Quasiperiodic dynamics in the nondipole x-ray strong field ionization in stabilization regime

TL;DR

This paper investigates quasiperiodic modulation of ionization yield in the stabilization regime of high-frequency XUV/x-ray fields under nondipole dynamics. By solving a 2D Foldy–Wouthuysen transformed TDDE with a coordinate-scaling method, the authors reveal that slow Coulomb-driven oscillations of the continuum electron along the propagation direction modulate the ionization yield as a function of pulse duration, with a distinct mechanism from the dipole dynamic interference. They also analyze Coulomb momentum transfer and photon momentum sharing between the photoelectron and ion, showing that ZEP and ATI peaks exhibit markedly different momentum partitioning. The results provide experimentally testable predictions for XFEL facilities and deepen the understanding of Coulomb-nondipole interplay in relativistic strong-field ionization.

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.

Figures (11)

• Figure 1: The dependence of the ionization probability of hydrogen-like helium on the laser pulse duration. Each line represents a different $a_0$ parameter indicated in the inset, $a_0 = 0.13-0.29$ corresponding to the intensity range of $I=2\times 10^{21}-1.1\times 10^{22} \text{W/cm}^2$. The duration of the pulse is $T = N T_0 +{4} \tau$. The laser frequency is $\omega = 14 \text{ a.u.}$
• Figure 2: Comparison of the dipole and nondipole calculations for the ionization probability vs the laser pulse duration. (a) $a_0 = 0.06, ~ E = 120 \text{ a.u.}$, (b) $a_0 = 0.09, ~ E = 180 \text{ a.u.}$, (c) $a_0 = 0.11, ~ E = 210 \text{ a.u.}$, (d) $a_0 = 0.13, ~ E = 240 \text{ a.u.}$; (blue line) -- dipole approximation, (red line) -- nondipole calculations. Duration of the pulse is $T = N T_0 + 4\tau$, $\omega = 14$ a.u.
• Figure 3: Photoelectron momentum distributions (PED) in the dipole case. PED near ZEP in the dipole calculations at different pulse durations, $a_0 = 0.13$, $\omega = 14$ a.u.: (a)-(d) The number of cycles $N$ is indicated in the insets and corresponds to the maxima and minima of the ionization probabilities of Fig. \ref{['Fig-2']}; (e) Comparison of the dynamic model Eq. \ref{['SE']} (dotted line) with PEDs.
• Figure 4: Photoelectron momentum distributions (PED) in the nondipole regime. PED for different pulse durations indicated in the inset: $a_0 = 0.11$. The dipole calculations are shown by the dashed lines, the nondipole by the solid ones.
• Figure 5: The expectation value for the electron coordinates during the interaction. The coordinate in the laser polarization direction is $\langle x(t) \rangle$, and along the propagation direction $\langle z(t) \rangle$. Different lines represent different $a_0$ values indicated in the inset. The frequency is $\omega = 14$ a.u.