Quantum reflection times and space shifts for Casimir–van der Waals potential tails

Abstract

When cold atoms approach a surface, they can be quantum reflected by quantal regions in the tail of the atom-surface potential. We study the phase of the reflection amplitude for Casimir-van der Waals potential tails, depending on the critical parameter {rho}={rho}(C{sub 3},C{sub 4}), which describes the relative importance of the -C{sub 3}/r{sup 3} and -C{sub 4}/r{sup 4} parts of the potential. The phase is related to observable kinematic quantities, the space and time shifts, the reflected atom experiences. We study three different models for the shape of the potential between the asymptotic limits and observe that the phases are more sensitive to the potential shape than the quantum reflection probabilities. At threshold, there are always time delays in comparison to the free movement. This is in contrast to the classical movement, which shows time gains. Further above threshold, the quantum reflected atom experiences a time gain relative to free motion, but this time gain is generally smaller than that of the classical particle.