Master equation approach to propagation in nonlinear fibers

In this Letter, we revisit the quantum theory of propagation in nonlinear fibers. Unlike previous works, we present an effective propagation equation for the reduced density matrix of the complex envelope of the electric field. This original proposal is shown to be in agreement with the theory of quantum noise in fibers and puts forth a powerful tool for the study of fiber-based quantum devices. To underscore its applicability, we analyze the performance of a heralded single-photon scheme in terms of probabilities, an approach that conveniently lends itself to the optimization of such sources.