Collective excitations of a strongly-correlated photon fluid stabilized by incoherent drive and dissipation

Utilizing a simple and original approach to Gaussian quantum fluctuations around the Lindblad dynamics, we explore theoretically the spectral properties of the non-equilibrium photonic phases hosted by a lattice of coupled cavities in the presence of non-Markovian driving and dissipation, as well as strong photon interactions. In particular, we analyze how the elementary excitations of the system evolve across the Mott/superfluid-like dynamical transition exhibited by the model and point out the emergence of a diffusive Goldstone mode in the symmetry-broken phase whose structure indicates a close intertwining between dissipation and coherence as a consequence of strong correlations. Moreover, we investigate the one-body coherence of the insulating phase, showing how the dynamical properties of quasiparticles make this regime significantly different from its equilibrium counterpart. Our study goes in the direction of investigating the potential of driven-dissipative photonic fluids to quantum simulate a wider range of many-body scenarios.