We experimentally observe a new type of quantum-path interference, in two-dimensional(2D-QPI), in high-harmonic generation (HHG) driven by an orthogonally-polarised highly-bichromatic field. This regime is marked by comparable intensities of the two orthogonal colours. In this highly-bichromatic regime, we demonstrate that 2D-QPI is encoded in the measured harmonic intensity modulations with respect to the relative phase of the two-colour field. The modulations of the odd-order harmonics show a monomodal behaviour, whereas the even harmonics are modulated in a bimodal structure. Our calculations using the strong-field approximation and saddle-point method disentangle contributions from multiple quantum orbits in this HHG regime, revealing that the dipole response for both odd and even harmonics inherits the dynamic symmetry of the orthogonally-polarised driving field. This new type of 2D-QPI offers a novel route to HHG spectroscopy of attosecond electron dynamics by lifting up the dimensionality of the quantum paths involved in the interference.

We present TDSE-Z, a high-performance open-source framework for strong-field quantum dynamics in atomic, molecular, and semiconductor effective-mass systems. The core engine implements a weak-form Galerkin discretisation of the Hermitian BenDaniel-Duke operator, T̂_BDD = -1/2∇·(m^-1(𝐫)∇), on geometry-adapted B-spline meshes, supporting arbitrary potentials and customisable laser configurations in one to three dimensions. We validate the static position-dependent-mass (PDM) eigensolver through two stringent benchmarks: a comparison to the analytical Quesne PDM model and a GaAs/Al_0.3Ga_0.7As double quantum well, where the exponential decay of computed tunnel splittings follows Wentzel-Kramers-Brillouin (WKB) theory at the sub-percent level. We further demonstrate the time-propagation engine on constant-mass systems, accurately reproducing high-harmonic generation (HHG) spectra in atomic benchmarks and confirming the importance of dimensionality in fully capturing the strong light-matter interaction. Our implementation demonstrates robust strong-scaling efficiency, maintaining performance across hundreds of CPU cores. While the static eigensolver currently supports optional GPU offloading, the time-propagation engine is CPU-optimised, providing a modular architecture for future expansion toward exascale quantum dynamics.

Ultrafast optical control of solids has uncovered new phenomena and advanced non-equilibrium condensed matter physics, where photon dressed electronic states - Floquet Bloch states (FBSs) - emerge under a strong oscillating laser field, also known as Floquet engineering. Although FBSs have been extensively investigated using time and angle resolved photoemission spectroscopy, direct evidence of their role in high-harmonic generation spectroscopy (HHGS) has remained elusive. Here, we present combined experimental and theoretical evidence that FBSs can be probed by HHG emission in the wide-bandgap solid magnesium oxide (MgO) driven by few cycle near infrared pulses. Experimentally, we observe clear evidence of FBSs in the HHG yield dependence on the crystal orientation. This specific feature is attributed to nonadiabatic coupling between FBSs and conduction bands near the Brillouin zone edge, where the strong laser field transiently breaks time reversal symmetry. We have confronted the experimental findings with numerical solutions of the time dependent Schrödinger equation, which reproduce the new feature and confirm its Floquet origin. The theoretical results show a coupling inducing a local band structure renormalization and Floquet like hybridization under strong field excitation. It also shows that FBS nonadiabatic dynamics persist in the strong field regime, establishing HHGS as a powerful probe of ultrafast light induced band hybridization in solids.

The emerging field of high harmonic generation in condensed matter systems lies at the confluence of strong-field physics, ultrafast optics, and nanotechnology and offers numerous avenues for fundamental research and applications. The goals of this JOSA B feature issue on high harmonic generation in condensed and engineered materials are to facilitate interaction between the different communities and to provide an up-to-date snapshot of the current status of this rapidly developing interdisciplinary field at the frontier of condensed materials and ultrafast physics.

The Nobel Prize in Physics 2023 was awarded to Pierre Agostini, Ferenc Krausz and Anne L'Huillier for "experimental methods that generate attosecond pulses of light for the study of electron dynamics in matter." We review the history of attosecond physics, recount the laureates' achievements and their place within the field, discuss the breakthroughs made possible by the creation of attosecond pulses, and look to the future advances in attoscience.

The XUV beams generated via high order harmonic generation (HHG) in gases have spatial properties evolving with the harmonic order. It leads to chromatic aberrations when the harmonics are focussed so that, locally, the spectral content can change significantly during propagation [1]–[3] especially near focus.

