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Recollision processes are fundamental to strong-field physics and attoscience, thus models connecting recolliding trajectories to quantum amplitudes are a crucial part in furthering understanding of these processes. We report developments in the semiclassical path-integral-based Coulomb quantum-orbit strong-field approximation model for strong-field ionization by including an additional phase known as Maslov's phase and implementing a new solution strategy via Monte-Carlo-style sampling of the initial momenta. In doing so, we obtain exceptional agreement with solutions to the time-dependent Schr\"odinger equation for hydrogen, helium, and argon. We provide an in-depth analysis of the resulting photoelectron momentum distributions for these targets, facilitated by the quantum-orbits arising from the solutions to the saddle-point equations. The analysis yields a new class of rescattered trajectories that includes the well-known laser-driven long and short trajectories, along with novel Coulomb-driven rescattered trajectories. By virtue of the precision of the model, it opens the door to detailed investigations of a plethora of strong-field phenomena such as photoelectron holography, laser-induced electron diffraction and high-order above threshold ionization., Comment: 15 pages, 7 figures

High-harmonic generation has emerged as a pivotal process in strong-field physics, yielding extreme ultraviolet radiation and attosecond pulses with a wide range of applications. Furthermore, its emergent connection with the field of quantum optics has revealed its potential for generating non-classical states of light. Here, we investigate the process of high-harmonic generation in semiconductors under a quantum optical perspective while using a Bloch-based solid-state description. Through the implementation of quantum operations based on the measurement of high-order harmonics, we demonstrate the generation of non-classical light states similar to those found when driving atomic systems. These states are characterized using diverse quantum optical observables and quantum information measures, showing the influence of electron dynamics on their properties. Additionally, we analyze the dependence of their features on solid characteristics such as the dephasing time and crystal orientation, while also assessing their sensitivity to changes in driving field strength. This study provides insights into HHG in semiconductors and its potential for generating non-classical light sources., Comment: 22 pages (16 main text + 6 appendix), 7 figures (5 main text + 2 appendix)

Spin-orbit dynamics and relativistic corrections to the kinetic energy in strong-field dynamics, have long been ignored for near- and mid-IR fields with intensities $10^{13}$--$10^{14}$ W/cm$^2$, as the final photoelectron energies are considered too low for these effects to play a role. However, using a precise and flexible path-integral formalism, we include all correction terms from the fine-structure, Breit-Pauli Hamiltonian. This enables a treatment of spin, through coherent spin-states, which is the first model to use this approach in strong-field physics. We are able to show that the most energetically rescattered wavepackets, undergo huge momentum transfer and briefly reach relativistic velocities, which warrants relativistic kinetic energy corrections. We probe these effects and show that they yield notable differences for a $1600$ nm wavelength laser field on the dynamics and the photoelectron spectra. Furthermore, we find that the dynamical spin-orbit coupling is strongly overestimated if relativistic corrections to kinetic energy are not considered. Finally, we derive a new condition that demonstrates that relativistic effects begin to play a role at intensities orders of magnitude lower than expected. Our findings may have important implication for imaging processes such as laser-induced electron diffraction, which includes high-energy photoelectron recollisions., Comment: 24 pages, 7 figures

Deep learning models have provided huge interpretation power for image-like data. Specifically, convolutional neural networks (CNNs) have demonstrated incredible acuity for tasks such as feature extraction or parameter estimation. Here we test CNNs on strong-field ionization photoelectron spectra, training on theoretical data sets to `invert' experimental data. Pulse characterization is used as a `testing ground', specifically we retrieve the laser intensity, where `traditional' measurements typically lead to 20% uncertainty. We report on crucial data augmentation techniques required to successfully train on theoretical data and return consistent results from experiments, including accounting for detector saturation. The same procedure can be repeated to apply CNNs in a range of scenarios for strong-field ionization. Using a predictive uncertainty estimation, reliable laser intensity uncertainties of a few percent can be extracted, which are consistently lower than those given by traditional techniques. Using interpretability methods can reveal parts of the distribution that are most sensitive to laser intensity, which can be directly associated with holographic interferences. The CNNs employed provide an accurate and convenient ways to extract parameters, and represent a novel interpretational tool for strong-field ionization spectra., Comment: 13 pages, 5 figures

