Relativistic features and time delay of laser-induced tunnel-ionization

TL;DR

This paper explores relativistic tunnel-ionization, revealing a momentum shift in the electron wave packet and analyzing tunneling time delays, with implications for understanding electron dynamics in intense laser fields.

Contribution

It introduces a gauge invariant energy operator to identify the relativistic forbidden region and provides a one-dimensional model describing relativistic tunnel-ionization with new insights into tunneling time delays.

Findings

Electron wave packet exhibits a momentum shift along laser propagation.

Tunneling time delay is detectable in near-threshold regimes.

Relativistic effects alter the tunneling dynamics compared to nonrelativistic cases.

Abstract

The electron dynamics in the classically forbidden region during relativistic tunnel-ionization is investigated. The classical forbidden region in the relativistic regime is identified by defining a gauge invariant total energy operator. Introducing position dependent energy levels inside the tunneling barrier, we demonstrate that the relativistic tunnel-ionization can be well described by a one-dimensional intuitive picture. This picture predicts that, in contrast to the well-known nonrelativistic regime, the ionized electron wave packet arises with a momentum shift along the laser's propagation direction. This is compatible with results from a strong field approximation calculation where the binding potential is assumed to be zero-ranged. Further, the tunneling time delay, stemming from Wigner's definition, is investigated for model configurations of tunneling and compared with results obtained from the exact propagator. By adapting Wigner's time delay definition to the ionization process, the tunneling time is investigated in the deep-tunneling and in the near-threshold-tunneling regimes. It is shown that while in the deep-tunneling regime signatures of the tunneling time delay are not measurable at remote distance, it is detectable, however, in the latter regime.