Lifshitz theory of atom-wall interaction with applications to quantum reflection

TL;DR

This paper applies Lifshitz theory to analyze atom-wall interactions, revealing negative entropy effects and providing analytical formulas, with implications for quantum reflection experiments involving metastable helium and metal or dielectric surfaces.

Contribution

It offers the first detailed Lifshitz theory analysis of atom-wall interactions including negative entropy effects and compares exact energies with phenomenological models.

Findings

Negative Casimir-Polder entropy occurs at certain temperatures and separations.

Analytical expressions for free energy and force are derived.

Exact interaction energies differ from phenomenological models, especially for metal walls.

Abstract

The Casimir-Polder interaction of an atom with a metallic wall is investigated in the framework of the Lifshitz theory. It is demonstrated that in some temperature (separation) region the Casimir-Polder entropy takes negative values and goes to zero when the temperature vanishes. This result is obtained both for an ideal metal wall and for real metal walls. Simple analytical representations for the Casimir-Polder free energy and force are also obtained. These results are used to make a comparison between the phenomenological potential used in the theoretical description of quantum reflection and exact atom-wall interaction energy, as given by the Lifshitz theory. Computations are performed for the atom of metastable He${}^{\ast}$ interacting with metal (Au) and dielectric (Si) walls. It is shown that the relative differences between the exact and phenomenological interaction energies are smaller in the case of a metallic wall. This is explained by the effect of negative entropy which occurs only for a metal wall. More accurate atom-wall interaction energies computed here can be used for the interpretation of measurement data in the experiments on quantum reflection.