Strong-field Physics Encounters Quantum Electro Dynamics

Attosecond photoelectron interferometry is a corner stone of attosecond and strong field physics. Traditional photoelectron interferometry combining an attosecond pulse train and a short infrared pulse has allowed the characterization of the radiation emitted via high-order harmonic generation as well as the measurement of photoionization dynamics in a variety of systems. This scheme, however, faces limitations when dealing with partially coherent photoelectron wave packets. In my talk I will discuss how novel interferometric schemes using tailored infrared fields offer new perspectives for the characterization of mixed photoelectron quantum states as well as for the study of ion-photoelectron entanglement.

A quantum optical model for high-order harmonic generation is presented in which both the exciting field and the high-order harmonic modes are quantized, while the target material appears only via parameters. As a consequence, the model is independent of the excited material system to a large extent and allows us to focus on the properties of the electromagnetic fields. Technically, the Hamiltonian known for parametric down-conversion is adopted, where photons in the ????⁢th harmonic mode are created during the annihilation of ???? photons from the fundamental mode. In our treatment, initially, the fundamental mode is in a coherent state corresponding to large photon numbers, while the high-order harmonic modes are in vacuum state. Due to the interaction, the latter modes get populated while the fundamental one loses photons. Analytical approximations are presented for the time evolution that are verified by numerically exact calculations. For multimode, finite-bandwidth excitation, the time dependence of the high-order harmonic radiation is also given.

Through a very stable attosecond interferometer we are now able capable of measuring XUV pulses in quadrature and determine the sequeeze level of such photons relative to each arm of the interferometer. We discuss photon statistics and possible squeeze states of the XUV.

In order to fully understand the processes in attosecond and strong-field physics, the quantum evolution of an involved atomic system driven by a strong laser pulse is usually needed. In the case of linearly polarized driving laser pulses, the main dynamics happen along the direction of the electric field of the laser pulse, which underlies the success of some one-dimensional (1D) approximations. In our earlier works [1, 2], we introduced the MSC potential, a 1D soft-core Coulomb potential with improved parameters, which defines a ground state density approximating the reduced density of the 3D ground state, resulting in very accurate low-frequency quantum dynamics. In the present contribution, we highlight a new 1D atomic model potential [3], designed for the quantum simulation of a single active electron atom in a strong, linearly polarized laser field. This new GSC potential balances accuracy and efficiency, enabling TDSE simulations to produce reliable HHG spectra within minutes for peak intensities in the 100 TW/cm2 range, in the full CEP range and in the practically important chirp parameter range. References: [1] Sz Majorosi, et al., Phys. Rev. A, 98, 023401 (2018) [2] Sz Majorosi, et al., Phys. Rev. A, 101, 023405 (2020) [3] K Sallai, et al., Phys. Rev. A 110, 063117 (2024)

Exploiting the infinite-order continuous dynamical rotational symmetry of circularly or elliptically polarized classical light pulses, we establish the conservation law between the angular momentum and energy in strong-field ionization that is applicable at the subcycle level. We illustrate the conservation law through the correlated spectrum of angular momentum and energy of photoelectrons, both at the tunnel exit and in the asymptotic region. Moreover, we propose a protocol based on electron vortices to directly visualize the existence of the subcycle conservation law. Our work paves the pathway towards a deeper understanding of fundamental light-matter interactions on the subcycle scale.

We investigate the liberation of an atomic electron by a linearly polarized single-cycle near-infrared laser pulse in the tunneling regime. Using phase space analysis with the Wigner function and the quantum momentum function (QMF), we reveal the essential role of quantum interference between tunneling and over-the-barrier escape paths. Our results highlight that tunneling is inherently blurred in space and time, and contributions near the mean energy are negligible. Based on this understanding, we propose improved initial conditions for classical trajectory-based models of strong-field ionization, derived from the QMF. These conditions ensure consistency with quantum dynamics and show good agreement with experimental observations, providing a theoretically consistent and experimentally relevant description of strong-field electron ionization.

Strongly pumped parametric down-conversion produces a state of light that, on the one hand, is as intense as laser light, and on the other hand, has pronounced quantum features. This state, known as bright squeezed vacuum, has zero mean electric field and consists only of quantum fluctuations, enhanced or suppressed on a subcycle scale. Recently, we have used this state to drastically modify the dynamics of strong-field effects, such as non-perturbative harmonics generation and electron ejection from needle tips.

Strong-field physics of quantum particles in Euclidean space is well documented. On the other hand, geometry and topology of the underlying space dictate an equation of motion different from the standard one. We find, for strongly laser-driven electronic systems new effects beyond those known for flat spaces appear. For a quantum particle in a two-dimensional Riemannian manifold embedded in a three-dimensional hyperspace, the specific geometric properties of space result in a potential-like term that supports bound states on the manifold. In the presence of a laser field, we derive expressions for a generalized Kramers-Henneberger-type unitary transformation which is shown to be generally space- and time-dependent. In contrast to a flat (geometrically trivial) space, new time-averaged coefficients of differential operators and operator-valued perturbation terms appear which determine the geometry-dependent laser-dressed states on Riemannian manifolds. Effects of quantized external fields will be briefly discussed.