Strong laser physics is a research direction that relies on the use of high-power lasers and has led to fascinating achievements ranging from relativistic particle acceleration to attosecond science. On the other hand, quantum optics has been built on the use of low photon number sources and has opened the way for groundbreaking discoveries in quantum technology, advancing investigations ranging from fundamental tests of quantum theory to quantum information processing. Despite the tremendous progress, until recently these directions have remained disconnected. This is because, the majority of the interactions in the strong-field limit have been successfully described by semi-classical approximations treating the electromagnetic field classically, as there was no need to include the quantum properties of the field to explain the observations. The link between strong laser physics, quantum optics, and quantum information science has been developed in the recent past. Studies based on fully quantized and conditioning approaches have shown that intense laser--matter interactions can be used for the generation of controllable entangled and non-classical light states. This achievement opens the way for a vast number of investigations stemming from the symbiosis of strong laser physics, quantum optics, and quantum information science. Here, after an introduction to the fundamentals of these research directions, we report on the recent progress in the fully quantized description of intense laser--matter interaction and the methods that have been developed for the generation of non-classical light states and entangled states. Also, we discuss the future directions of non-classical light engineering using strong laser fields, and the potential applications in ultrafast and quantum information science., Comment: 60 pages, 20 figures. Comments are welcome

The development of sources delivering non-classical states of light is one of the main needs for applications of optical quantum information science. Here, we demonstrate the generation of non-classical states of light using strong-laser fields driving a solid-state system, by using the process of high-order harmonic generation, where an electron tunnels out of the parent site and, later on, recombines on it emitting high-order harmonic radiation, at the expense of affecting the driving laser field. Since in solid-state systems the recombination of the electron can be delocalized along the material, the final state of the electron determines how the electromagnetic field gets affected because of the laser-matter interaction, leading to the generation of entanglement between the electron and the field. These features can be enhanced by applying conditioning operations, i.e., quantum operations based on the measurement of high-harmonic radiation. We study non-classical features present in the final quantum optical state, and characterize the amount of entanglement between the light and the electrons in the solid. The work sets the foundation for the development of compact solid-state-based non-classical light sources using strong-field physics., Comment: We present a different formulation to that of the previous version, more in line with the approach followed in our previous works. 12 pages (8 main text + 4 Methods), 4 figures. Comments are welcome

Light-matter entanglement plays a fundamental role in many applications of quantum information science. Thus, finding processes where it can be observed is an important task. Here, we address this matter by theoretically investigating the entanglement between light and electrons generated in above-threshold ionization (ATI) process. The study is based on the back-action of the ATI process on the quantum optical state of the system, and its dependence on the kinetic energy and direction of the emitted photoelectrons. Taking into account the dynamics of the process, we demonstrate the creation of hybrid entangled states. The amount of entanglement has been studied in terms of the entropy of entanglement. Additionally, we use the Wigner function of the driving field mode to motivate the entanglement characterization when considering electrons propagating in opposite directions., Comment: 20 pages (13 main text + 7 supplementary material), 8 figures (6 main text + 2 supplementary material). Comments are welcome

Ultrafast imaging of molecular chirality is a key step towards the dream of imaging and interpreting electronic dynamics in complex and biologically relevant molecules. Here, we propose a new ultrafast chiral phenomenon exploiting recent advances in electron optics allowing access to the orbital angular momentum of free electrons. We show that strong-field ionization of a chiral target with a few-cycle linearly polarized 800 nm laser pulse yields photoelectron vortices, whose chirality reveals that of the target, and we discuss the mechanism underlying this phenomenon. Our work opens new perspectives in recollision-based chiral imaging., Comment: 4 pages main text, 2 figures, 8 equations

