Among the novel sources of nonclassical light that have recently been studied are a number of novel lasers. Conventional laser theory describes a classical stochastic field. I show that with a change in the standard operating conditions the conventional laser model produces nonclassical fields. Deviations from the classical description in standard laser theory are small by some inverse power of the threshold photon number. Operating conditions are designed to make stimulated emission dominant; thus laser cavities are good cavities that store photons and give a high threshold photon number. Low threshold photon numbers are achieved in bad cavities and most readily in a single-atom bad-cavity system. Such a system trades phase coherence for reduced intensity noise.
We investigate theoretically the statistical properties of the bad-cavity laser with field and population fluctuations. This system is equivalent to the stochastic Toda oscillator, whose probability distribution obeys the Kramers equation with a position-dependent diffusion coefficient. An approximate probability distribution function is calculated in the stationary state by the method of the orthogonal polynomial expansion. We predict novel statistical features of the laser intensity resulting from the power tail of the intensity distribution. Diverging intensity moments and the deviation of the photon-counting statistics from the Poisson type are also given.
Lasers with two-photon saturable absorbers exhibit a phase instability similar to that of two-photon optical bistability. Beyond the phase instability threshold the output intensity breaks into spontaneous oscillations. Analytical perturbative solutions have been found and we have linearized the Fokker-Planck equation around these solutions. The drift and diffusion matrices have been perturbatively developed and we obtained a time-dependent Ornstein-Uhlenbeck stochastic process. We have calculated the amplitude correlations and squeezing spectrum near but above the threshold for a Hopf bifurcation in bad cavity conditions.