There is currently great interest in the strong coupling between the
quantized photon field of a cavity and electronic or other degrees of freedom
in materials. A major goal is the creation of novel collective states
entangling photons with those degrees of freedom. Here we show that the
cooperative effect between strong electron interactions in quantum materials
and the long-range correlations induced by the photon field leads to the
stabilization of coherent phases of light and matter. By studying a two-band
model of interacting electrons coupled to a cavity field, we show that a phase
characterized by the simultaneous condensation of excitons and photon
superradiance can be realized, hence stabilizing and intertwining two
collective phenomena which are rather elusive in the absence of this
cooperative effect.Comment: 5 pages, 4 figure
