Dipole-dipole interaction of floquet states

We formulate a Floquet-Markov master equation, which combines an open quantum system approach with Floquet theory, for two spatially separated two-level atoms driven by a strong electromagnetic field and coupled to a common electromagnetic bath. This equation features a modified form of dipole-dipole interactions compared to the case of weakly driven atoms, giving rise to new, previously undescribed shifts of the Floquet quasienergies. We provide a detailed physical interpretation of the modified dipole-dipole interactions of two-level atoms, discuss their manifestations in two-atom resonance fluorescence, and extract the distance dependence of the dipole-dipole force between the atoms. The extensive discussion of two-level atoms is complemented by a brief study of one-dimensional hydrogen atoms (otherwise essentially described without approximations), with focus on the dipole-dipole interactions of periodically driven atoms whose electronic degrees of freedom are locked in non-dispersive wave packet states.