Causality and quantum interference in time-delayed laser-induced nonsequential double ionization

TL;DR

This paper investigates how causality influences the quantum interference patterns in laser-induced nonsequential double ionization, revealing its critical role in shaping electron momentum distributions during the RESI process.

Contribution

It introduces a causality condition for complex times in the RESI pathway, affecting the calculation of transition amplitudes and electron momentum distributions in strong-field ionization.

Findings

Causality constrains saddle points in the steepest descent analysis.

Causality significantly alters electron momentum distribution shapes.

Quantum interference patterns are explained through dominant electron orbits.

Abstract

We perform a detailed analysis of the importance of causality within the strong-field approximation and the steepest descent framework for the recollision-excitation with subsequent tunneling ionization (RESI) pathway in laser-induced nonsequential double ionization (NSDI). In this time-delayed pathway, an electron returns to its parent ion, and, by recolliding with the core, gives part of its kinetic energy to excite a second electron at a time $t^{\prime}$. The second electron then reaches the continuum at a later time $t$ by tunneling ionization. We show that, if $t^{\prime}$ and $t$ are complex, the condition that recollision of the first electron occurs before tunnel ionization of the second electron translates into boundary conditions for the steepest-descent contours, and thus puts constraints on the saddles to be taken when computing the RESI transition amplitudes. We also show that this generalized causality condition has a dramatic effect in the shapes of the RESI electron momentum distributions for few-cycle laser pulses. Physically, causality determines how the dominant sets of orbits an electron returning to its parent ion can be combined with the dominant orbits of a second electron tunneling from an excited state. All features encountered are analyzed in terms of such orbits, and their quantum interference.