Superradiant phase transitions with three-level systems

TL;DR

This paper analyzes the phase diagram of three-level quantum systems interacting with light, revealing conditions under which superradiant phase transitions can occur despite constraints that usually prevent them.

Contribution

It demonstrates that, unlike two-level systems, three-level systems can exhibit superradiant phase transitions even with the TRK inequalities and diamagnetic terms present.

Findings

Superradiant phase transitions are possible in three-level systems.

TRK inequalities do not always prevent superradiance in three-level systems.

First-order phase transitions are discussed in the context of three-level systems.

Abstract

We determine the phase diagram of $N$ identical three-level systems interacting with a single photonic mode in the thermodynamical limit ($N \to \infty$) 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 presence of a diamagnetic term.