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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 maximize the purity and minimize correlation in the joint spectral amplitude using birefringent phase matching and short pump pulses. We find that nonlinear 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 has only a small effect on the purity for the realistic parameters considered.
|Journal||Physical Review A: Atomic, Molecular and Optical Physics|
|Publication status||Published - 20 Nov 2015|