Coherent light fields and quantum light fields represent two complementary degrees of freedom of light—one associated with classical spatial structures, such as orbital angular momentum (OAM), and the other rooted in quantum optics, defined by photon statistics and quantum fluctuations. Exploring their interplay offers new opportunities for the light-matter interactions in ultrafast strong-field physics. Recent studies have uncovered key insights into how these degrees of freedom influence ionization dynamics and high harmonic generation (HHG). Through strong-field ionization experiments, we demonstrated the in-situ detection of spin-orbit coupling in vector-vortex beam, where the momentum distribution of photoelectrons reveals underlying angular momentum transfer. We have also developed novel photoelectron-based techniques to directly measure the OAM topological charge of intense vortex pulses without disturbing their phase structure.In our research on HHG, we established the conservation of transverse OAM, offering a robust method for controlling harmonic spectral patterns. More notably, by combining transverse and longitudinal OAM, we discuss the potential generation of optical hopfions—topologically nontrivial light structures with promising applications in quantum information processing and ultrafast optics. By integrating structured and quantum light fields, it has the potential applications in attosecond science, quantum technologies, and the creation of exotic topological light structures under extreme conditions.

Xenon atoms were photoionized with high-order harmonics in order to create an entangled photo- electron+photoion system. We measured the partially coherent quantum state of the photoelectron wavepacket using the Mixed-FROG scheme, from which we reconstructed the attosecond dynamics of the unobserved but entangled ion.

For more than three decades, high harmonic generation has been the corner stone of attosecond technology. The quantum nature of the material response to intense driving light has never been in doubt, in spite of the many nearly classical aspects of this response. However, during these past three decades, the nature of the generated light was universally assumed to be classical. Recently, this view has started to change. The first reason for the change is the availability of bright quantum sources of incident light, which are already intense enough to enable harmonic generation on their own. These sources can also be mixed with intense classical light, providing well-controlled “hybrid” light at the input that can generate quantum light at the output. The second reason is the possibility of correlated measurements of light, where multiple generated light frequencies are measured in coincidence with the measurement of the transmitted incident light, possibly inducing correlations in the measured photons. But what about the quantum dynamics of the material system? Can the quantum properties of these material dynamics, triggered and controlled by the classical incident light, be mapped onto the quantum properties of the generated harmonic light? It appears that the answer is “yes”, and that achieving this goal might be simpler than one could have expected. I will present our latest results on controlled generation of quantum light in resonant atomic gases and in quantum systems coupled to structured photonic continua, such as a two-level system inside the waveguide. Our results suggest that the dream of generating multiple harmonics of the incident laser light entangled across multiple octaves, from the infrared (IR) to the extreme ultraviolet (XUV) range, is completely realistic.

The exploration of resource state generation for quantum applications has gained increased attention in recent years. Higher harmonics, generated through non-linear effects, stand out as potential candidates for their potential quantum attributes. To delve deeper into this phenomenon, our study focuses on the generation of non-classical light via laser-driven semiconductor intraband excitations, as investigated in [1]. Building upon the parametrical-connection approximation method [2], we adopt the approach outlined in [1] to characterize the generated states. Extending the linearized Hamiltonian approximation up to the quadratic order results in the extension of the underlying single-photon algebra to a multimode two-photon algebra. Untangling this high dimensional Lie algebra allows to characterize the quantum light state as a multimode squeezed displaced vacuum. We determine the squeezing and displacement parameters and study their dependencies on initial conditions, such as interaction time, laser intensity and semiconductor material. Furthermore, we investigate the resulting states, exploring their photon number statistics by simulating second order coherence correlations. We find a non-trivial structure, highly dependent on initial conditions. This examination will provide a more nuanced understanding of the quantum properties inherent in states generated through laser-driven semiconductor intraband excitations and aims to extend current models to extend our understanding of non-classical effects in macroscopic experiments. [1] I. Gonoskov, R. Sondenheimer, C. Hünecke, D. Kartashov, U. Peschel, and S. Gräfe, Nonclassical light generation and control from laser-driven semiconductor intraband excitations, 2211.06177 [quant-ph]. [2] I. Gonoskov and S. Gräfe, Light-matter quantum dynamics of complex laser-driven systems, 154, 234106.

