Thermalization of a two-level atom in a planar dielectric system out of thermal equilibrium

Abstract

We study the thermalization of an elementary quantum system modeled by a two-level atom interacting with stationary electromagnetic fields out of thermal equilibrium near a dielectric slab. The slab is held at a temperature different from that of the region where the atom is located. We find that when the slab is nonabsorbing and nondispersive, out-of-thermal-equilibrium effects exist only when its thickness is infinite. In other words, no out-of-thermal-equilibrium effects appear for a real dielectric slab of a finite thickness $d$. Furthermore, a finite thick dielectric slab with a tiny imaginary part in the relative permittivity $\mathrm{Im}\ensuremath{\epsilon}$ behaves like a half-space dielectric substrate if $\frac{\mathrm{Im}\ensuremath{\epsilon}}{\sqrt{\mathrm{Re}\ensuremath{\epsilon}\ensuremath{-}1}}\frac{d}{{\ensuremath{\lambda}}_{0}}>1$ is satisfied, where ${\ensuremath{\lambda}}_{0}$ is the transition wavelength of the atom. This condition can serve as a guide for an experimental verification, using a dielectric substrate of a finite thickness, of the effects that arise from out-of-thermal-equilibrium fluctuations with a half-space (infinite thickness) dielectric.