Due to the dependence of the dynamic interference phenomenon on the AC-Stark energy shift and atomic stabilization mechanism under extreme ultraviolet (XUV) fields, a higher XUV light intensity is necessary to observe the dynamic interference phenomenon of hydrogen atoms. This poses a challenge for experimental verification. Accordingly, in this work, infrared (IR) auxiliary pulses were introduced to modulate the ionized electrons, providing a solid theoretical basis for the experimental verification of dynamic interference phenomena.

Numerical solutions of the three-dimensional time-dependent Schr?dinger equation (TDSE) were employed to compute the photoelectron energy spectrum of ground-state hydrogen atoms exposed to IR + XUV two-color laser pulses. The radial part of the wave function was discretized using the finite element discrete variable method (FEDVR), while the split-Lanczos method was utilized for the wave function propagation. By varying the pulse delay, IR pulse intensity, and full width at half maximum (FWHM) of the XUV pulse, we comprehensively analyzed their impact on the multi-peak structure observed in the photoelectron energy spectrum. Utilizing the strong field approximation (SFA) and saddle point approximation (SPA), we successfully replicated the multi-peak structure observed in the TDSE calculations and examined the underlying physical mechanisms responsible for this intricate phenomenon.

Initially, for a short period of the infrared pulse, the dynamic interference phenomenon was most pronounced when the peak position of the XUV pulse coincided with the extreme position of the infrared pulse. This caused a shift in the peak position and variation in the number of peaks in the photoelectron energy spectrum (Fig. 2). Furthermore, an increase in the intensity of the infrared laser light led to a transition from a single peak to a multi-peak structure in the photoelectron energy spectrum, with simultaneous shifts in the peak positions and troughs. Consequently, a higher intensity of the infrared pulse accentuates the dynamic interference phenomenon (Fig. 3). Additionally, as the FWHM of the XUV pulse increased, the amplitude and number of peaks expanded, while the positions of the peaks and troughs remained constant, highlighting the close relationship between the dynamic interference phenomenon and the duration of the XUV pulse (Fig. 4). Our calculations using SPA reveal that in scenarios where both the infrared laser pulse and XUV pulse comprise a few periods, dynamic interference arose from the interference between the emitted electron wave packets at the rising and falling edges (Fig. 5). The subsequent analysis focused on the variation in the photoelectron energy spectrum with the FWHM of the XUV pulse in multicycle infrared pulse settings. We discovered that as the FWHM of the XUV pulse increased, the photoelectron energy spectrum transformed from broad bands to finer stripes, indicating that the spectral structure is a result of the mutual interference of all the emitted electron wave packets, rather than just the interference in the few-cycle scenario (Fig. 6). Moreover, our calculations demonstrate that with a small FWHM of the XUV pulse, the peak spacing on the photoelectron spectrum exceeds the infrared photon energy. However, as the FWHM of the XUV pulse increased, additional small peaks emerged on the photoelectron spectrum, with their peak components aligning with the energy of a single infrared photon (Fig. 7).

The time multi-slit interference of ground-state hydrogen atoms exposed to linearly polarized IR and XUV two-color fields was investigated and our calculations reveal that the most pronounced dynamic interference occurs when the peak position of the XUV pulse coincides with the extreme position of the infrared pulse. In the XUV laser field, the AC-Stark energy shift induced by a strong laser causes a significant phase difference in the emitted electron wave packet, giving rise to the observed dynamic interference phenomenon. Furthermore, we found that the dynamic interference phenomenon in the XUV laser field is intricately linked to the atomic stabilization mechanism, necessitating sufficient laser light intensity in a single XUV laser. Regarding infrared-assisted dynamic interference, our model calculations demonstrate a close relationship between the dynamic interference in the two-color field and the infrared pulse vector potential, which modulates the ionized electrons to generate the required phase difference between the interfering electron wave packets. Comparing our theoretical findings with the experimental conditions of XUV pulse ground-state hydrogen atom ionization, the required XUV laser peak intensity is significantly reduced under a two-color field. This reduction has the potential to streamline the experimental laser requirements. Furthermore, our analysis of the temporal multi-slit interference structure, which emerges as the lengths of the infrared and XUV pulses increase, provides valuable insights beyond the temporal double-slit interference of the rising and falling edges of the pulse. In conclusion, our calculations offer substantial theoretical guidance for experimentally verifying the existence of dynamic interference phenomena, paving the way for the further exploration and validation of these intriguing quantum dynamics.