Recent advances in attosecond science and quantum information technology have enabled the generation of large-scale optical Schrödinger cat states [1]. In this study, we investigate the electron dynamics induced by such quantum cat-state light [2]. In particular, we develop an effective theory of the electron dynamics aimed at extending the analysis to condensed electron systems. We find that the driving effect of quantum interference terms manifests as non-Hermitian electron dynamics induced by complex-valued electromagnetic fields. We term this phenomenon interferential non-Hermitian dynamics and demonstrate that it leads to the generation of entanglement and quantum interference among electrons. We also discuss comparisons with effective theories based on classically driven electron wavefunctions, as proposed in Refs. [3]. This work is in collaboration with Prof. Atsushi Ono (Tohoku University) and Prof. Naoto Tsuji (University of Tokyo). [1] M. Lewenstein et al., Nat. Phys. 17, 1104 (2021). [2] S. Imai et al., arXiv:2501.16801. [3] A. Gorlach et al., Nat. Phys. 19, 1689 (2023).

Quantum photonic states generated on an attosecond time scale are attracting a heightened attention. In addition to lending themselves well to storing and manipulating quantum information, they turn out to herald quantum correlations in the emitter, imprinting them on the generated photonic states. Yet, these states remain an almost uncharted territory due to the complexity entailed by both observing them in experiment and accurately predicting them in theory. The latter has to do with the sheer dimension of the Hilbert space involved. Indeed, a Hilbert space necessary to faithfully describe a driven system which emits photons into a quantum electromagnetic vacuum is, strictly speaking, infinite. One way to get around this limitation is to constrain our description to the perturbative limit. However, it is insufficient for describing situations involving multiple re-emissions and re-absorption of photons. We adopt a novel non-perturbative approach which allows us to contain the growth of the Hilbert space for the quantum light modes, putting ourselves in a position to simulate the behaviour of driven systems. The non-classical properties of the final state are most pronounced when the emission occurs into a mode resonant with a single- or multiple-photon transition in the emitter. We consider a system consisting of many (10-500) indistinguishable qubits with no explicit coupling between them, driven classically by a perturbatively weak resonant light field, and coupled strongly to a narrow-band waveguide. The waveguide's own resonant frequency can either equal a single qubit's transition frequency, or be its integer multiple. This combination ensures that after a photon is emitted by one qubit, it can be reabsorbed by another while still retaining entanglement with the original one, giving rise to quantum correlations between the two. In addition, making the waveguide resonant frequency a multiple of the qubit's resonant frequency forces cooperative emission. The correlated qubits undergo superradiance-like collective transitions, prompting the spontaneous formation of a correlated light-matter state. The correlations for the many-body state grow over time which, in turn, gives rise to highly non-classical photonic emissions, manifesting as a nontrivial Husimi function corresponding to a cat-like state.

Spatiotemporal optical vortices (STOVs) are structured light pulses exhibiting a unique coupling of spatial and temporal degrees of freedom, characterized by transverse orbital angular momentum (OAM). While their generation has so far been confined to the visible and infrared regions, extending them to the extreme-ultraviolet (EUV) via high-order harmonic generation (HHG) offers promising opportunities for ultrafast and nanoscale science. In this work, we present both theoretical and experimental evidence of EUV STOV generation driven by elliptical STOV beams. Using analytical models for focused STOVs and macroscopic HHG simulations, we demonstrate the generation of conjugate spatiotemporal and spatiospectral vortex pairs at EUV frequencies, characterized in both near and far fields. Additionally, we explore the fundamental behavior of the topological charge scaling in STOV-driven HHG. We show that HHG driven by spatio-spectral optical vortices, the spectral counterparts of STOVs produces EUV-STOV harmonics with non-scaling topological charge –i.e. all harmonics are emitted with the same topological charge. This distinction reveals that the scaling of topological charge in HHG driven by spatiotemporal fields is not universally tied to the scaling of the intrinsic OAM. Together, these results provide new insight into the interplay between structured light topology and frequency up-conversion, offering pathways for generating attosecond STOV beams for applications in ultrafast science, magnetic materials, and chiral media.

Particle production within strong-field quantum electrodynamics is the epitome of what happens when a quantum many-body system is pushed to its limits. It challenges our understanding of non-equilibrium physics, fundamental particle physics, and our conception of emergent phenomena and collective dynamics. In this talk, we focus on the most extreme form of light-matter interaction, namely coherent light driving the non-perturbative Schwinger effect as well as multiphoton processes. As such, we discuss the production of electron-positron pairs in vacuum, triggered by the collision of high-intensity light waves. Key discussion points include the characteristic signatures in the particle momentum spectra and the spin-state distribution of the emergent particle pairs (for each regime). Lastly, our findings on "when" particles are created, made possible by the use of Relativistic Quantum Transport Theory (i.e. the Wigner formalism), are also presented.

