Persistent subradiant correlations in a random driven Dicke model

We study theoretically the driven-dissipative dynamics of an array of two-level emitters, coupled to a single photonic mode, in the presence of disorder in the resonant frequencies. We introduce the notion of subradiant correlations in the dynamics, corresponding to the eigenstates of the Liouvillian with a low decay rate, that can also oscillate in time. While the usual collective subradiant states do not survive the emitter resonant frequency fluctuations, these subradiant correlations are immune to such a type of disorder. These long-living correlations exist in finite-size systems, when their lifetime is parametrically longer than in the so-called Dicke time crystal phase.