Extended superradiance in two mechanically coupled Dicke models

In this work, we explore the superradiant behavior of two Dicke models mechanically coupled through a shared vibrating membrane. Using a variational mean-field approach, we analyze the system's critical behavior and derive analytical expressions that reveal a threshold for the mechanical coupling. Below this threshold, the system allows for higher atomic-radiation couplings before resonant damping occurs, thereby extending the superradiant region compared to a single-cavity optomechanical Dicke model. Additionally, we examine the behavior of relevant observables across all regions of the phase diagram. Our findings suggest that these observables provide a more accurate characterization of the system's critical behavior than the traditionally used coupling parameters.