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arXiv:quant-ph/0607038 · The European Physical Journal D

Tunneling times through a barrier with inelasticity

Arya Paul, A. Saha, Swarnali Bandopadhyay, Binayak Dutta-Roy

Published Mar 8, 2007• 8 citations
arXivHTMLPDF
DOI
10.1140/epjd/e2007-00050-8

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We calculate the time taken by a wave packet to tunnel through a series of complex barrier potentials using stationary phase method to show its saturation (Hartman-Fletcher effect) with number of barriers in various situations. We numerically study the effect of the coupling between the elastic and inelastic channels, width of the individual barrier, separation between the consecutive barriers on the saturation of tunneling time. Nature of HF effect has further been investigated for more realistic barriers with random inelasticity and also for emissive inelastic channels.
The frequency-dependent transmission coefficient for a particle tunneling through a time-dependent barrier is calculated taking into account inelastic and virtual processes. We consider a barrier of arbitrary shape with a time-dependent modulation of single frequency ω. For small modulation amplitudes V 1 , our result is exact up to order V 1 2 . The result is obtained in the low transmission limit and is consistent with the exact calculation for a rectangular barrier. We find that the virtual processes can make a significant contribution to the tunneling current, especially at low ω. In the static approximation ωτ << 1, where τ is the barrier transit time, the contribution of the second order virtual process is equal to one half of the tunneling current from the first order inelastic processes.
One of several contradictory existing results for the time a tunneling particle interacts with its barrier is confirmed, by considering tunneling through a time-modulated barrier. At low modulation frequencies the traversing particle sees a static barrier. At high frequencies the particle tunnels through the time-averaged potential, but can do it inelastically, losing or gaining modulation quanta. The transition between the two regimes yields $\ensuremath{\int}\mathrm{dx}{[\frac{m}{2(V\ensuremath{-}E)}]}^{\frac{1}{2}}$ for the traversal time.