Approximate Solutions for anN-Molecule-Radiation-Field Hamiltonian

Three approximation schemes are discussed and compared with the exact solutions for a Hamiltonian describing the interaction of a single-mode quantized radiation field and $N$ two-level "molecules," each resonant with the mode frequency. In particular, the approximation of treating the molecules as uncorrelated is found to be accurate when the system energy is several times larger than the cooperation number of the molecular system.