  A laser model is formulated in terms of quantum harmonic oscillators.
Emitters in the low lasing states are usual harmonic oscillators, and emitters
in the upper states are inverted harmonic oscillators. Diffusion coefficients,
consistent with the model and necessary for solving quantum nonlinear laser
equations analytically, are found. Photon number fluctuations of the lasing
mode and fluctuations of the population of the lasing states are calculated.
Collective Rabi splitting peaks are predicted in the intensity fluctuation
spectra of the superradiant lasers. Population fluctuation mechanisms in
superradiant lasers and lasers without superradiance are discussed and compared
with each other.