Attosecond pulses created by high-order harmonic generation in gases often exhibit strong chromatic aberrations, arising from the broad bandwidth and wavelength-dependent nonlinear light-matter interaction. When the driving laser intensity varies spatially, as for Gaussian driving beams, the apparent source position of the harmonics differs significantly from one order to the next, thus affecting the achievable intensity and duration of the attosecond pulses when they are focused on a target. We show that these chromatic aberrations can be reduced by spatially shaping the fundamental beam to generate high-order harmonics with a driver having a flat-top profile inside the gas medium. By measuring both the intensity profile and wavefront for each harmonic in a plane, we access the extreme ultra-violet (XUV) beam properties and investigate these properties near focus. We observe that controlling chromatic aberrations by flat-top spatial shaping strongly reduces the variation of the XUV spectrum on the beam axis during propagation and, in return, the longitudinal sensitivity of both the temporal profiles and the temporal shifts of the focused attosecond pulses.

With a combination of numerical methods, including quantum Monte Carlo, exact diagonalization, and a simplified dynamical mean-field model, we consider the attosecond charge dynamics of electrons induced by strong-field laser pulses in two-dimensional Mott insulators. The necessity to go beyond single-particle approaches in these strongly correlated systems has made the simulation of two-dimensional extended materials challenging, and we contrast their resulting high-harmonic emission with more widely studied one-dimensional analogues. As well as considering the photo-induced breakdown of the Mott insulating state and magnetic order, we also resolve the time and ultra-high frequency domains of emission, which are used to characterize both the photo-transition, and the sub-cycle structure of the electron dynamics. This extends simulation capabilities and understanding of the photo-melting of these Mott insulators in two-dimensions, at the frontier of attosecond non-equilibrium science of correlated materials.

We measure for the first time the duration of long-quantum path EUV high harmonics produced in xenon gas. The long-quantum path contribution to the high-harmonic signal was carefully controlled by employing a two-colour driving laser field and a high-harmonic spatial selection in the far field, over a range of $18-25\,eV$ in photon energy. To characterise the temporal profile of long quantum path high harmonics, we performed a second order volume autocorrelation ($2-IVAC$) via two EUV photon double ionization in argon. Our results show the production and characterisation of a train of EUV pulses from the long-path with pulse duration as short as $1.4\,fs$. This measurement demonstrates that the long-quantum path emission can have enough flux for performing non-linear EUV experiments, and that the long trajectories enable a pulse duration short enough to support measurements with a temporal resolution below $2\,fs$.

We generate attosecond pulse train (APT) in argon driven by the high repetition rate (HR) laser of the extreme light infrastructure-attosecond light pulse source (ELI-ALPS), providing 100 kHz, 80 W, 1030 nm, 40 fs pulses from a fiber chirped-pulse amplification (fiber-CPA) laser system. Under the current operating conditions of the high harmonic generation beamline (HR-GHHG), we observed the average pulse duration to be 395 as measured using the technique of reconstruction of attosecond beating by interference of two-photon transitions. The beamline uses an annular-shape laser beam so that the main part of the driving laser co-propagating with the APT can be eliminated by reflection on a holey mirror. An additional 100 nm aluminum foil is used to filter out the remaining laser and the low order harmonics, allowing 2 pJ APT with a bandwidth from 25 eV to 50 eV to be transported to the target position where the APT interacts with matter. The implementation of the HR-GHHG beamline in ELI-ALPS delivering attosecond pulse trains at 100 kHz paves the way for time-resolved experiments in the infrastructure, especially those that involve rare events and coincidence analysis, both of which need high statistics.

This work theoretically investigates high-order harmonic generation in rare-gas atoms driven by two temporally delayed ultrashort laser pulses. Apart from their temporal delay, the two pulses are identical. Using a single-atom model of the laser-matter interaction it is shown that the photon energy of the generated harmonics is controllable within the range of one eV-a bandwidth comparable to the photon energy of the fundamental field-by varying the time delay between the generating laser pulses. It is also demonstrated that high-order harmonics generated by double pulses have advantageous characteristics, which mimick certain properties of an extreme ultraviolet monochromator. With the proposed method, a simpler setup at a much lower cost and comparatively higher spectral yield can be implemented in contrast to other approaches.

The reconstruction of ultrashort optical pulses with a complex intensity substructure is demonstrated using the Self-Referenced Spectral Interferometry (SRSI) pulse characterization technique with a modified phase retrieval algorithm. A correction spectral phase term is extracted by the manipulation of the temporal interferogram, allowing the treatment of scenarios with complicated pulse shapes, where the original algorithm fails. The improved SRSI algorithm is verified through the application on two temporally well-separated pulses having the same polarization direction and spectral shape, generated by duplicating 37 fs-long amplified pulses of a Ti:Sa based laser system. The spectral phase of highly chirped double pulses with equal or different amplitude ratios is numerically retrieved. The collinear and achromatic experimental arrangement results in a compact and easy-to-align system.

