Phase shifts of atomic de Broglie waves at an evanescent wave mirror

TL;DR

This paper provides a comprehensive quantum mechanical analysis of atomic de Broglie wave reflection at an evanescent wave mirror, revealing phase shifts and regimes of reflection beyond classical descriptions.

Contribution

It introduces an exact wave-mechanical solution for the phase shift and identifies quantum reflection regimes not captured by semiclassical methods.

Findings

Exact phase shift calculation for atomic reflection

Identification of quantum reflection regime with large de Broglie wavelength

Comparison between classical, semiclassical, and quantum reflection regimes

Abstract

A detailed theoretical investigation of the reflection of an atomic de Broglie wave at an evanescent wave mirror is presented. The classical and the semiclassical descriptions of the reflection process are reviewed, and a full wave-mechanical approach based on the analytical soution of the corresponding Schr\"odinger equation is presented. The phase shift at reflection is calculated exactly and interpreted in terms of instantaneous reflection of the atom at an effective mirror. Besides the semiclassical regime of reflection describable by the WKB method, a pure quantum regime of reflection is identified in the limit where the incident de Broglie wavelength is large compared to the evanescent wave decay length.