Phase transitions in a system of atoms interacting with a coherent field

Abstract

The driven Dicke model exhibits interesting critical behaviour. Within the conservation of Ŝ²>, a mathematical condition required for the model, the model predicts a second order phase transition for resonant coherent driving field; bistable behaviour is predicted if the system is placed in a cavity in resonance with the external field as well as with the atomic transition. If interaction between the atoms is included, the system predicts a first order phase transition for certain values of the parameters related to the interaction, field amplitude and frequency detuning. At this stage it is an open question, where these critical phenomena can be observed in an experiment. Experiments with very large wavelength (low frequency) and large dipole moment characteristic of Rydberg atoms may perhaps yield this information. Because of the exactness of the model, it may also be possible to explain the critical behaviour in a more fundamental way. This issue is, however, open and needs further thought.