Longitudinal momentum of the electron at the tunneling exit

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.

On the quantum tunneling time: Instantaneous, finite or probabilistic?

“…This is in line with previous works, e.g. [38], that have also shown that for a 1D model the tunneling ionization produces a non-zero outgoing momentum at the tunnel exit. Clearly, the simple-man's scenario does not apply for this specific situation as there is a pronounced delay and the arrival time exhibits a broad distribution.…”

Extended virtual detector theory including quantum interferences

“…(See, e.g., a summary of several different criteria in [36]) What should be the velocity of the electron at the tunneling exit point? [37][38][39][40][41][42] It is found that the final electron momentum distribution depends sensitively on how these initial conditions are assigned.…”

“…The VD method has been shown to yield good agreements with TDSE calculations on photoelectron momentum distributions [43,44,48], although quantum interferences are necessarily lost due to the transformation to classical trajectories. Besides, the VD technique has been found very useful in gaining insights into the ultrafast ionization process [41,42,[49][50][51]. The goal of the current paper is to present a further development of the VD method.…”

Quantum interference in strong-field ionization by a linearly polarized laser pulse, and its relevance to tunnel exit time and momentum

“…it is beyond the validity range of well-known theories [31]. Recent theoretical approximations of strong-field ionization meeting such conditions often employ classical dynamics, where the choice of proper initial conditions, including the longitudinal momentum, is an important open question [18,[32][33][34][35][36][37][38][39],…”