Comparative study of various quasiprobability distributions in different models of correlated-emission lasers.

Abstract

We make a comparative study of various quasiprobability distributions in phase-sensitive quantum-optical systems. Starting from a general, linear master equation for the field, which emerges in different models of correlated-emission lasers, we derive the Fokker-Planck equations in the CJlauber-Sudarshan P, the antinormal ordering Q, the Wigner W, the complex P, and the positive P representations and find the steady-state solutions for the five distributions. Simple relations between the complex and positive P functions are discovered for the first time. Various moments calculated by using these distributions are found to be identical, as expected. An application of these distributions to the two-photon correlated-emission laser shows that the intracavity field can be near-perfectly squeezed in the phase quadrature and the maximum quadrature squeezing is reached when the mean laser amplitude vanishes. I. INTRODUCTION Recently, several mechanisms for the correlatedemission laser (CEL) have been considered. ' The correlated emission is based on using atoms prepared in a coherent superposition of the states between which the laser emission takes place. The initial atomic coherence can lead to the reduction in either phase or amplitude noise. It can even lead to the squeezing in one of the quadratures of the field. The microscopic theories of the (single-mode) CEL show that the dynamical equation for the density matrix for the field mode a can be written in the form'