Retarded Casimir-Polder force on an atom near reflecting microstructures

TL;DR

This paper derives the fully retarded Casimir-Polder energy shifts for a neutral atom near microstructured reflecting surfaces, providing analytical and numerical tools for understanding atom-surface interactions in microfabricated geometries.

Contribution

It presents new exact and asymptotic expressions for the Casimir-Polder force near cylindrical wires and half-planes, advancing modeling capabilities for microstructure-related quantum forces.

Findings

Derived the energy shift for a wire in various limits

Obtained an exact integral representation for the half-plane case

Provided simple asymptotic formulas for practical estimates

Abstract

We derive the fully retarded energy shift of a neutral atom in two different geometries useful for modelling etched microstructures. First we calculate the energy shift due to a reflecting cylindrical wire, and then we work out the energy shift due to a semi-infinite reflecting half-plane. We analyze the results for the wire in various limits of the wire radius and the distance of the atom from the wire, and obtain simple asymptotic expressions useful for estimates. For the half-plane we find an exact representation of the Casimir-Polder interaction in terms of a single, fast converging integral, which is easy to evaluate numerically.