Timescales of tunneling decay of a localized state

TL;DR

This paper investigates the short-term and long-term timescales involved in the tunneling decay of a localized quantum state, highlighting the initial flux development and the quasistationary decay process, with implications for ultrafast atom ionization experiments.

Contribution

It provides a detailed analysis of the transient dynamics and timescales of tunneling decay, connecting initial state localization to flux development and defining operational tunneling times.

Findings

Initial tunneling flux starts immediately but takes time to develop.

The flux propagation timescale near the barrier is close to the Büttiker-Landauer traversal time.

A longer extrapolated tunneling time is obtained by backward propagation of the wave packet.

Abstract

Motivated by recent time domain experiments on ultrafast atom ionization, we analyze the transients and timescales that characterize, besides the relatively long lifetime, the decay by tunneling of a localized state. While the tunneling starts immediately, some time is required for the outgoing flux to develop. This short-term behavior depends strongly on the initial state. For the initial state tightly localized so that the initial transients are dominated by over-the-barrier motion, the timescale for the flux propagation through the barrier is close to the B\"uttiker-Landauer traversal time. Then a quasistationary, slowly decay process follows, which sets ideal conditions for observing diffraction in time at longer times and distances. To define operationally a tunnelling time at the barrier edge, we extrapolate backwards the propagation of the wave packet escaped from the potential. This extrapolated time is considerably longer than the timescale of the flux and density buildup at the barrier edge.