Comparing experiments on quantum traversal time with the predictions of a space-time-symmetric formalism

TL;DR

This paper applies a space-time-symmetric quantum formalism to derive and test a new expression for quantum traversal time, showing improved accuracy over traditional approximations in a specific experimental scenario.

Contribution

It introduces a novel time operator within a symmetric space-time framework and derives an analytic traversal time expression tested against experimental data.

Findings

The new formalism yields a closed analytic traversal time expression.

It outperforms B"uttiker-Landauer and phase-time approximations.

Experimental comparison shows better agreement with observed data.

Abstract

The question of how long a particle takes to pass through a potential barrier is still a controversial topic in quantum mechanics. Arguably, the main theoretical problem in obtaining estimates for measurable times is the fact that previously defined time operators, that remained within the borders of standard quantum mechanics, present some kind of pathology. Recently, a time operator acting on an additional Hilbert space has been shown to support both Hermiticity and canonical relation with an energy observable. The theory is built in a framework which treats space and time as symmetrically as possible, in the nonrelativistic regime. In this work, we use this formalism to derive a closed analytic expression for the traversal time of a quantum particle impinging on a constant-potential barrier. We test our theory in the specific experimental scenario of a realization by Rafagni et al [Appl. Phys. Lett. {\bf 58}, 774 (1991)]. The proposed approach displays a much better performance in comparison with the B\"uttiker-Landauer and the phase-time approximations.