Quantum-statistical theory of the growth and stabilization of fields in a two-photon medium with competing nonlinear processes

Abstract

We formulate a quantum-statistical theory of the generation of the fields in a two-photon medium in which several competing nonlinear processes such as four-wave mixing, two-photon absorption, and amplified spontaneous emission are taking place. We derive the equation for the density matrix of the generated fields. We give numerical results for the time-dependent solutions, which enable us to understand the growth and stabilization of the fields in such a medium. We show the generation of new types of the coherent states of the radiation field. Our analysis shows that the generated fields, both in transient and the steady-state domain, have very striking quantum properties leading to squeezing, sub-Poissonian statistics, and violations of Cauchy-Schwarz inequalities. Wherever possible we compare our results with the experiment of Malcuit et al. and the semiclassical theory of Boyd et al.