Quantum theory of coupled parametric down-conversion and up-conversion with simultaneous phase matching

Abstract

A two-step nonlinear optical interaction consisting of (i) a spontaneous frequency down-conversion process coupled with (ii) a frequency up-conversion process is treated quantum mechanically in the experimentally observed case of simultaneous collinear phase matching of both processes. The temporal behavior of the output signals is found to depend on which process, (i) or (ii), predominates. The nature of the photon statistics for each of the output modes is found to be "super-Poisson," regardless of which process, (i) or (ii), is dominant, and the zero-point fluctuations characteristic of parametric amplification are exhibited.