The time-modulated barrier approach to traversal times from the Bohm trajectory point of view

Abstract

Büttiker and Landauer introduced the time-modulated barrier method for determining the average traversal time τ T for an electron incident on a static barrier. This approach was motivated by the expectation that with the addition to the barrier of a small oscillatory component, V 1cosωt, the tunneling behaviour would exhibit distinct low (ω⪡τ T −1) and high (ω⪢τ T −1) frequency regimes. Recently De Raedt, García and Huyghebaert studied the scattering of gaussian wave packets by time-modulated rectangular barriers. They were unable to extract τ T from the frequency dependence of the calculated transmission probability |T(ω)| 2. In the present paper, possible reasons are suggested. In particular, it is argued that, at least within the Bohm trajectory interpretation of quantum mechanics, a very small increase in the transmission probability actually involves atypically long reflection times rather than the average transmission time of the unperturbed barrier. Hence, there is no reason to expect a signature of τ T in |T(ω)| 2. The Bohm trajectory approach is then used to investigated the ω dependence of the average traversal time and the distribution of traversal times both of which are found to exhibit interesting resonant behavior.