Energy shift and Casimir-Polder force for an atom out of thermal equilibrium near a dielectric substrate

TL;DR

This paper investigates how an atom's energy levels and Casimir-Polder force are affected when out of thermal equilibrium near a dielectric surface, revealing new distance-dependent behaviors and extending existing theoretical models.

Contribution

It generalizes the formalism for energy shifts and forces out of thermal equilibrium, providing detailed analysis and identifying new behaviors of atom-surface interactions.

Findings

Identifies distinct effects of substrate and environment thermal fluctuations.

Reveals new distance-dependent behavior of atom-wall force out of thermal equilibrium.

Confirms and extends recent findings on atom-wall force at large distances in low-temperature regimes.

Abstract

We study the energy shift and the Casimir-Polder force of an atom out of thermal equilibrium near the surface of a dielectric substrate. We first generalize, adopting the local source hypothesis, the formalism proposed by Dalibard, Dupont-Roc and Cohen-Tannoudji, which separates the contributions of thermal fluctuations and radiation reaction to the energy shift and allows a distinct treatment to atoms in the ground and excited states, to the case out of thermal equilibrium, and then use the generalized formalism to calculate the energy shift and the Casimir-Polder force of an isotropically polarizable neutral atom. We identify the effects of the thermal fluctuations that originate from the substrate and the environment and discuss in detail how the Casimir-Polder force out of thermal equilibrium behaves in three different distance regions in both the low-temperature limit and the high-temperature limit for both the ground-state and excited-state atoms, with special attention devoted to the new features as opposed to thermal equilibrium. In particular, we recover the new behavior of the atom-wall force out of thermal equilibrium at large distances in the low temperature limit recently found in a different theoretical framework and furthermore we give a concrete region where this behavior holds.