Heralding single photons from an SPDC source using photon number resolving superconducting nanowire detectors

High rate and pure single photon sources are essential for experimental realizations of quantum communication tasks such as quantum key distribution and quantum teleportation. A practical way of producing these single photons has been through photon pair generation and heralding using optical non-linear processes such as spontaneous parametric down conversion (SPDC). Due to thermal photon number statistics, the single photon pair probability of SPDC is limited to 1/4 per mode, resulting in multiphoton pair noise that dominates at high mean photon numbers, thus limiting experimental rates. One way to avoid this is to use photon number resolving detectors to filter out multiphoton noise. Here we demonstrate an improvement in the purity of a single photon source by heralding on single and multiphoton events with photon number resolving NbN superconducting nanowires which have been also shown to have high efficiency, low dark counts, and low jitter. We present a detailed theoretical model based on the Gaussian formalism by constructing the symplectic matrix of the PNR detector from a network of beamsplitters. We use the model to predict the expected heralded single photon rates for given losses and imperfections in the experiment.