Thermodynamics and superradiant phase transitions in a three-level Dicke model

We analyze the thermodynamic properties of a generalized Dicke model, i.e., a collection of three-level systems interacting with two bosonic modes. We show that at finite temperatures the system undergoes first-order phase transitions only, which is in contrast to the zero-temperature case where a second-order phase transition exists as well. We discuss the free energy and prominent expectation values. The limit of vanishing temperature is discussed as well.