We advance transmission electron microscopy to resolve dynamical processes with attosecond time resolution. To this end, we exploit the field-cycles of a laser wave to modulate the electron wave function into a rapid sequence of electron pulses with sub-cycle duration, and use an energy filter to resolve electromagnetic near-fields in and around a material as a movie in space and time. Experiments on nanostructured needle tips, dielectric resonators and metamaterial antennas reveal a directional launch of chiral surface waves, a delay between dipole and quadrupole dynamics, a subluminal buried waveguide field and a symmetry-broken multi-antenna response. These results signify the value of combining electron microscopy and attosecond laser science to understand light–matter interactions in terms of their fundamental dimensions in space and time. Generalizing the attosecond beam shaping concepts to modulation fields carrying a topological charge, we further demonstrate formation of chiral electron wavefunctions on attosecond and nanometer scales. In this way, we facilitate chiral coupling of shaped electrons and a specimen via spiralling distributions of mass and charge. Using higher orders of topological charge and free-space dispersion, we achieve internally torqued electron pulses featuring a time-dependent orbital angular momentum, promising application of forces at atomic dimensions in space and time.

The interaction between strong laser fields and atoms gives rise to many intriguing new phenomena, such as high-order harmonic generation (HHG) and high-order above-threshold ionization (HATI). Currently, the laser field is usually described by a classical field because of its relatively high photon number density and the fact that the behavior of coherent light is extremely similar to that of classical light. Due to the remarkable progress in laser technology, it has become possible to experimentally generate high-intensity quantum light, such as bright squeezed vacuum. The interaction between strong quantum light and atoms has attracted considerable attention (see, e.g., [1-4]). In this talk, I will present our recent work on strong-field atomic physics in quantum light based on QED theory. These include a novel approach to control the HATI process [5], a new method to control the amplitude of the short and long trajectories in the HHG [6], and a unique way to synthesize attosecond pulses [6]. In addition, we will present recent findings on the influence of vacuum quantum fluctuations on harmonic generation [7], which provide new insights compared to previous studies. References: [1]M. Lewenstein, et al., Nat. Phys. 17, 1104 (2021). [2]M. E. Tzur, et al., Nat. Photon. 17, 501 (2023). [3] A. Gorlach, et al., Nat. Phys. 19, 1689 (2023). [4] A. Rasputnyi et al., Nat. Phys. 20, 1960 (2024). [5] S. J. Wang and X. Y. Lai, Phys. Rev. A 108, 063101 (2023). [6] S. J. Wang, X. Y. Lai, and X. J. Liu, arXiv:2406.10443 [7] S. J. Wang, S. G. Yu, X. Y. Lai, and X. J. Liu, Phys. Rev. Research 6, 033010 (2024)

High harmonic generation was recently observed in quantum dots [Nakagawa et al 2022] opening the route to HHG spectroscopy in nanoscale quantum materials. Quantum dots are a very interesting system, hosting properties between semiconductor description of bands and topology and atom-like description analogue to particle in a box. In the attosecond quantum physics lab at King's, we are interested in exploring these descriptions and using double quantum dots (DQD) as a candidate qubit platform. To this end, we develop a model at the boundary between strong field interaction and quantum information in conjunction with the current experimental development in our laboratory. In this presentation, we will explore the HHG process description on double quantum dots, which has been identified as a good candidate, providing long coherence time and a potential for high fidelity [Wang et al 2022]. Our first model is based on the resolution of the time-dependent Schrödinger equation and a model potential for DQD, where we explore the concept of quantum confinement in DQD and its signature in the HHG yield. This model is extended to address a 2-level system in the DQD and explore the manipulation of a qubit system. [Nakagawa et al 2022]: Nakagawa, Y., Uesugi, T., Matsui, H., Takeuchi, H., Okamura, K., et al. (2022). Size-controlled quantum dots reveal the impact of intraband transitions on high-order harmonic generation in solids. arXiv:2212.11483. https://www.nature.com/articles/s41567-022-01639-3 [Wang et al 2022] : Wang, Z., Li, H., Li, J., Xu, Y., Song, K., et al. (2022). Coherent manipulation of charge states in a double quantum dot system for high-fidelity operations. Nature Communications, 13, 1375. https://doi.org/10.1038/s41467-022-29006-1

Abstract Intense laser-matter interaction leads to high harmonic generation (HHG), where the low frequency photons of a driving laser field are converted into photons of higher frequencies. This process has enabled breakthroughs in AMO physics and attosecond science [1]. Until recently, it was described by classical or semi-classical approaches [2], ignoring the quantum nature of light. In our recent fully quantized investigations [3-7], we have shown how conditioning measurements on the HHG process and can lead to the generation of optical Schrödinger "cat" states and entangled light states. Here, after a brief introduction, I will present findings on high-photon-number optical "cat" states and their role in nonlinear optics [8]. We aim to use laser-driven materials and semiconductor crystals [9,10] to develop a new class of non-classical and massively entangled states for applications quantum technologies. References [1] P. Agostini, F. Krausz and A. L’Huillier Nobel prize in physics 2023 [2]. K. Amini, et al., Rep. Prog. Phys. 82, 116001 (2019) (and references herein). [3] M. Lewenstein, et al., Nat. Phys. 17, 1104 (2021). [4] J. Rivera-Dean, et al., Phys. Rev. A 105, 033714 (2022). [5] P. Stammer, et al., PRL 128, 123603 (2022). [6] P. Stammer, et al., PRX Quantum 4, 010201 (2023). [7] U. Bhattacharya, et al., Rep. Prog. Phys. 86, 094401 (2023). [8] Th. Lamprou, et al., PRL 134, 013601 (2025). [9] J. Rivera-Dean et al., PRB 109, 035203 (2024). [10] A. Nayak et al., Nat. Commun. 16,1428 (2025)

