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arXiv:quant-ph/0005050 · Physical Review A

Transient interference of transmission and incidence

A. L. Pérez Prieto, S. Brouard, Juan Gonzalo Muga

Published Jun 7, 2001• 20 citations
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Abstract

Due to a transient quantum interference during a wave packet collision with a potential barrier, a particular momentum, that depends on the potential parameters, but is close to the initial average momentum, becomes suppressed. The hole left pushes the momentum distribution outwards leading to a significant constructive enhancement of lower and higher momenta. This is explained in the momentum complex-plane language in terms of a saddle point and two contiguous ``structural'' poles, which are not associated with resonances but with incident and transmitted components of the wave function.

DOI
10.1103/physreva.64.012710

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Due to a transient quantum interference during a wave packet collision with a potential barrier, a particular momentum, that depends on the potential parameters, but is close to the initial average momentum, becomes suppressed. The hole left pushes the momentum distribution outwards leading to a significant constructive enhancement of lower and higher momenta. This is explained in the momentum complex-plane language in terms of a saddle point and two contiguous ``structural'' poles, which are not associated with resonances but with incident and transmitted components of the wave function.
A transient interference during the collision of a broad quantum particle wave packet with a properly chosen potential barrier suppresses, for energies well above the barrier top, the main incident momentum. This collision enhances the momenta below and above the central one, violating the classical conservation of energy. For the double square barrier the effect is due to the interference between three components (incident, transmitted, and interbarriers terms) and survives much longer than for the single barrier, facilitating its observation. A quantum optical realization with two-level atoms and effective laser barriers is discussed.
An interesting analytical expression is obtained for the coordinate probability distribution of a wave packet transmitted through a potential barrier. In the large-time asymptotics the distribution is given in terms of the transmission amplitude and the phase-space quasidistribution of the initial (not necessarily pure) state. The distortion of a (broad) wave packet due to the barrier penetration is determined by two timelike parameters, given by the energy derivative of the complex transmission amplitude. The resulting change of the packet shape reveals a dependence on the detector position and incorporates a possible speed-up effect and a negative dispersion.