Operational approach to indirectly measuring the tunneling time

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.