# The field-induced interaction between non-resonant magnetic dipoles

## TL;DR

This paper derives a general magnetic dipole-dipole interaction model mediated by the quantized electromagnetic field, applicable to non-resonant dipoles and including counter-rotating and mixed terms, without relying on the rotating-wave approximation.

## Contribution

It provides a novel derivation of dipole-dipole interactions that accounts for non-resonant conditions and includes previously neglected interaction terms.

## Key findings

- Interaction strength depends on dipole frequency difference.
- Includes counter-rotating and mixed interaction terms.
- No rotating-wave approximation needed.

## Abstract

We make a general derivation for the magnetic dipole-dipole interaction based on the mediation of the quantized electro-magnetic field. Due to the interaction with the dipoles, the dynamics of the field is added by a dipole field, which finally gives rise to the dipole-dipole interaction. Different from previous studies, the rotating-wave-approximation is no longer needed throughout this derivation, and our result naturally gives the interaction for non-resonant dipoles. Moreover, our derivation also gives the counter-rotating interaction terms, and even the mixed interaction terms between the permanent and transition dipoles. We notice that this field-induced interaction is associated with the interference of the virtual/real photons emitted from the two dipoles, thus the interaction strength could be influenced by the frequency difference of the two dipoles.