Casimir-Polder interatomic potential between two atoms at finite temperature and in the presence of boundary conditions

TL;DR

This paper derives an analytical expression for the Casimir-Polder potential between two atoms near a conducting boundary at finite temperature, highlighting the effects of boundary conditions and thermal fluctuations.

Contribution

It introduces a method based on equal-time spatial correlations of the electric field to evaluate the potential, including boundary and temperature effects, with explicit near and far zone formulas.

Findings

Analytical expressions for the potential in different regimes

Effects of boundary conditions on interatomic forces

Influence of temperature on the Casimir-Polder interaction

Abstract

We evaluate the Casimir-Polder potential between two atoms in the presence of an infinite perfectly conducting plate and at nonzero temperature. In order to calculate the potential, we use a method based on equal-time spatial correlations of the electric field, already used to evaluate the effect of boundary conditions on interatomic potentials. This method gives also a transparent physical picture of the role of a finite temperature and boundary conditions on the Casimir-Polder potential. We obtain an analytical expression of the potential both in the near and far zones, and consider several limiting cases of interest, according to the values of the parameters involved, such as atom-atom distance, atoms-wall distance and temperature.