Theory of photon condensation in an arbitrary gauge condensed matter cavity model

TL;DR

This paper develops a gauge-invariant theoretical framework for photon condensation in condensed matter systems within electromagnetic fields, revealing new conditions and gauge-dependent aspects of the phase transition.

Contribution

It introduces an arbitrary-gauge criterion for photon condensation, generalizing previous Coulomb-gauge results and clarifying the gauge-relative nature of photon condensation phenomena.

Findings

Photon condensation can occur in spatially uniform fields.

The gauge choice affects the magnetic and electric character of the instability.

The theory is gauge-invariant and unifies different gauge perspectives.

Abstract

We derive an arbitrary-gauge criterion under which condensed matter within an electromagnetic field may transition to a photon condensed phase. Previous results are recovered by selecting the Coulomb-gauge wherein photon condensation can only occur for a spatially-varying field and can be interpreted as a magnetic instability. We demonstrate the gauge-invariance of our description directly, but since matter and photons are gauge-relative concepts we find more generally that photon condensation can occur within a spatially uniform field, and that the relative extent to which the instability is both magnetic and electric versus purely magnetic depends on the gauge.