Luciano Bracci | Searcharxiv

arXiv1996

Interaction time of a wave packet interact with a potential barrier

We study the evolution of a wave packet impinging onto a one dimensional potential barrier. The transmission and reflection times discussed in the literature for stationary states do not correspond to the times required for the emergence of a transmitted or a reflected packet. We propose new definitions for the interaction (dwell) time and the transmission and reflection times which are suitable for packets and fit better the actual time evolution of the packet.

quant-ph↗

arXiv1996

The tunneling time for a wave packet as measured with a physical clock

We study the time required for a wave packet to tunnel beyond a square barrier, or to be reflected, by envisaging a physical clock which ticks only when the particle is within the barrier region. The clock consists in a magnetic moment initially aligned with the $x$ axis which in the barrier region precesses around a constant magnetic field aligned with the $z$ axis, the motion being in the $y$ direction. The values of the $x$ and $y$ components of the magnetic moment beyond or in front of the barrier allow to assign a tunneling or reflection time to every fraction of the packet which emerges from the barrier and to calculate tunneling times $τ_{\rm T,x}$ and $τ_{\rm T,y}$ and reflection times $τ_{\rm R,x}$ and $τ_{\rm R,y}$. The times $τ_{\rm T,x}$ and $τ_{\rm T,y}$ ($τ_{\rm R,x}$ and $τ_{\rm R,y}$) are remarkably equal, and independent of the initial position (in front of the barrier) of the packet.

quant-ph↗