Superradiant phase transition in a model of three-level-lambda systems interacting with two bosonic modes

TL;DR

This paper investigates a model of three-level lambda systems coupled to two bosonic modes, demonstrating the existence of both first and second order superradiant quantum phase transitions and exploring their relation to Hamiltonian symmetries.

Contribution

It introduces a generalized Dicke-model for three-level lambda systems with two bosonic modes, revealing superradiant phase transitions even with diamagnetic contributions.

Findings

Supports superradiant phase transition in the thermodynamic limit

Identifies both first and second order phase transitions

Shows superradiance occurs despite Thomas-Reiche-Kuhn sum rule constraints

Abstract

We consider an ensemble of three-level particles in lambda-configuration interacting with two bosonic modes. The Hamiltonian has the form of a generalized Dicke-model. We show that in the thermodynamic limit this model supports a superradiant quantum phase transition. Remarkably, this can be both a first and a second order phase transition. A connection of the phase diagram to the symmetries of the Hamiltonian is also given. In addition, we show that this model can describe atoms interacting with an electromagnetic field in which the microscopic Hamiltonian includes a diamagnetic contribution. Even though the parameters of the atomic system respect the Thomas--Reiche--Kuhn sum rule, the system still shows a superradiant phase transition.