ATOM-ATOM INTERACTION IN STRONGLY MODIFIED RESERVOIRS

We extend recent work on two closely spaced atoms interacting through the narrow band of strongly coupled modes at the edge of a photonic ba nd gap. The resonant dipole-dipole interaction (RDDI) is strongly modi fied for atomic transition frequencies in the vicinity of the band-gap edge, but we show that an analytical approximation to the RDDI agrees very well with the exact RDDI obtained by numerical integration using the exact dispersion relation. Having established the value of the RD DI, we can derive the amplitudes for the two atoms without resorting t o the pole approximation which is necessary due to the strongly modifi ed mode structure in the dielectric host. For a wide range of paramete rs we find beating and population trapping in the long time limit. The distribution of population in the photonic continuum is investigated in the long time limit in the case of one and two atoms. It is found t o be strongly asymmetric and to exhibit a strong signature of the unus ual mode structure in the material at the band-gap edge.