We investigate twisted electrons with a well defined orbital angular momentum, which have been ionised via a strong laser field. By formulating a new variant of the well-known strong field approximation, we are able to derive conservation laws for the angular momenta of twisted electrons in the cases of linear and circularly polarised fields. In the case of linear fields, we demonstrate that the orbital angular momentum of the twisted electron is determined by the magnetic quantum number of the initial bound state. The condition for the circular field can be related to the famous ATI peaks, and provides a new interpretation for this fundamental feature of photoelectron spectra. We find the length of the circular pulse to be a vital factor in this selection rule and, employing an effective frequency, we show that the photoelectron OAM emission spectra is sensitive to the parity of the number of laser cycles. This work provides the basic theoretical framework with which to understand the OAM of a photoelectron undergoing strong field ionisation., Comment: 11 pages, 4 figures and 44 equations. Publication prepared for the EPJ D Topical Issue: Quantum Aspects of Attoscience

The perceived dichotomy between analytical and ab initio approaches to theory in attosecond science is often seen as a source of tension and misconceptions. This Topical Review compiles the discussions held during a round-table panel at the 'Quantum Battles in Attoscience' CECAM virtual workshop, to explore the sources of tension and attempt to dispel them. We survey the main theoretical tools of attoscience -- covering both analytical and numerical methods -- and we examine common misconceptions, including the relationship between ab initio approaches and the broader numerical methods, as well as the role of numerical methods in 'analytical' techniques. We also evaluate the relative advantages and disadvantages of analytical as well as numerical and ab initio methods, together with their role in scientific discovery, told through the case studies of two representative attosecond processes: non-sequential double ionisation and resonant high-harmonic generation. We present the discussion in the form of a dialogue between two hypothetical theoreticians, a numericist and an analytician, who introduce and challenge the broader opinions expressed in the attoscience community., Comment: Proceedings of the round-table panel discussion 'Quantum Battle 3 - Numerical vs Analytical Methods' at the Quantum Battles in Attoscience online conference (https://www.quantumbattles.com/), the livestream for which can be found at https://www.youtube.com/watch?v=VJnFfHVDym4

This paper has been prepared by the Symphony collaboration (University of Warsaw, Uniwersytet Jagiello\'nski, DESY/CNR and ICFO) on the occasion of the 25th anniversary of the "simple man's models" which underlie most of the phenomena that occur when intense ultrashort laser pulses interact with matter. The phenomena in question include High-Harmonic Generation, Above-Threshold Ionization, and Non-Sequential Multielectron Ionization. "Simple man's models" provide, both an intuitive basis for understanding the numerical solutions of the time-dependent Schr\"odinger equation, and the motivation for the powerful analytic approximations generally known as the Strong Field Approximation (SFA). In this paper we first review the SFA in the form developed by us in the last 25 years. In this approach SFA is a method to solve the TDSE using a systematic perturbation theory in a part of the Hamiltonian describing continuum-continuum transitions in the presence of the laser field. In this review we focus on recent applications of SFA to HHG, ATI and NSMI from multi-electron atoms and from multi-atom. The main novel part of the presented theory concerns generalizations of SFA to: (i) time-dependent treatment of two-electron atoms, allowing for studies of an interplay between Electron Impact Ionization (EII) and Resonant Excitation with Subsequent Ionization (RESI); (ii) time-dependent treatment in the single active electron (SAE) approximation of "large" molecules and targets which are themselves undergoing dynamics during the HHG or ATI process. In particular, we formulate the general expressions for the case of arbitrary molecules, combining input from quantum chemistry and quantum dynamics. We formulate also theory of time-dependent separable molecular potentials to model analytically the dynamics of realistic electronic wave packets for molecules in strong laser fields., Comment: We dedicate this work to the memory of Bertrand Carr\'e, who passed away in March 2018 at the age of 60. This Accepted Manuscript is available under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/3.0/)