General theory of cavity-mediated interactions between low-energy matter excitations

TL;DR

This paper develops a comprehensive theoretical framework for understanding how cavity electromagnetic modes induce electrostatic and magnetostatic interactions among low-energy matter excitations, extending previous models beyond simple approximations.

Contribution

It extends existing theories by including full polarization, magnetization, diamagnetic interactions, and general media responses, providing a more complete description of cavity-mediated matter interactions.

Findings

Interactions are electrostatic and magnetostatic in nature.

Multimode cavity description is necessary for accurate modeling.

Framework applies to general optical environments with complex media.

Abstract

The manipulation of low-energy matter properties such as superconductivity, ferromagnetism and ferroelectricity via cavity quantum electrodynamics engineering has been suggested as a way to enhance these many-body collective phenomena. In this work, we investigate the effective interactions between low-energy matter excitations induced by the off-resonant coupling with cavity electromagnetic modes. We extend previous work by going beyond the dipole approximation accounting for the full polarization and magnetization densities of matter. We further include the often neglected diamagnetic interaction and, for the cavity, we consider general linear absorbing media with possibly non-local and non-reciprocal response. We demonstrate that, even in this general scenario, the effective cavity-induced interactions between the matter degrees of freedom are of electrostatic and magnetostatic nature. This confirms the necessity of a multimode description for cavity engineering of matter systems where the low-energy assumption holds. Our findings provide a theoretical framework for studying the influence of general optical environments on extended low-energy matter excitations.