Theory of Photon Condensation in a Spatially-Varying Electromagnetic Field

Understand

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.