Causality of ultrafast photoionization from argon 3s using an ab initio relativistic approach

Abstract

We study real-time photoionization flux at the $3s$ Amusia-Cooper minimum (ACM) in argon using \textit{ab initio} simulations with the relativistic time-dependent configuration-interaction singles (RTDCIS) method in length (LG) and velocity (VG) gauges. A simple analytical model is used to interpret the results, and to construct Wigner delays and Wigner distributions for both gauges and relativistic channels of the photoelectron ($\epsilon p_j$ with $j=1/2$ and $3/2$). The two gauges are found to produce qualitatively different ionization dynamics, with LG having positive and VG having negative Wigner delays. The advancement of several femtoseconds, found for Wigner delays in VG, raises some concern for causality when atoms are ionized by attosecond pulses that are shorter than the absolute value of the Wigner delay. Reassuringly, numerical simulations of wave packets with RTDCIS show that the electrons behave in a causal way in both gauges. Weighted delays that take into account the temporal window of excitation (or the bandwidth of the pulses) are constructed from the Wigner distribution to reach agreement between the numerical simulations and our simple wave packet model. Furthermore, a strong effect of spin-orbit coupling of the photoelectron ($j$) is reported for ultrafast photoionization dynamics, and Schr\"odinger kitten and cat states are identified in the Wigner distributions as a result of the ACM. Our work paves the way for a deeper understanding of ultrafast photoionization and the role of causality in systems with strong electron-electron correlation effects.