# Dicke model

The **Dicke model** is one of the basic models of quantum optics that describe the interaction between light and matter. Specifically, the Dicke model considers a quantized bosonic mode, coupled to $N$ two level systems. The model was introduced in 1972 by Hepp and Lieb ^{[1]} and named after the physicist Dicke. In the limit of the Dicke model shows a mean-field phase transition that belongs to the Ising universality class and was recently demonstrated in cavity quantum electrodynamics experiments. This transition, often referred to as the *superradiance transition*, bares some analogy with the lasing transition.

## Contents

- 1 The model
- 2 Symmetries
- 3 The open Dicke model
- 4 The Dicke model and the Dicke superradiance
- 5 The Dicke transition
- 6 Mean field description of the transition
- 7 Experimental realizations of the Dicke model
- 8 The generalized model
- 9 The counter-rotating transition
- 10 The Dicke model in the world
- 11 Pages that should refer to here
- 12 References

## The model

Here we give the model and

## Symmetries

## The open Dicke model

Discuss the

## The Dicke model and the Dicke superradiance

## The Dicke transition

Short historical background. In the 1970’s, studies of this model [1, 2] discovered an equilibrium phase transition (both at temperature T = 0 and T 6= 0). This transition separates a normal phase from a superradiant one [3]. In the normal phase, the cavity occupation does not scale with N, the number of “spins” in the system; whereas in the superradiant phase, the cavity occupation scales linearly with N. At a first glance, one can consider the superradiant phase a lasing phase. However, as we clarify below there is a clear distinction between these two effects. A naive approach towards a realization of the Dicke model involves the dipole coupling between N atoms and an optical cavity. This approach proved to be insufficient to realize the Dicke transition, due to a no-go theorem obtained by taking into account the electrical field gauge invariance [4]. In the 2000’s a new realization of the Dicke model was proposed by Refs. [5, 6]. This realization uses stimulated Raman emission to create an effective coupling between a cavity mode and effective two-level systems. While being out of equilibrium, this realization was shown to have a superradiant phase as in the equilibrium case. By using stimulated Raman emission, this approach circumvents the no-go theorem. Furthermore, this realization of the Dicke model allowed researchers to realize a generalized model in which co-rotating and counter-rotating terms can be tuned independently

## Mean field description of the transition

## Experimental realizations of the Dicke model

Mention the two possibilities

## The generalized model

Relation to other models Tavis-Cummings

## The counter-rotating transition

Explain Pitchfork vs. Hopf

## The Dicke model in the world

For example, Chaos ^{[2]}

## Pages that should refer to here