Resonant dipole-dipole interaction in the presence of dispersing and absorbing surroundings

Within the framework of quantization of the macroscopic electromagnetic field, equations of motion and an effective Hamiltonian for treating both the resonant dipole-dipole interaction between two-level atoms and the resonant atom-field interaction are derived, which can suitably be used for studying the influence of arbitrary dispersing and absorbing material surroundings on these interactions. The theory is applied to the study of the transient behavior of two atoms that initially share a single excitation, with special emphasis on the role of the two competing processes of virtual- and real-photon exchange in the energy transfer between the atoms. In particular, it is shown that for weak atom-field interaction there is a time window, where the energy transfer follows a rate regime of the type obtained by ordinary second-order perturbation theory. Finally, it is shown that the resonant dipole-dipole interaction can change the singlet line of the emitted light to a doublet spectrum for weak atom-field interaction and the doublet spectrum to a triplet spectrum for strong atom-field interaction.