# 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 $\displaystyle N\to\infty$ 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.

## The model

Here we give the model and

Discuss the

## 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

## 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]

## References

1. ^ Hepp and Lieb
2. ^ Emary and Brandes