In non-relativistic physics the concepts of geometry and topology are usually applied to characterize spatial structures, or structures in momentum space. We introduce the concept of temporal geometry [1], which encompasses geometric and topological properties of temporal shapes, e.g. trajectories traced by a tip of a time-dependent vector on sub-cycle time scale, and apply it to light-driven ultrafast electron currents in chiral molecules. The geometric concepts: curvature and connection emerge as ubiquitous features of photoexcited chiral electron dynamics opening a way to ultrafast, topologically non-trivial, enantio-sensitive chemical dynamics and new highly-sensitive robust chiral observables. To demonstrate the link between the geometric fields and spin, we extend the concept of curvature to spin-resolved photoionization, and show that it is responsible for enantio-sensitive locking of the cation orientation to the photoelectron spin [2]. This translates into chirality induced spin selectivity in photoionization of oriented chiral molecules both in one photon and two-photon processes. Finally, we show that an enantiosensitive current in the plane of polarization of light manifests itself as a spin polarization vortex, i.e., the spin vortex rotates in opposite direction for opposite enantiomers [3] reminiscent of Rashba effect in solids. This observable arises from the *coupling* of the geometric field to spin, and can lead to high spin polarization even for very small spin-orbit interaction. Previously this effect was predicted by Cherepkov [4]. In our work we connected this effect to geometric field and quantified it using synthetic chiral matter. To quantify the link between chirality and spin-polarization in chiral targets, we construct chiral superpositions of electronic states in Argon and perform ab initio simulations of spin dynamics in photoionization using fully coupled spin-orbit code [5]. Our results provide a new perspective on the interplay of chirality and spin in photodynamics which does not rely on the interaction with the magnetic field component of light. [1] Geometry of temporal chiral structures, A. F. Ordonez, A. Roos, P. Mayer, D.Ayuso, O. Smirnova, arXiv preprint arXiv:2409.02500, 2024 [2] Spin-orientation locking in photoionization of chiral molecules, P. C. M. Flores, A.F. Ordonez, O. Smirnova, in preparation [3] Enantio-sensitive spin polarization vortices in photoionization of chiral molecules by circularly polarized light, P. C. M. Flores, S. Carlstroem, S. Patchkovskii, A. F. Ordonez, O. Smirnova, in preparation [4] N. Cherepkov, J. Physics B. 16, 1543 (1983). [5] General time dependent configuration interaction singles, S. Carlstroem et al, Phys. Rev. A 106, 2022, 042806

The ability to generate attosecond-duration light pulses provides powerful tools to probe and track the ultrafast dynamics of electrons in atoms, molecules, and condensed matter. At the heart of these new light sources lies high-order harmonic generation (HHG), a process traditionally understood as the interaction between matter and an intense laser field. Recently, however, HHG has been revisited as a versatile platform for extreme quantum optics. When driven by two laser beams, multiple harmonic beamlets are emitted for each order, naturally leading to an interpretation in terms of photon interactions. This framework allows for a retrieval of fundamental conservation laws, including those governing energy, spin, and orbital angular momenta, as established over the past decade. However, a fully photon-based interpretation for the yield of the harmonic beamlets has remained elusive. We will present experimental evidence showing that HHG can indeed be described as a superposition of simultaneous photonic processes. Specifically, the harmonic generation results from the coherent addition of multiple interfering processes. Beyond the minimum number of photons required to produce a given harmonic, each harmonic channel involves one or more additional photon pairs, associated with the combination of stimulated absorption and emission events. A simple theoretical model enumerating the different contributing pathways has been proposed and is in agreement with experimental data. References [1] Vimal, M. et al., 2023. Physical Review Letters, 131(20), 203402. http://¬dx.doi.org/¬10.1103/¬physrevlett.131.203402 [2] Luttmann, M. et al., 2023. Physical Review A, 108(5), 053509. http://¬dx.doi.org/¬10.1103/¬physreva.108.053509

