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Physical Review A

Atomic resonance interaction in dielectric media

M. Boström, Barry William Ninham

Published May 12, 2004• 10 citations
Publisher

Abstract

A theory is presented for the retarded resonance interaction in dielectric media between a ground state atom and an excited atom. We demonstrate in the retarded limit large deviations compared to earlier incorrect evaluations of this important quantity.
DOI
10.1103/physreva.69.054701

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We use the master equation approach to calculate the energy level shifts of an atom in the presence of a general dielectric semi-infinite medium characterized by a dielectric constant ε(ω)ε(ω)ε(ω). Particularly, we analyze the case of a non-dispersive medium for which we obtain a general expression for the interaction as well as the asymptotic behaviors for k0z≪1k_0 z \ll 1k0​z≪1 (non-retarded regime) and k0z≫1k_0 z \gg 1k0​z≫1 (retarded regime), where ω0=k0cω_0 = k_0 cω0​=k0​c is the main transition frequency of the atom. The limiting cases ε≃1ε\simeq 1ε≃1 and ε≫1ε\gg 1ε≫1 are discussed for both retarded and non-retarded limits. For the retarded limit, we compute the non-additivity contribution of van der Waals forces.
The problem considered is that of two identical two-level atoms a fixed distance rrr apart, one of which is excited at t=0t=0t=0. A simple improvement on the usual on-shell approximation (which in the single-atom case is part of the Weisskopf-Wigner approximation) yields new solutions for the various probability amplitudes in the form of infinite series involving all the retardation times nrc\frac{\mathrm{nr}}{c}cnr​. The truncated solutions involving only the single retardation time rc\frac{r}{c}cr​ are compared with previously published results both when all photon modes are allowed and when only photons propagating along the interatomic axis are allowed. When the retardation times are neglected, the series are summed to give the well-known results of Stephen and others.
The Casimir-Polder potential for interaction between an excited atom and a ground-state one in the retarded case is obtained with the help of perturbation technique. The potential drops as ${R}^{\ensuremath{-}2}$ with the distance between the atoms [E. A. Power and T. Thirunamachandran, Phys. Rev. A 47, 2539 (1993)]. It results in divergent integrals for interaction between an excited atom and a dilute gas medium. We investigate interaction between two atoms embedded in a dielectric medium with the help of a method that enables us to make calculations beyond the perturbation technique. We take into account absorption of photons in the medium. This approach solves the problem of divergence. We consider interaction between an excited atom and a planar dielectric gas medium of ground-state atoms. We show that the retarded interaction between an excited atom and a gas of ground-state atoms is not oscillating but follows a simple power law. We show that to obtain a conventional nonretarded expression for the van der Waals force between an excited atom and a dilute gas, the distance between the atom and the interface should be much smaller than the free mean path of a photon in the medium. Interaction between an excited atom and a hemisphere of ground-state atoms is considered.
The energy–level shifts and the change in the rate of spontaneous emission are calculated for an atom located at a distanceZ from a dielectric half–space. The dielectric is a non–dispersive and non–absorbing medium characterized by a constant real refractive indexn. The explicit analytic formulae derived are applicable for arbitrary values ofn. All results are analysed in the non-retarded and retarded limits, which apply to the atom being close to or far from the interface, respectively, i.e. toZ being small or large on the scale of a wavelength of a typical atomic transition. For ground-state atoms, the energy–level shift varies as 1/Z3 in the non–retarded regime and as 1/Z4 in the retarded regime, which agrees with the Casimir–Polder result for the limitn→α. For excited–state atoms, the energy–level shifts receive additional contributions that oscillate with the distanceZ from the interface.