Quantum thermalization and vanishing thermal entanglement in the open Jaynes-Cummings model

We study quantum thermalization of the Jaynes-Cummings (JC) model in both equilibrium and non-equilibrium open-system cases, in which the two subsystems: a two-level system and a single-mode bosonic field, are in contact with either two individual heat baths or a common heat bath. We find that, in the individual heat-bath case, the JC model can only be thermalized when the two heat baths have the same temperature or when the coupling of the JC system to one of the two baths is turned off, while the JC system can be thermalized in the common heat-bath case irrespective of the bath temperature and the system-bath coupling strengths. We also study the thermal entanglement in this system. We find and prove a counterintuitive phenomenon of vanishing thermal entanglement in the JC system. In addition, we compare the dynamics of the open JC system when it is described by the dressed-state master equations in the individual and common heat-bath cases and a phenomenological master equation.