Introduction to the Dicke model: from equilibrium to nonequilibrium, and vice versa

TL;DR

This paper introduces the Dicke model, exploring its equilibrium and nonequilibrium phase transitions, emphasizing the superradiant phase, and comparing it with lasing, with insights into experimental realizations and dynamics.

Contribution

It provides a comprehensive review of the Dicke model's critical properties, distinguishing equilibrium and nonequilibrium phases, and clarifies the differences between superradiant transitions and lasing.

Findings

Superradiant phase transition belongs to the mean-field Ising universality class.

Recent experiments have realized the superradiant transition in optical cavities.

Different quantum simulators exhibit distinct equilibrium and nonequilibrium behaviors.

Abstract

The Dicke model describes the coupling between a quantized cavity field and a large ensemble of two-level atoms. When the number of atoms tends to infinity, this model can undergo a transition to a superradiant phase, belonging to the mean-field Ising universality class. The superradiant transition was first predicted for atoms in thermal equilibrium and was recently realized with a quantum simulator made of atoms in an optical cavity, subject to both dissipation and driving. In this Progress Report, we offer an introduction to some theoretical concepts relevant to the Dicke model, reviewing the critical properties of the superradiant phase transition, and the distinction between equilibrium and nonequilibrium conditions. In addition, we explain the fundamental difference between the superradiant phase transition and the more common lasing transition. Our report mostly focuses on the steady states of atoms in single-mode optical cavities, but we also mention some aspects of real-time dynamics, as well as other quantum simulators, including superconducting qubits, trapped ions, and using spin-orbit coupling for cold atoms. These realizations differ in regard to whether they describe equilibrium or non-equilibrium systems.