Quantum Theory of an Optical Maser. II. Spectral Profile

In Paper I of this series, we derived equations of motion for a quantum-laser field interacting with atomic reservoirs. In the usual region of sustained oscillation, the off-diagonal elements of the radiation density matrix ${\rho }_{n,n+k}\mathrm{}\left(t\right)\mathrm{}$ were found to have an expontential decay associated with phase diffusion. In I we found the spectrum of the laser radiation by calculating the single time-ensemble average electric field implied by ${\rho }_{n,n+1\mathrm{}}\mathrm{}\left(t\right)\mathrm{}$. This electric field was then treated as a classical variable whose Fourier analysis gave the spectrum. In the present paper, we establish the validity of this procedure by analyzing a simple model for a spectrometer. It is also shown that the same spectrum can be obtained from a two-time correlation function derived from the equations of motion.