Field-induced magnetic dipolar interaction for general boundary conditions

By properly considering the propagation dynamics of the dipole field, we obtain the full magnetic dipolar interaction between two quantum dipoles for general situations. With the help the Maxwell equation and the corresponding Green function, this result applies for general boundary conditions and naturally unifies all the interaction terms between permanent dipoles, resonant or nonresonant transition dipoles, and even the counter-rotating interaction terms altogether. In particular, we study the dipolar interaction in a rectangular three-dimensional cavity with discrete field modes. When the two dipoles are quite near to each other and far from the cavity boundary, their interaction simply returns the free-space result; when the distance between the two dipoles is comparable to their distance to the cavity boundary and the field mode wavelength, the dipole images and near-resonant cavity modes bring in significant changes to the free-space interaction. This approach also provides a general way to study the interaction mediated by other kinds of fields.