This paper has been prepared by the Symphony collaboration (University of Warsaw, Uniwersytet Jagielloński, 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 (HHG), above-threshold ionization (ATI), and non-sequential multielectron ionization (NSMI). 'Simple man's models' provide both an intuitive basis for understanding the numerical solutions of the time-dependent Schrödinger 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 the SFA is a method to solve the TDSE, in which the non-perturbative interactions are described by including continuum–continuum interactions in a systematic perturbation-like theory. In this review we focus on recent applications of the SFA to HHG, ATI and NSMI from multi-electron atoms and from multi-atom molecules. The main novel part of the presented theory concerns generalizations of the SFA to: (i) time-dependent treatment of two-electron atoms, allowing for studies of an interplay between electron impact ionization and resonant excitation with subsequent ionization; (ii) time-dependent treatment in the single active electron approximation of 'large' molecules and targets which are themselves undergoing dynamics during the HHG or ATI processes. 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. We dedicate this work to the memory of Bertrand Carré, who passed away in March 2018 at the age of 60.

We present a robust experimental design for performing time-resolved measurement with IR femtosecond laser pulses and attosecond extreme ultraviolet (XUV) pulses. The setup contains no reflective optical elements and provides an IR-XUV delay control down to 5 attoseconds without any active stabilization. Temporal characterization of an attosecond XUV pulse train generated in krypton is presented here to demonstrate the validity of our approach. (C) 2018 Optical Society of America

We have studied high-order harmonic generation (HHG) in an indium ablation plume driven by intense few-cycle laser pulses centered at 775 nm as a function of the frequency chirp of the laser pulse. We found experimentally that resonant emission lines between 19.7 eV and 22.3 eV (close to the 13th and 15th harmonic of the laser) exhibit a strong, asymmetric chirp dependence, with pronounced intensity modulations. The chirp dependence is reproduced by our numerical time-dependent Schrödinger equation simulations of a resonant HHG by the model indium ion. As demonstrated with our separate simulations of HHG within the strong field approximation, the resonance can be understood in terms of the chirp-dependent HHG photon energy coinciding with the energy of an autoionizing state to ground state transition with high oscillator strength. This supports the validity of the general theory of resonant four-step HHG in the few-cycle limit.

We propose a method to compensate for the extreme ultra violet (XUV) attosecond chirp associated with the long quantum-path in the high harmonic generation process. Our method employs an isolated attosecond pulse (IAP) issued from the short trajectory contribution in a primary target to assist the infrared driving field to produce high harmonics from the long trajectory in a secondary target. In our simulations based on the resolution of the time-dependent Schrodinger equation, the resulting high harmornics present a clear phase compensation of the long quantum-path contribution, near to Fourier transform limited attosecond XUV pulse. Employing time-frequency analysis of the high harmonic dipole, we found that the compensation is not a simple far-field photonic interference between the IAP and the long-path harmonic emission, but a coherent phase transfer from the weak IAP to the long quantum-path electronic wavepacket. Our approach opens the route to utilizing the long quantum-path for the production and applications of attosecond pulses.

Quasifree field-driven electron trajectories are a key element of strong-field dynamics.Upon recollision with the parent ion, the energy transferred from the field to the electron may be released as attosecondduration extreme ultaviolet emission in the process of high-harmonic generation.The conventional sinusoidal driver fields set limitations on the maximum value of this energy transfer and the efficient return of the launched electron trajectories.It has been predicted that these limits can be significantly exceeded by an appropriately ramped-up cycle shape [L.E. Chipperfield et al., Phys.Rev. Lett.102, 063003 (2009)].Here, we present an experimental realization of similar cycle-shaped waveforms and demonstrate control of the high-harmonic generation process on the single-atom quantum level via attosecond steering of the electron trajectories.With our improved optical cycles, we boost the field ionization launching the electron trajectories, increase the subsequent field-to-electron energy transfer, and reduce the trajectory duration.We demonstrate, in realistic experimental conditions, 2 orders of magnitude enhancement of the generated extreme ultraviolet flux together with an increased spectral extension.This application, which is only one example of what can be achieved with cycle-shaped high-field light waves, has significant implications for attosecond spectroscopy and molecular self-probing.

Peptides are irradiated by femtosecond near-infrared pulses, initiating tunnel ionisation and non-ergodic molecular dissociation. Mass spectrometric analysis of the fragments gives unique structural and dynamical information for femtosecond molecular dynamics research and bioanalytical applications.

We present theoretical investigations of high-order harmonic generation (HHG) resulting from the interaction of noble gases with different kind of temporally and spatially synthesized laser fields. These fields, based on localized surface plasmons, are produced when, for instance, a metal nanoparticle or nanostructure, is illuminated by a few-cycle laser pulse. The enhanced field, which largely depends on the geometrical shape of the metallic nanostructure, has a strong spatial dependency in a scale comparable to the one where the electron dynamics takes place. We demonstrate that the spatial nonhomogeneous character of this laser field plays an important role in the HHG process and leads to a significant increase of the harmonic cutoff energy and modifications in the electron trajectories. The use of metal nanostructures appears to be an alternative way of generating coherent XUV light with a laser field whose characteristics can be spatially synthesized locally.