On the longitudinal momentum of the electron at the tunneling exit

TL;DR

This paper demonstrates that the quantum mechanical flow momentum at the tunneling exit is inherently nonzero, providing a better understanding of electron dynamics during tunneling ionization, especially under nonadiabatic conditions.

Contribution

It introduces the flow momentum of the probability fluid as a quantum definition for tunneling-exit momentum, showing it is nonzero even in static conditions.

Findings

Flow momentum is a sensible quantum measure for tunneling exit momentum.

Nonzero tunneling exit momentum persists in static or adiabatic limits.

Nonadiabaticity and finite wavelength can significantly increase this momentum.

Abstract

The longitudinal momentum of the electron at the tunneling exit is a useful quantity to make sense of the tunneling ionization process. It was usually assumed to be zero from a classical argument, but recent experiments show that it must be nonzero in order to explain the measured electron momentum distributions. In this article we show that the flow momentum of the probability fluid is a sensible quantum mechanical definition for tunneling-exit momentum, and it can be (and in general is) nonzero at the tunneling exit point where the kinetic energy is zero by definition. We show that this longitudinal momentum is nonzero even in the static or adiabatic limit, and this nonzero momentum is a purely quantum mechanical effect determined by the shape of the wave function in the vicinity of the tunneling exit point. Nonadiabaticity or finite wavelength may increase this momentum substantially, and the detailed value depends on both the atomic and the laser parameters.