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arXiv:2602.06762

Quasiperiodic nondipole ionization dynamics in the x-ray stabilization regime

Aleksandr V. Boitsov, Karen Z. Hatsagortsyan, Christoph H. Keitel

physics.atom-phquant-phSubmitted Feb 6, 2026• Announced Feb 9, 2026• Revised Jun 25, 2026 (v3)
v1 · Feb 6, 2026v2 · Feb 16, 2026v3 · Jun 25, 2026
arXivHTMLPDF

Abstract

Recent advances in strong x-ray laser techniques enable the study of nonlinear multiphoton ionization in extreme high-frequency fields. Although the stabilization regime in such fields is theoretically established, its modified properties in the nondipole regime for long laser pulses remains unknown. Here, we numerically investigate the strong-field ionization of an atom in a long XUV laser pulse in the nondipole regime. Our study of the time-dependent quantum dynamics reveals a quasiperiodic modulation of the ionization yield as a function of pulse duration. We demonstrate that the Coulomb-field-induced slow oscillation of the ionized electron wave packet during the interaction is responsible for the observed modulation of the ionization yield. Furthermore, we scrutinize the unusual photon momentum sharing between the photoelectron and the ion in this extreme regime. These effects are observable in upcoming x-ray free-electron laser facilities.

Journal reference
Phys. Rev. A 114, 033110 (2026)
DOI
10.1103/qhyv-x54g
Comments
Submitted to Physical Review A. Revised and updated

