Ionization Time and Exit Momentum in Strong-Field Tunnel Ionization

TL;DR

This paper demonstrates through numerical solutions of the Schrödinger equation that tunnel ionization involves a measurable time delay and nonzero exit momentum, challenging the traditional two-step model assumptions.

Contribution

It reveals nonzero ionization time delays and exit momenta, emphasizing the importance of initial electron momentum in tunneling time analysis.

Findings

Nonzero positive time delay between electric field maximum and ionization.

Nonzero exit momentum in the direction of the electric field.

Proper tunneling times require accounting for initial electron momentum.

Abstract

Tunnel ionization belongs to the fundamental processes of atomic physics. The so-called two-step model, which describes the ionization as instantaneous tunneling at the electric field maximum and classical motion afterwards with zero exit momentum, is commonly employed to describe tunnel ionization in adiabatic regimes. In this contribution, we show by solving numerically the time-dependent Schr\"odinger equation in one dimension and employing a virtual detector at the tunnel exit that there is a nonvanishing positive time delay between the electric field maximum and the instant of ionization. Moreover, we find a nonzero exit momentum in the direction of the electric field. To extract proper tunneling times from asymptotic momentum distributions of ionized electrons, it is essential to incorporate the electron's initial momentum in the direction of the external electric field.