Dissipative chaos and steady state of an open Tavis-Cummings dimer

We consider a coupled atom-photon system described by the Tavis-Cummings dimer (two coupled cavities) in an open environment, to investigate the quantum signature of dissipative chaos. The appropriate classical limit of this model allows us to obtain a phase diagram identifying different dynamical phases, especially the onset of chaos. Both classically and quantum mechanically, we demonstrate the emergence of a steady state in the chaotic regime and analyze its properties. The interplay between quantum fluctuation and chaos leads to enhanced mixing dynamics and dephasing, resulting in the formation of an incoherent photonic fluid. The steady state exhibits an intriguing phenomenon of subsystem thermalization even outside the chaotic regime; however, the effective temperature increases with the degree of chaos. Moreover, the statistical properties of the steady state show a close connection with the random matrix theory, which, in contrast, is absent in the Liouvillian spectrum for this system. Finally, we discuss the experimental relevance of our findings, which can be tested in cavity and circuit quantum electrodynamics (QED) setups.