated with the atom-surface interaction, and the claimed violation of the Nernst theorem [2]. [1] E. Eiszner, B. Horovitz, and C. Henkel, Eur. Phys. J. D 66, 321 (2012). [2] G. L. Klimchitskaya, E. V. Blagov, and V. M. Mostepanenko, Int. J. Mod. Phys. A 24, 1777-88 (2009).

The dynamics of nanoplasmas generated from size-selected atomic clusters is investigated by photoemission and charge-state resolving ion recoil energy spectrometry. Single pulse exposure leads to broad and nearly unstructured energy spectra, whereas pump-probe excitation addressing the plasmon resonance exhibits pronounced peaks, which stem from the emission of ions from different geometrical shells. The feature becomes particularly pronounced upon reaching the icosahedral shell closing at a cluster size $N=55$. This indicates, that despite electron-ion recombination and ion screening by plasma electrons in the developing nanoplasma, information on the initial geometry of Ag$_{55}^-$, and in the end also shown for Ag$_{147}^-$, prevails in laser-triggered Coulomb explosions. The plasmon-assisted concept minimizes interfering many-body effects and is thus a stepping stone towards structural decoding of large many-atom systems.