Thermal dispersion potential of a diamagnetic atom

Abstract

We study the diamagnetic interaction between a ground-state atom, which is located at a distance $z$ from a planar body, e.g., a perfect mirror or a nondispersive and nonabsorbing dielectric substrate, and the body-assisted electromagnetic fields from vacuum, equilibrium, and out of equilibrium thermal fluctuations. We find that the diamagnetic potential at zero temperature is always proportional to ${z}^{\ensuremath{-}4}$ in both the retarded and the nonretarded zones, and the Casimir-Polder (CP) force is attractive. The CP potential due to the thermal fluctuations at equilibrium dominates over that due to the zero-point fluctuations in the long-distance or high-temperature limit and behaves like $T/{z}^{3}$, and the corresponding force is attractive. However, in the case of out of thermal equilibrium, the CP potential exhibits a different behavior with slower dependence on the distance and stronger dependence on temperature in the same limit, and it decays like $({T}_{e}^{2}\ensuremath{-}{T}_{s}^{2})/{z}^{2}$, where ${T}_{e}$ is the temperature of the environment and ${T}_{s}$ is that of the substrate, yielding a CP force that can either be attractive or repulsive. Meanwhile, in the short-distance or low-temperature limit the CP potential is always dominated by the contribution due to the vacuum fluctuations.