Cavity quantum electrodynamics between parallel dielectric surfaces

We use a quantum-mechanical linear-response formalism in the dipole approximation to calculate the decay-rate change and the energy-level shift of an atom between two parallel dielectric surfaces. Our results can be applied to various problems such as two conductor plates, one conductor and one dielectric, and two different dielectrics. In particular, we calculate the decay rate and the level shift in the case of two identical dielectric plates. The dependences of the transition rate on the atomic position in the gap and on the dielectric constant of the surfaces are investigated in detail. In the case of the level shift, we are able to obtain analytic expressions for two limiting cases (the short-range instantaneous van der Waals interaction energy and the long-range Casimir-Polder retarded interaction energy).