An operational approach to indirectly measuring tunneling time

TL;DR

This paper presents an operational method to measure tunneling time in quantum mechanics by relating it to the dwell time operator and using weak measurement techniques involving Larmor precession.

Contribution

It introduces a novel indirect measurement approach for tunneling time using the dwell time operator and contextual values formalism, applicable to quantum tunneling experiments.

Findings

Reconstruction of the conditioned dwell time from spin measurements

Tunneling time expressed as a weak value plus disturbance term

Method enables extraction of moments of dwell time from experimental data

Abstract

The tunneling time through an arbitrary bounded one-dimensional barrier is investigated using the dwell time operator. We relate the tunneling time to the conditioned average of the dwell time operator because of the natural post-selection in the case of successful tunneling. We discuss an indirect measurement by timing the particle, and show we are able to reconstruct the conditioned average value of the dwell time operator by applying the contextual values formalism for generalized measurements based on the physics of Larmor precession. The experimentally measurable tunneling time in the weak interaction limit is given by the weak value of the dwell time operator plus a measurement-context dependent disturbance term. We show how the expectation value and higher moments of the dwell time operator can be extracted from measurement data of the particle's spin.