Resonant light enhances phase coherence in a cavity QED simulator of fermionic superfluidity

Cavity QED experiments are natural hosts for non-equilibrium phases of matter supported by photon-mediated interactions. In this work, we consider a cavity QED simulation of the BCS model of superfluidity, by studying regimes where the cavity photons act as dynamical degrees of freedom instead of mere mediators of the interaction via virtual processes. We find an enhancement of long time coherence following a quench whenever the cavity frequency is tuned into resonance with the atoms. We discuss how this is equivalent to enhancement of non-equilibrium superfluidity and highlight similarities to an analogous phenomena recently studied in solid state quantum optics. We also discuss the conditions for observing this enhanced resonant pairing in experiments by including the effect of photon losses and inhomogeneous coupling in our analysis.