Virtual-detector approach to tunnel ionization and tunneling times

TL;DR

This paper introduces a virtual detector method to precisely define tunneling times in atomic ionization, revealing nonzero velocities at tunneling exit and clarifying the timing relative to the electric field.

Contribution

It presents a novel virtual detector approach that unambiguously determines tunneling entry and exit times from first principles.

Findings

Tunneling times do not coincide with the electric field maximum.

Electrons have nonzero velocity at tunneling exit.

The approach clarifies the timing of tunneling events.

Abstract

Tunneling times in atomic ionization are studied theoretically by a virtual detector approach. A virtual detector is a hypothetical device that allows one to monitor the wave function's density with spatial and temporal resolution during the ionization process. With this theoretical approach, it becomes possible to define unique moments when the electron enters and leaves with highest probability the classically forbidden region from first principles and a tunneling time can be specified unambiguously. It is shown that neither the moment when the electron enters the tunneling barrier nor when it leaves the tunneling barrier coincides with the moment when the external electric field reaches its maximum. Under the tunneling barrier as well as at the exit the electron has a nonzero velocity in the electric field direction. This nonzero exit velocity has to be incorporated when the free motion of the electron is modeled by classical equations of motion.