Superradiant phase transitions with three-level systems

We determine the phase diagram of N identical three-level systems interacting with a single photonic mode in the thermodynamical limit (N -> infinity) by accounting for the so-called diamagnetic term and the inequalities imposed by the Thomas-Reich-Kuhn (TRK) oscillator strength sum rule. The key role of transitions between excited levels and the occurrence of first-order phase transitions is discussed. We show that, in contrast to two-level systems, in the three-level case the TRK inequalities do not always prevent a superradiant phase transition in the presence of a diamagnetic term. DOI: 10.1103/PhysRevA.87.023813