Longitudinal fields in interactions between atoms and absorptive dielectrics

The properties of atoms close to an absorptive dielectric are studied using the phenomenological Maxwell’s equations. Although radiative decay has been considered by many authors, the coupling of atoms with longitudinal modes does not seem to have been treated in detail. Here we show that there are two main effects. The first is a change in the atomic interaction potential from the Coulomb one to a static potential, i.e., one that satisfies a Poisson equation featuring the static dielectric function ε_stat=ε(ω)∣_ω=0. The second is the decay of excited atomic states through longitudinal field interactions. We find that the corresponding decay constant is nonzero only for atom-dielectric distances in the order of an atomic diameter and that it decreases exponentially fast on an atomic scale with increasing distance. We also show that the Hamiltonian used by the Jena group [ Dung et al. Phys. Rev. A 65 043813 (2002)], featuring the Coulomb potential, is unitarily equivalent to one containing the static potential.