Multipartite quantum correlations in a two-mode Dicke model

We analyze multipartite correlations in a generalized Dicke model involving two optical modes interacting with an ensemble of two-level atoms. In particular, we examine correlations beyond the standard bipartite entanglement and derive exact results in the thermodynamic limit. The model presents two superradiant phases involving the spontaneous breaking of either a $\mathbb{Z}_2$ or $\mathrm{U}(1)$ symmetry. The latter is characterized by the emergence of a Goldstone excitation, found to significantly affect the correlation profiles. Focusing on the correlations between macroscopic subsystems, we analyze both the mutual information as well as the entanglement of formation for all possible bipartitions among the optical and matter degrees of freedom. It is found that while each mode entangles with the atoms, the bipartite entanglement between the modes is zero, and they share only classical correlations and quantum discord. We also study the monogamy of multipartite entanglement and show that there exists genuine tripartite entanglement, i.e. quantum correlations that the atoms share with the two modes but that are not shared with them individually, only in the vicinity of the critical lines. Our results elucidate the intricate correlation structures underlying superradiant phase transitions in multimode systems.