Canonical extension of a problem in parametric frequency up-conversion with stochastic pumping

A canonical model for the frequency up-conversion process with stochastic coupling function is proposed. Based on it the first-order coherence functions, the time dependence of the mean photon numbers and the secondorder coherence functions are found and compared with the corresponding results already available in the literature. It is shown that the total photon number, as a function of time, has a turning point. The antibunching effect is predicted regardless of the mean photon numbers available in the process. © 1979 Taylor & Francis Group, LLC.