Possibility of tunneling time determination

Abstract

We show that it is impossible to determine the time a tunneling particle spends under the barrier. However, it is possible to determine the asymptotic time, i.e., the time the particle spends in a large area including the barrier. We propose a model of time measurements. The model provides a procedure for calculation of the asymptotic tunneling and reflection times. The model also demonstrates the impossibility of determination of the time the tunneling particle spends under the barrier. Examples for δ-form and rectangular barrier illustrate the obtained results. 03.65.Xp, 03.65.Ta, 03.65.Ca, 73.40.Gk

Weak measurement of arrival time

“…We take the operator describing the interaction between the particle and the detector of the form [17,26,27]…”

Time problem in quantum mechanics and its analysis by the concept of weak measurements

“…If we want to measure the time when the system is in a large region of χ, one has to use many detectors. In the case of tunnelling a similar model was introduced by Steinberg [35] and developed in our paper [23]. The strong limit of such a model for analysis of the measurement effect for the quantum jumps has been used in [25].…”

“…(14) yields the well-known expression for the dwell time [3,23]. This time is the average over the entire ensemble of the systems, regardless of their final states.…”

“…We take the operator describing the interaction between the particle and the detector of the form [22,23,[25][26][27][28]]…”

“…Second, since in the classical mechanics all quantities can have definite values simultaneously, weak measurements give the correct classical limit. The concept of weak measurements has been al-ready applied to the time problem in quantum mechanics [22][23][24].…”