Time-dependent Interactions in Tunnelling Dynamics

TL;DR

This paper investigates how time-dependent perturbations, related to energy measurements, influence quantum tunnelling dynamics, providing exact solutions and proposing a new method to estimate tunnelling time through energy measurements.

Contribution

It introduces an exact solution to the time-dependent Schrödinger equation with measurement-induced perturbations and proposes a novel energy-based method to estimate tunnelling time.

Findings

Tunnelling dynamics are affected by interference between transmitted and reflected waves.

Interference terms are time-dependent and influence the scattering duration.

A new energy measurement method for estimating tunnelling time is proposed.

Abstract

In this paper, the tunnelling of a particle through a potential barrier is investigated in the presence of a time-dependent perturbation. The latter is attributed to the process of the energy measurement of the scattered particle. The time-dependent Schrodinger equation of the model is exactly solved. The calculation of the probability density inside the barrier proves that the tunnelling dynamics is determined not only by the transmitted and reflected waves but also by their interference. Furthermore, the interference term is time-dependent and contribute to the scattering process duration. The tunnelling time is calculated as the time to stop the flow of probability density inside the barrier. This is the minimum duration of the measurement process before detecting the particle beyond the barrier. Based on this, a new method of estimating the tunnelling time by energy experimental measuring is proposed.