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We demonstrate Rabi oscillations in nonlinear ionization of argon by an intense femtosecond extreme ultraviolet (XUV) laser field produced by high-harmonic generation. We monitor the formation of Ar2+\mathrm{A}{\mathrm{r}}^{2+}Ar2+ as a function of the time delay between the XUV pulse and an additional near-infrared (NIR) femtosecond laser pulse, and show that the population of an Ar+∗\mathrm{A}{\mathrm{r}}^{+*}Ar+∗ intermediate resonance exhibits strong modulations both due to an NIR laser-induced Stark shift and XUV-induced Rabi cycling between the ground state of Ar+\mathrm{A}{\mathrm{r}}^{+}Ar+ and the Ar+∗\mathrm{A}{\mathrm{r}}^{+*}Ar+∗ excited state. Our experiment represents a direct experimental observation of a Rabi-cycling process in the XUV regime.
Abstract We present a theoretical study on the quantum control of ultrafast Rabi dynamics in atoms driven by chirped extreme ultraviolet (XUV) pulses. Motivated by recent experimental advances using free-electron lasers, we derive an analytical solution of the Rabi oscillation under the rotating wave approximation, incorporating the spectral chirp of the XUV field. Within the essential-states model, we demonstrate how the chirp modulates the phase of the excited-state amplitude, inducing an observable asymmetry in the Autler–Townes (AT) doublets of the photoelectrons. Our theoretical predictions, benchmarked against time-dependent Schrödinger equation simulations, reveal that chirp-dependent phase modulation governs the spectral asymmetry, offering a time-domain perspective for interpreting strong-field photoionization at short wavelengths. This work provides a compact analytical framework for chirp-mediated coherent control in the XUV regime and sheds light on recent experimental observations of asymmetric AT structures in helium.
Non-perturbative resonant multiphoton ionization (1+1)(1+1)(1+1) is studied using the resolvent operator technique. Scaling parameters for effective two-level Hamiltonians are computed for hydrogen and helium atoms to provide a quantitative description of Rabi oscillations at XUV wavelengths, which were recently observed using a seeded Free-Electron Laser [S. Nandi et al., Nature 608, 488-493 (2022)]. The resulting photoelectron spectra exhibit a range of Autler-Townes doublets, which are studied for different intensities, detunings and interaction times. We identify a photoelectron signature that originates from stabilization against ionization of helium atoms interacting with intense circularly polarized XUV light. Thus, our work shows how it is possible to test the prediction of dressed-atom stabilization by Beers and Armstrong [B. L. Beers and L. Armstrong, Phys. Rev. A 12, 2447 (1975)], without the demanding requirement of atomic saturation in the time domain.
Nonperturbative resonant multiphoton ionization (1+1)(1+1)(1+1) is studied using the resolvent operator technique. Scaling parameters for effective two-level Hamiltonians are computed for hydrogen and helium atoms to provide a quantitative description of Rabi oscillations at XUV wavelengths, which were recently observed using a seeded free-electron laser [S. Nandi et al., Nature (London) 608, 488 (2022)]. The resulting photoelectron spectra exhibit a range of Autler-Townes doublets, which are studied for different intensities, detunings, and interaction times. We identify a photoelectron signature that originates from stabilization against ionization of helium atoms interacting with intense circularly polarized XUV light. Thus, our study shows how it is possible to test the prediction of dressed-atom stabilization by Beers and Armstrong [B. L. Beers and L. Armstrong, Phys. Rev. A 12, 2447 (1975)], without the demanding requirement of atomic saturation in the time domain.
Photoionization of Rydberg atoms is considered in the framework of the quasiclassical (WKB) approach. Distribution of the photoelectron density in space and time is found and analyzed. This distribution is shown to consist of two main parts: the temporary population, which exists only as long as the light field is on; and the population corresponding to irreversible ionization. The irreversible-ionization wave packets are shown to experience the effect referred to as Coulomb narrowing. An origin of this effect and the conditions of its existence are discussed. In a strong field, rather simple analytical expressions are found for the partial probabilities of above-threshold ionization and for the total probability of ionization. In contrast to many earlier works, in the present theory neither the rotating-wave nor ``pole'' approximations are used, and the results are derived for an arbitrary pulse shape. Strong-field interference stabilization of Rydberg atoms is confirmed to occur at pulse durations shorter than the Kepler period. The arising regimes of interference stabilization are analyzed in comparison with the predictions of earlier works.
The past thirty years witnessed rapid developing of strong field physics that leads to the first generation of attosecond (10−18 s) pulses. The duration of available pulses has recently been reduced to less than 100 as, approaching the Kepler period of a classical electron revolving around the nucleus. For the first time, electron motions inside atoms, molecules and solids can be traced, probed and even steered in real time. It pushed the study on ultrafast dynamic processes into a new frontier, giving birth to attosecond physics. The development of attosecond pulses provides unprecedented coherent ultrashort XUV (extreme ultra-violet) of soft X-ray sources that enable imaging the atomic structure and resolving the related quantum dynamics for matter science. In particular, it allows the probing and monitoring of electron dynamics in the natural time scale of attoseconds with atomic spatial resolution. The generation and applications of attosecond pulses are directly related to the control and manipulation of the sub-cycle electron dynamics. Recent studies on the correlated multielectron dynamics have provided insight into the optical and dynamical properties of matter in the perspectives of time, phase and entanglement. It deepens our understanding on some of the fundamental questions, e.g., how the single or multiple photons are absorbed and how short are the quantum processes such as photoionization, tunneling ionization and charge migration. Although currently attosecond pulses are limited by the flux and pulse duration, the combination of attosecond pulses with intense infrared laser pulses paves new ways of controlling and probing electron dynamics in the domains of energy, time and space that lays the foundation for petahertz optoelectronics and attosecond pulse based transient spectroscopy. In this review, we will first briefly summarize the advancement of strong field and ultrafast physics including the relevant experimental findings, the theoretical explorations, the related technologies and the possible applications. Then we focus on the sub-cycle electron or multielectron dynamics and their manifestation on the ionization and coherent radiation properties. We start with the time behavior of Fano resonance and how it can be probed in time domain. In section 2, the correlated electron dynamics is discussed in term of anti-screening effect and Pauli effect that influence strong field ionization and high harmonic generation processes. In section 3, the coherent emission with frequency from terahertz to soft XUV and their joint measurement are discussed by emphasizing the generation mechanism of terahertz wave in two-color laser pulses. The developed high-harmonic and terahertz wave spectroscopy (HATS) is shown capable of imaging the molecular structure and dynamics. In section 4, the time-resolving of electron and hole dynamics and their coherence is proposed based on attosecond transient absorption technique. The coherence of ionization and the correlated electron dynamics is hinted crucial for electron-hole interaction. The topics are very limited and mainly selected from the perspectives of our group.