High-harmonic generation (HHG) is a fundamental optical phenomenon arising from strong light-matter interaction. Initially observed in gases, HHG research expanded to semiconductors as well as to condensed matter systems. While most studies focused on semiconductors and band insulators, recent interest has been further expanded toward strongly correlated electron systems (SCESs). SCESs offer a new frontier for HHG research due to their nontrivial excitation structures, strong coupling between charge, spin, and orbital degrees of freedom, and diverse, tunable phases. These unique properties suggest that HHG in SCESs may exhibit distinct features not seen in conventional semiconductors. We elucidate the physics of HHG in Mott insulators—a prototypical phase in SCESs driven by strong Coulomb interactions—using state-of-the-art numerical methods based on the field theory and tensor networks. First, we demonstrate that the basic mechanism of HHG in Mott insulators can be understood through a three-step picture involving charged elementary excitations, known as doublons and holons, emerging from strong correlations [1,2]. This contrasts with semiconductors, where the conventional three-step model describes electron-hole pairs directly reflecting the single-particle spectrum. Our results suggest that HHG can serve as a probe of emergent excitations in SCESs. Second, we show that characteristic spin-charge couplings in Mott insulators, which is activated depending on the dimensionality of the system, produce multifaceted and unique effects on HHG [3,4]. Specifically, we demonstrate that spin-charge couplings lead to unique dephasing processes, fractionalization of the HHG signal as well as a peculiar temperature dependence of HHG. We further discuss the relevance of these effects to the recently reported nontrivial HHG behavior in a Mott insulator Ca2RuO4 [5]. Our results provide important insights into both the similarities and the key differences between HHG in Mott insulators and semiconductors, which sets a useful basis for spectroscopic applications of HHG in SCESs. [1] Y. Murakami, M. Eckstein and P. Werner, Phys. Rev. Lett. 121, 057405 (2018). [2] Y. Murakami, S. Takayoshi, A. Koga, and P. Werner, Phys. Rev. B 103, 035110 (2021). [3] Y. Murakami, T. Hansen, S. Takayoshi, L. Madsen, P. Werner, arXiv:2407.01936 (2024) (to be published from PRL). [4] Y. Murakami, K. Uchida, A. Koga, K. Tanaka and P. Werner, Phys. Rev. Lett. 129, 157401 (2022). [5] K. Uchida, G. Mattoni, S. Yonezawa, F. Nakamura, Y. Maeno, K. Tanaka, Phys. Rev. Lett. 128, 127401 (2022).

We derive a universal system of equations describing the quantum dynamics of laser-driven systems coupled to their quantized radiation field. Our approach is based on a special factorization [1] which takes into account the entanglement of light and matter which is the origin of the radiation nonclassicality in our description. This provides an accurate quantum description of the radiation and explains the emergence of non-classical light in some strongly laser-driven systems. The presented method allows to overcome a number of common numerical limitations and accurately calculate the response of quantum systems of various natures [2, 3, 4]. Based on this approach, we compare different quantum systems such as atoms, molecules, quantum dots, and semiconductors, for their potential use in generating of high-photon-number non-classical light [5, 6] or even high intensity non-classical pulses. We discuss and identify the special quantum optical features, and demonstrate how one can control or modify the non-classical parameters of emitted radiation as well as the quantum corrections to the transmitted strong-field laser pulse. References [1] Ivan Gonoskov and Stefanie Graefe, Light–matter quantum dynamics of complex laser-driven systems, J. Chem. Phys. 154, 234106, (2021). [2] N. Tsatrafyllis, et al. High-order harmonics measured by the photon statistics of the infrared driving-field exiting the atomic medium, Nat. Commun. 8, 15170, (2017). [3] N. Tsatrafyllis, et al. Quantum Optical Signatures in a Strong Laser Pulse after Interaction with Semiconductors, Phys. Rev. Lett. 122, 193602, (2019). [4] I. Gonoskov, et al. Nonclassical light generation and control from laser-driven semiconductor intraband excitations, PRB 109, 125110, (2024). [5] P. Stammer, et al. High Photon Number Entangled States and Coherent State Superposition from the Extreme Ultraviolet to the Far Infrared, Phys. Rev. Lett. 128, 123603, (2022). [6] M. Lewenstein, et al. Generation of optical Schr¨odinger cat states in intense laser–matter interactions, Nat. Phys. 17, 1104–1108, (2021).

