The driven Dicke model and its macroscopic extension  Bistability or bifurcation
Abstract
The relation between recent work on the driven Dicke model of N twolevel 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 cnumber theory of the cusp catastrophe in optical bistability. An operator theory is presented which involves a natural powerdependent refractive index and is considered likely to appear as the parameter in common treatments of the FabryPerot 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.
 Publication:

Optical Bistability
 Pub Date:
 1981
 Bibcode:
 1981opbi.proc..367H
 Keywords:

 Atomic Excitations;
 Bistable Circuits;
 Continuous Wave Lasers;
 Laser Target Interactions;
 Nonlinear Optics;
 Switching Circuits;
 Atomic Energy Levels;
 FabryPerot Interferometers;
 Field Mode Theory;
 Mathematical Models;
 Particle Interactions;
 Refractivity;
 Lasers and Masers