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

TL;DR

We address causality and time delays in ultrafast photoionization from Argon $3s$ across the Amusia–Cooper minimum (ACM) using ab initio relativistic RTDCIS in both length and velocity gauges, complemented by an analytic dipole-model and a time-energy framework. The study shows gauge-dependent Wigner delays, with velocity gauge producing negative delays and length gauge producing positive delays near the ACM, yet causal wave-packet propagation is recovered when employing weighted delays derived from the Wigner distribution. Spin-orbit coupling yields distinct $j=1/2$ and $j=3/2$ channel dynamics and reveals Schrödinger kitten/cat structures in the Wigner distributions, highlighting rich interchannel coupling effects. The results clarify how causality manifests in correlated ultrafast photoionization and provide practical tools for interpreting attosecond experiments in multi-electron atoms.

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 ($εp_j$ 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 Schrödinger 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.

Figures (5)

• Figure 1: (a) Photoionization CS for the argon $3s$ orbital calculated using RTDCIS (squares) and analytical model (curves) in LG (blue) and VG (red), together with experimental TOF measurements (orange circles) from Ref.mobus1993PRA3S. Panels (b) and (c) show the partial CS for the $3s_{1/2} \rightarrow \epsilon p_{1/2}$ (cyan curves) and $3s_{1/2} \rightarrow \epsilon p_{3/2}$ (magenta curves) relativistic channels in VG and LG, respectively.
• Figure 2: Wigner time delays extracted from the analytical model using parameters obtained by fitting the CS of the model to that of RTDCIS simulations for total $3s$ orbital (a) and relativistic channels in VG (b) and LG (c). The vertical dotted lines in panels (b) and (c) mark the photon energies where the total Wigner delay reaches its extrema for the corresponding gauges shown in panel (a).
• Figure 3: (a) Photoelectron fluxes observed at $R \simeq 87.55$ Bohr for LG with $\tau=362.7$ as, ACM photon energy, and $I=10^{12}$ W/cm$^2$ in RTDCIS and the model. (b) channel-resolved ($\epsilon p_{j}$) fluxes corresponding to the RTDCIS correlated case and the model with a negative sign of $\Delta \varphi$ in (a)
• Figure 4: Channel resolved photoelectron fluxes at $R\simeq 87.55$ Bohr for a pulse of $4.84$ fs duration, intensity of $I=10^{12}$ W/cm$^2$, and the photon energy tuned to the ACM frequency of each gauge. Panels (a) and (b) show the RTDCIS results for LG and VG, respectively, and panels (c) and (d) display the corresponding model calculations. In all panels, curve colors indicate the particle’s angular momentum $\epsilon p_{j}$. The dash–dot–dotted curves show the uncorrelated RTDCIS results, whereas the solid curves show the correlated RTDCIS results. Dotted curves represent the uncorrelated model calculations, while the dashed and dash–dotted curves correspond to the correlated model results with positive and negative phases, respectively.
• Figure 5: Wigner distributions in VG with positive correlation phase for different pulse durations and relativistic channels: top row corresponds to $j=1/2$ and bottom row to $j=3/2$, pulse durations are $363$ as for panels (a) and (e), $1.93$ fs for panels (b) and (f), $4.84$ fs for panels (c) and (g), and $10$ fs for panels (d) and (h).