Tunneling Time, Exit Time and Exit Momentum in Strong Field Tunnel Ionization

Abstract

Tunnel ionization belongs to the fundamental processes of atomic physics. It is still an open question when does the electron tunnel ionize and how long is the duration of tunneling. In this work we solve the time-dependent Schr{\o}dinger equation in one and two dimensions and use \textit{ab initio} quantum calculations in order to answer these questions. Additionally, we determine the exit momentum of the tunnel ionized electron from first principles. We find out results that are different from the assumptions of the commonly employed two-step model, which assumes that the electron ionizes at the instant of electric field maximum with a zero momentum. After determining the quantum final momentum distribution of tunnel ionized electrons we show that the two-step model fails to predict the correct final momentum. Accordingly we suggest how to correct the two-step model. Furthermore, we determine the instant at which tunnel ionization starts, which turns out to be different from the instant usually assumed. From determining the instant at which it is most probable for the electron to enter the tunneling barrier and the instant at which it exits we determine the most probable time spent under the barrier. Moreover, we apply a quantum clock approach in order to determine the duration of tunnel ionization. From the quantum clock we determine an average tunneling time which is different in magnitude and origin with respect to the most probable tunneling time. By defining a probability distribution of tunneling times using virtual detectors we relate both methods and explain the apparent discrepancy. The results found have in general an effect on the interpretation of experiments that measure the spectra of tunnel ionized electrons, and specifically on the calibration of the so called attoclock experiments, because models with imprecise assumptions are usually employed in order to interpret experimental results.