Casimir-Polder shifts on quantum levitation states

TL;DR

This paper investigates quantum levitation states of ultracold atoms near a mirror influenced by Casimir-Polder forces, using a novel transformation to analyze energy shifts and lifetimes relevant for testing fundamental physics.

Contribution

It introduces a Liouville transformation approach to model Casimir-Polder effects on quantum states and proposes an accurate approximation for energy shifts in antihydrogen spectroscopy.

Findings

Numerical calculation of Casimir-Polder energy shifts for cavity resonances.

Development of a precise approximate method for spectroscopy analysis.

Discussion of cavity resonance lifetimes through complex energy calculations.

Abstract

An ultracold atom above a horizontal mirror experiences quantum reflection from the attractive Casimir-Polder interaction, which holds it against gravity and leads to quantum levitation states. We analyze this system by using a Liouville transformation of the Schr\"odinger equation and a Langer coordinate adapted to problems with a classical turning point. Reflection on the Casimir-Polder attractive well is replaced by reflection on a repulsive wall and the problem is then viewed as an ultracold atom trapped inside a cavity with gravity and Casimir-Polder potentials acting respectively as top and bottom mirrors. We calculate numerically Casimir-Polder shifts of the energies of the cavity resonances and propose a new approximate treatment which is precise enough to discuss spectroscopy experiments aiming at tests of the weak equivalence principle on antihydrogen. We also discuss the lifetimes by calculating complex energies associated with cavity resonances.