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The challenging requirements of large scale quantum information processingusing parametric heralded single photon sources involves maximising theinterference visibility whilst maintaining an acceptable photon generationrate. By developing a general theoretical framework that allows us to includelarge numbers of spatial and spectral modes together with linear and non-linearoptical elements, we investigate the combined effects of spectral and photonnumber impurity on the measured Hong--Ou--Mandel interference visibility ofparametric photon sources, considering both threshold and number resolvingdetectors, together with the effects of spectral filtering. We find that forany degree of spectral impurity, increasing the photon generation ratenecessarily decreases the interference visibility, even when using numberresolving detection. While tight spectral filtering can be used to enforcespectral purity and increased interference visibility at low powers, we findthat the induced photon number impurity results in a decreasing interferencevisibility and heralding efficiency with pump power, while the maximumgeneration rate is also reduced.

apl photonics

A general framework for multimode Gaussian quantum optics and  photo-detection: application to Hong-Ou-Mandel interference with filtered  heralded single photon sources