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College Physics

Goos-Hanchen effect in quantum mechanics

Jian Zhang

Published Jan 1, 2004• 0 citations
OpenAlex

Abstract

Goos-Hanchen effect exists in quantum mechanics as well as in electromagnetism. The model of two-dimensional wave-packet scattering by a two-dimensional potential step is constructed to analyse the inherent cause of Goos-Hanchen effect.

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We explore the analogy between following the motion of a reflected wave packet and a quantum measurement of the spatial delay imposed on the particle by the scattering potential. It is shown that converting such delays into temporal durations can lead to “negative times,” and best be avoided. It is also demonstrated that a “soft” potential can be replaced by a superposition of hard walls. This representation is used for calculating the Goos-Hänchen shift of a Gaussian beam incident on a potential step or a barrier at an oblique angle.
We consider a matter wave packet of cold atom gas impinging upon a step potential created by an optical light field. In the presence of spin-orbit coupling, the atomic eigenstates contain two types of evanescent states, one of which is an ordinary evanescent state with a pure imaginary wave vector while the other possesses a complex wave vector and is recognized as an oscillating evanescent state. We show that the presence and interplay of these two types of evanescent states can give rise to two different mechanisms for total internal reflection, and thus lead to an unusual Goos-H\"anchen (GH) effect. As a result, not only large positive but also large negative GH shifts can be observed in the reflected atomic beam. The dependence of the GH shift on the incident angle, energy, and height of the step potential is studied numerically.