Nonequilibrium Atom-Dielectric Forces Mediated by a Quantum Field

TL;DR

This paper derives a detailed microscopic model of the nonequilibrium forces between an atom and a dielectric medium mediated by a quantum electromagnetic field, using open quantum systems techniques.

Contribution

It introduces a first-principles derivation of atom-dielectric forces considering nonequilibrium conditions and back action effects, extending previous equilibrium models.

Findings

Provides a dynamical equation for atomic motion including back action.

Recovers known equilibrium and stationary nonequilibrium force results.

Uses coarse-graining to connect microscopic variables to macroscopic forces.

Abstract

In this paper we give a first principles microphysics derivation of the nonequilibrium forces between an atom, treated as a three dimensional harmonic oscillator, and a bulk dielectric medium modeled as a continuous lattice of oscillators coupled to a reservoir. We assume no direct interaction between the atom and the medium but there exist mutual influences transmitted via a common electromagnetic field. By employing concepts and techniques of open quantum systems we introduce coarse-graining to the physical variables - the medium, the quantum field and the atom's internal degrees of freedom, in that order - to extract their averaged effects from the lowest tier progressively to the top tier. The first tier of coarse-graining provides the averaged effect of the medium upon the field, quantified by a complex permittivity (in the frequency domain) describing the response of the dielectric to the field in addition to its back action on the field through a stochastic forcing term. The last tier of coarse- graining over the atom's internal degrees of freedom results in an equation of motion for the atom's center of mass from which we can derive the force on the atom. Our nonequilibrium formulation provides a fully dynamical description of the atom's motion including back action effects from all other relevant variables concerned. In the long-time limit we recover the known results for the atom-dielectric force when the combined system is in equilibrium or in a nonequilibrium stationary state.