Casimir-Polder energy level shifts of an out-of-equilibrium particle near a microsphere

TL;DR

This paper derives a simple, accurate formula for the energy level shifts of out-of-equilibrium particles near a metallic sphere, accounting for retardation, conductivity, and geometry effects, useful for ultracold atom experiments.

Contribution

It introduces a new perturbative expansion method to calculate particle-surface interaction potentials with high accuracy, applicable to complex geometries.

Findings

The derived formula achieves better than 1% accuracy at room temperature.

Retardation and conductivity effects are quantitatively characterized.

The method is adaptable to other geometries.

Abstract

Rydberg atoms and beams of ultracold polar molecules have become highly useful experimental tools in recent years. There is therefore a need for accessible calculations of interaction potentials between such particles and nearby surfaces and structures, bearing in mind that the particles are far out of thermal equilibrium with their environment and that their interaction is predominantly non-retarded. Based on a new perturbative expansion with respect to the inverse speed of light and the inverse conductivity, we derive a simple, closed-form expression for the interaction potential (i.e., the particle energy level shifts) of a particle and a metallic sphere that is is accurate at better than 1% level for typical experimental set-ups at room temperature and above, and off by no more than a few percent at any temperature including zero. Our result illuminates the influence of retardation and imperfect conductivity and the interplay of these effects with geometry. The method developed for the present study may be applied to other, more complex geometries.