The field induced magnetic dipolar interaction for general boundary conditions

TL;DR

This paper derives a comprehensive formula for magnetic dipolar interactions between quantum dipoles under general boundary conditions, unifying various interaction types and analyzing cavity effects.

Contribution

It introduces a general method to calculate magnetic dipolar interactions considering boundary conditions, including cavity effects and different dipole types, using Maxwell equations and Green functions.

Findings

Interaction reduces to free-space form when dipoles are close and far from boundaries.

Cavity boundary effects significantly alter interactions when dipoles are near boundaries.

The approach can be extended to other field-mediated interactions.

Abstract

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 non-resonant transition dipoles, and even the counter-rotating interaction terms altogether. In particular, we study the dipolar interaction in a rectangular 3D 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 freespace 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 freespace interaction. This approach also provides a general way to study the interaction mediated by other kinds of fields.