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Dipole-Dipole Coupling in the Presence of Dispersing and Absorbing Bodies

An effective Hamiltonian and equations of motion 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. It is shown that the dipole-dipole interaction and the atom-field interaction, respectively, are closely related to the real part and the imaginary part of the (classical) Green tensor. 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. To illustrate the powerfulness of the theory, specific results for the case of the atoms being near a dispersing and absorbing microsphere are presented. In particular, the regimes of weak and strong atom-field coupling are addressed.