Dipole-dipole Interactions Through a Lens

We study the fluctuation-mediated interactions between two atoms in the presence of an aplanatic lens, demonstrating an enhancement in their resonant dipole-dipole interaction. We derive the field propagation of the linear optical system in terms of the electromagnetic Green's tensor for an aplanatic lens. The collective internal atomic dynamics is analyzed via a Lindblad master equation, which allows one to characterize the dispersive and dissipative interactions between atoms. We thus demonstrate that the resonant dipole-dipole coupling between the atoms can be enhanced in the focal plane of the lens, and the lens-modified energy exchange between the atoms can create a mutual trapping potential. Our work opens new avenues for expanding dipole-dipole interactions to macroscopic scales and the experimental platforms to study them.