Magnetic dipole-dipole interaction induced by the electromagnetic field

TL;DR

This paper derives how the electromagnetic field mediates magnetic dipole interactions, revealing differences between permanent and transition dipoles, especially in finite volumes and near boundaries, with implications for quantum and classical regimes.

Contribution

It provides a quantum field theoretical derivation of magnetic dipole-dipole interactions, highlighting boundary and volume effects on these interactions.

Findings

Permanent dipole interactions revert to classical form

Transition dipole interactions depend on near-resonant modes

Boundary proximity significantly alters dipole interactions

Abstract

We give a derivation for the indirect interaction between two magnetic dipoles induced by the quantized electromagnetic field. It turns out that the interaction between permanent dipoles directly returns to the classical form; the interaction between transition dipoles does not directly return to the classical result, yet returns in the short-distance limit. In a finite volume, the field modes are highly discrete, and both the permanent and transition dipole-dipole interactions are changed. For transition dipoles, the changing mechanism is similar with the Purcell effect, since only a few number of nearly resonant modes take effect in the interaction mediation; for permanent dipoles, the correction comes from the boundary effect: if the dipoles are placed close to the boundary, the influence is strong, otherwise, their interaction does not change too much from the free space case.