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Annalen der Physik

Transient increase of high momenta in quantum wave-packet collisions

S. Brouard, Juan Gonzalo Muga

Published Dec 1, 1998• 5 citations
Publisher

Abstract

We study the transient increase of the upper tail of the momentum distribution in quantum wave-packet collisions with an analytically solvable model; in particular its dependence with the barrier strength and incident momentum. This effect is a classically forbidden, universal feature of all quantum collisions.
DOI
10.1002/(sici)1521-3889(199812)7:7/8<679::aid-andp679>3.0.co;2-y

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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.