On the effects of self- and cross-phase modulation on photon purity for four-wave mixing photon-pair sources

TL;DR

This paper investigates how self- and cross-phase modulation affect photon purity in four-wave mixing sources, revealing that nonlinear effects limit quantum interference and providing approximate models to predict these impacts.

Contribution

It introduces an approximate analytical model for the joint spectral amplitude considering phase modulation effects in four-wave mixing photon sources.

Findings

Nonlinear phase modulation reduces photon purity and quantum interference visibility.

Group velocity dispersion has a minor impact on purity under realistic conditions.

Approximate expressions can effectively predict the effects of phase modulation on photon pairs.

Abstract

We consider the effect of self-phase modulation and cross-phase modulation on the joint spectral amplitude of photon pairs generated by spontaneous four-wave mixing. In particular, the purity of a heralded photon from a pair is considered, in the context of schemes that aim to maximise the purity and minimise correlation in the joint spectral amplitude using birefringent phase-matching and short pump pulses. We find that non-linear phase modulation effects will be detrimental, and will limit the quantum interference visibility that can be achieved at a given generation rate. An approximate expression for the joint spectral amplitude with phase modulation is found by considering the group velocity walk-off between each photon and the pump, but neglecting the group-velocity dispersion at each wavelength. The group-velocity dispersion can also be included with a numerical calculation, and it is shown that it only has a small effect on the purity for the realistic parameters considered.