The driven Dicke model and its macroscopic extension - Bistability or bifurcation

The relation between recent work on the driven Dicke model of N two-level atoms at the same site, driven by a CW laser field, and a corresponding theory for the more realistic, macroscopically extended system, is considered. The results of the driven Dicke model show two different decorrelation schemes yielding different results. The decorrelation of operator products with self correlation, or radiation damping, leads to the c-number theory of the cusp catastrophe in optical bistability. An operator theory is presented which involves a natural power-dependent refractive index and is considered likely to appear as the parameter in common treatments of the Fabry-Perot interferometer. Alternatively, by extracting a single mode theory in the mean field approximation, both the Bloch equations and the master equation for the driven Dicke model can be regained. The hierarchy of models relates to the realistic extended system model in a way similar to the hierarchy of the theory of superfluorescence.