Complete evolution equation for the joint amplitude in photon-pair generation

TL;DR

This paper derives a comprehensive evolution equation for the joint amplitude in photon-pair generation via four-wave mixing, enabling more accurate modeling of parasitic effects and comparison of photon generation schemes.

Contribution

It introduces a complete dual-pump evolution equation for the joint amplitude, allowing inclusion of various parasitic effects and providing numerical and analytical solution methods.

Findings

One scheme is highly sensitive to parasitic effects.

Another scheme demonstrates robustness against parasitic effects.

The method enables more accurate modeling of photon-pair sources.

Abstract

As four-wave-mixing-based photon-pair sources mature, accurate modelling of the photon-pair properties becomes important. Unlike spontaneous parametric down-conversion, four-wave mixing is accompanied by a number of parasitic effects such as nonlinear phase modulation. Currently, most modelling of photon-pair states are analytic in nature, which limits the number and type of effects that can be taken into account. In this work, we derive a complete, dual-pump evolution equation for the joint amplitude of photon pairs, wherein any desired effects can be included. We describe how to efficiently obtain numerical solution to this equation using a split-step approach. Lastly, we cover a few analytical solutions and compare two schemes for pure-photon generation under three different parasitic effects. We show how one scheme is highly sensitive to parasitic effects, while the other is very robust.