Heralded pure single-photon sources using nanophotonic waveguides with quadratic and cubic nonlinearities

This paper presents, to our knowledge, a new approach in developing integrated pure heralded single-photon sources based on the interplay between the spontaneous four-wave mixing and sum-frequency generation parametric processes. We introduce a comprehensive quantum model to exploit this interplay in AlGaAs and LiNbO$_3$ nanophotonic waveguides. The developed model is used to assess the performance of the sources based on the photon-pair generation and the associated spectral purity. We find that this approach can remarkably improve the spectral purity of low-pure generated photon pairs, relaxing the restrictions on the structure design and the used pump wavelength. In addition, it overcomes the current hurdles in implementing on-chip photon detectors operating at room temperature, paving the way for advanced applications in integrated quantum photonics and information processing.