Superradiant Quantum Phase Transition in Open Systems: System-Bath Interaction at the Critical Point

The occurrence of a second-order quantum phase transition in the Dicke model is a well-established feature. On the contrary, a comprehensive understanding of the corresponding open system, particularly in the proximity of the critical point, remains elusive. When approaching the critical point, the system inevitably enters first the system-bath ultra-strong coupling regime and finally the deep-strong coupling regime, causing the failure of usual approximations adopted to describe open quantum systems. In the thermodynamic limit, we study the interaction between the Dicke model and bosonic bath fields without resorting to additional approximations, which usually relies on the weakness of the system-bath coupling. We find that the critical point is not affected by interactions with environments displaying metastable minima. Moreover, such interactions cannot affect the system ground-state condensates in the superradiant phase, whereas the bath fields are infected by the system and acquire macroscopic occupations. The obtained reflection spectra display lineshapes which become increasingly asymmetric, both in the normal and superradiant phases, when approaching the critical point.