J. Pölloth, J. Heimerl (Department of Physics, Friedrich-Alexander-Universität Erlangen-Nürnberg, Erlangen, Germany), A. Rasputnyi (Max Planck Institute for the Science of Light, Erlangen, Germany; Department of Physics, Friedrich-Alexander-Universität Erlangen-Nürnberg, Erlangen, Germany), S. Meier (Department of Physics, Friedrich-Alexander-Universität Erlangen-Nürnberg, Erlangen, Germany), M. Chekhova (Max Planck Institute for the Science of Light, Erlangen, Germany; ECE Department, Technion - Israel Institute of Technology, Haifa, Israel; Department of Physics, Friedrich-Alexander-Universität Erlangen-Nürnberg, Erlangen, Germany), P. Hommelhoff (Max Planck Institute for the Science of Light, Erlangen, Germany; Department of Physics, Friedrich-Alexander-Universität Erlangen-Nürnberg, Erlangen, Germany; Faculty of Physics, Ludwig-Maximilians-Universität München, München, Germany) Investigating strong-field processes driven by quantum states of light both theoretically and experimentally constitutes one of the main approaches to strong-field quantum optics. Such studies aim at understanding the role of the quantum-optical nature of light in strong-field light-matter interaction processes such as high harmonic generation (HHG) or electron rescattering. Experimentally, the study of quantum light-driven strong-field phenomena has only become possible recently due to the development of intense sources of non-classical light, such as bright squeezed vacuum (BSV) [1]. BSV represents a quantum state of light, namely a squeezed vacuum state, where the mean electric field at each instant in time is zero. Thus, in a semiclassical view, one might expect that no strong driving of electrons occurs in such a light field. However, experimental studies have already demonstrated that several nonlinear processes can be driven by BSV. In a multiphoton photoemission experiment at a metallic needle tip, it was observed that the number statistics of the driving state of light is imprinted on the number statistics of the emitted electrons [2]. Recently, it was also demonstrated that optical high harmonics can be generated by BSV [3]. However, up to now, it has not been shown experimentally whether the tell-tale feature of strong-field physics, namely the plateau in the energy spectrum of either photons or electrons, also appears under quantum light driving, and in particular under BSV driving. Here, we present the measurement of strong-field energy spectra of electrons driven strongly at the apex of a nanometric metal needle tip by bright squeezed vacuum [4]. When averaging over many BSV pulses, we observe the generation of high-energy electrons, but no plateau is appearing in the spectra. However, if we post-select the electron energy spectra on fixed photon numbers in the individual BSV pulses, we observe a clear plateau and a cutoff in the spectra. We will discuss these experimental findings as well as their interpretation based on a generalized framework for the strong-field interaction of arbitrary states of light with matter [5]. [1] T. Sh. Iskhakov, A. M. Pérez, K. Yu. Spasibko, M. V. Chekhova, and G. Leuchs, Opt. Lett. 37, 1919-1921 (2012) [2] J. Heimerl, A. Mikhaylov, S. Meier, H. Höllerer, I. Kaminer, M. Chekhova, and P. Hommelhoff, Nat. Phys. 20, 945-950 (2024) [3] A. Rasputnyi, Z. Chen, M. Birk, O. Cohen, I. Kaminer, M. Krüger, D. Seletskiy, M. Chekhova, and F. Tani, Nat. Phys. 20, 1960-1965 (2024) [4] J. Heimerl, A. Rasputnyi, J. Pölloth, S. Meier, M. Chekhova, and P. Hommelhoff, arXiv: 2503.22464 (2025) [5] A. Gorlach, M. E. Tzur, M. Birk, M. Krüger, N. Rivera, O. Cohen, and I. Kaminer, Nat. Phys. 19, 1689-1696 (2023)

In 2022, Rabi oscillations were observed at extreme ultraviolet (XUV) wavelengths using the seeded FEL at FERMI [1], opening up a new domain of strong-coupling coherent-control experiments in atoms and molecules. The FEL parameter space allows for investigating quantum entanglement in the photoelectric effect, generated between a photoelectron and a light-dressed atomic ion [2]. The atom, $g$, is ionized into the ionic ground state, $\alpha$, and the field dresses the ion, inducing Rabi oscillations to the excited ionic state $\beta$. The entanglement is manifested in the photoelectron doublet, in agreement with the seminal work of Grobe and Eberly [3] and more recent works [4,5]. We show how this entanglement is fundamentally altered by harnessing time symmetry [6]. Using odd (zero-area) pulses changes the photoelectron distribution, forming non-overlapping photoelectron peaks and delayed entanglement generation. This allows for detecting entanglement without phase measurements and constitutes the first usage of the parity of time symmetry in strong-field interactions. Including spontaneous emission [7], letting the excited ionic state decay to the ionic ground state with an additional emitted photon, $\beta \rightarrow \gamma$, yields the characteristic the Mollow triplet in the, fluorescence spectra, during the pulse, and a narrow resonant peak after. The shape of the photoelectron spectra is conserved, with the population being transferred $\beta\rightarrow\gamma$. The population shows how $\alpha$ and $\beta$ increase during the pulse, and the subsequently decays $\beta\rightarrow\gamma$ on the timescale of spontaneous emission. The entanglement entropy, between electron and ion is built up during the interaction with the pulse to the maximum value of 1 (for a qubit system). After the pulse, this entanglement is quantum relayed to fully entangle the electron with the emitted photon. During the spontaneous decay, the full system entanglement (comprising: ion, electron and emitted photon) exceeds the maximum for a qubit system. Thus, we see how quantum entanglement, built up between ion and electron is entirely relayed to instead entangle electron and photon through spontaneous emission. References: [1] S Nandi et al., Nature 608, 488-493 (2022). [2] S Nandi, A Stenquist et al., Sci. Adv. 10, eado0668 (2024). [3] R Grobe and J H Eberly, Phys. Rev. A 48, 623-627 (1993). [4] S B Zhang and N Rohringer, Phys. Rev. A 89, 013407 (2014). [5] C Yu and L B Madsen, Phys. Rev. A 98, 033404 (2018). [6] A Stenquist and J M Dahlström arXiv:2405.03339 [7] A Stenquist et al. Manuscript in preparation

