Casimir effect and quantum reflection

TL;DR

This paper investigates how quantum reflection of antihydrogen atoms near a surface, influenced by the Casimir-Polder potential, can be understood through a Liouville transformation, aiding in antimatter free-fall experiments.

Contribution

It provides a detailed evaluation of the Casimir-Polder potential and introduces a Liouville transformation approach to better understand quantum reflection phenomena.

Findings

Quantum reflection is stronger with weaker potentials.

Liouville transformation offers an intuitive scattering perspective.

Enhanced reflection could impact antimatter free-fall measurements.

Abstract

The GBAR experiment will time the free fall of cold antihydrogen atoms dropped onto an annihilation plate to test the universality of free fall on antimatter. In this contribution, we study the quantum reflection of the anti-atom resulting from the Casimir-Polder attraction to the plate. We evaluate the Casimir-Polder potential and the associated quantum reflection amplitudes and find that reflection is enhanced for weaker potentials. A Liouville transformation of the Schr\"odinger equation is used to map the quantum reflection problem onto an equivalent problem of scattering on a barrier, leading to an intuitive understanding of the phenomenon.