Theory of Photon Condensation in a Spatially-Varying Electromagnetic Field

TL;DR

This paper demonstrates that photon condensation can occur in spatially-varying electromagnetic fields, bypassing previous no-go theorems, and identifies conditions based on electronic susceptibility for such phenomena in various materials.

Contribution

It introduces a new criterion for photon condensation in spatially-varying fields, extending the theory beyond uniform fields and applicable to strongly correlated electronic systems.

Findings

Photon condensation is possible in spatially-varying fields if the orbital magnetic susceptibility exceeds a critical value.

The criterion depends on the electronic system's susceptibility and cavity geometry.

The theory applies to strongly correlated electronic systems and two-dimensional materials.

Abstract

The realization of equilibrium superradiant quantum phases (photon condensates) in a spatially-uniform quantum cavity field is forbidden by a "no-go" theorem stemming from gauge invariance. We here show that the no-go theorem does not apply to spatially-varying quantum cavity fields. We find a criterion for its occurrence that depends solely on the static, non-local orbital magnetic susceptibility $\chi_{\rm orb}(q)$, of the electronic system (ES) evaluated at a cavity photon momentum $\hbar q$. Only 3DESs satisfying the Condon inequality $\chi_{\rm orb}(q)>1/(4\pi)$ can harbor photon condensation. For the experimentally relevant case of two-dimensional (2D) ESs embedded in quasi-2D cavities the criterion again involves $\chi_{\rm orb}(q)$ but also the vertical size of the cavity. We use these considerations to identify electronic properties that are ideal for photon condensation. Our theory is non-perturbative in the strength of electron-electron interaction and therefore applicable to strongly correlated ESs.