The work analyzes the HHG process driven by non-classical structured light with arbitrary polarization configurations, ranging from linear to fully-circular polarized light. By including squeezing along different directions—mainly phase and amplitude squeezing—we observed distinct effects on HHG. We also analyzed how the spectrum changes with varying squeezing directions, including simultaneous phase and amplitude squeezing. The HHG spectrum can give information about the quantum nature of the driving field. In addition it analyzes how the polarization state of the generated harmonics depends on that of the driving field. The ellipticity of the HHG spectrum can be analyzed in dependence of the ellipticity of the driving field. It was shown that even a single driver with elliptical polarization and squeezing is sufficient to achieve high ellipticity in the HHG spectrum—approaching near-circularly polarized light—an effect not previously demonstrated.

Although the earliest results with respect to the quantum optics of attophysics date back to 1981, the interest in related works have seen a rebirth after circa 2020. Recent developments (both theoretical and experimental) suggests that HHG can be a source of light with nonclassical quantum state. One can identify distinct branches of research among the recent works, involving differing techniques and underlying approaches. From the perspective of quantum technologies, one can categorize by the type of nonclassicalities resulting from HHG: i) Squeezed states; ii) Sub-Poissonian states; iii) Entangled states; iv) Cat-states. However, as nonclassical sources of light are being developed, at some point, the questions of scaling (for example: the number of modes in an entangled state vs the spatial size of the setup producing it) will need to be addressed. I argue HHG-based lightsource can avoid the problems of spatial scaling, which is almost certainly going to be a desirable attribute as quantum technologies become more widely used. On the other hand, more than just general results and demonstrations of nonclassicalities, a complete characterization of the produced quantum states is neccessary for any practical design. I will present a characterization of HHG when the material target is a two-level system. Although it is a highly idealized material model, it is possible to give both analytical results, and to estimate the limit of validity of the inherent approximation. The results imply that with carefully chosen parameters, one can produce either of the i)-iv) nonclassicalities.

The novel quantum effects induced by the free-electron–photon interaction have attracted increasing interest due to their potential applications in ultrafast quantum information processing. Here, we propose a scheme to generate optical cat states based on the quantum interference of multi-path free-electron–photon interactions that take place simultaneously with strong coupling strength. By performing a projection measurement on the electron, the state of light changes significantly from a coherent state into a non-Gaussian state with either Wigner negativity or squeezing property, both possess metrological power to achieve quantum advantage. More importantly, we show that the Wigner negativity oscillates with the coupling strength, and the optical cat states are successfully generated with high fidelity at all the oscillation peaks. This oscillation reveals the quantum interference effect of the multiple quantum pathways in the interaction of the electron with photons, by that various nonclassical states of light are promising to be fast prepared and manipulated. These findings inspire further exploration of emergent quantum phenomena and advanced quantum technologies with free electrons.

In this work, we investigate the electric-field-driven power-law random banded matrix(PLRBM) model where a variation in the power-law exponent α yields a delocalization-to-localization phase transition. We examine the periodically driven PLRBM model with the help of the Floquet operator. The level spacing ratio and the generalized participation ratio of the Floquet Hamiltonian reveal a drive-induced fractal phase accompanied by diffusive transport on the delocalized side of the undriven PLRBM model. On the localized side, the time-periodic model remains localized—the average spacing ratio corresponds to Poisson statistics, and logarithmic transport is observed in the dynamics. Extending our analysis to the aperiodic Thue-Morse (TM) driven system, we find that the aperiodically driven clean long-range hopping model (clean counterpart of the PLRBM model) exhibits the phenomenon of exact dynamical localization (EDL) on tuning the drive-parameters at special points. The disordered time-aperiodic system shows diffusive transport followed by relaxation to the infinite-temperature state on the delocalized side and a prethermal plateau with subdiffusion on the localized side. Additionally, we compare this with a quasi-periodically driven AAH model that also undergoes a localization-delocalization transition. Unlike the disordered long-range model, it features a prolonged prethermal plateau followed by subdiffusion to the infinite temperature state, even on the delocalized side.