Deterministic generation of single photons is essential for many quantum information technologies. A bulk optical nonlinearity emitting a photon pair, where the measurement of one of the photons heralds the presence of the other, is commonly used with the caveat that the single-photon emission rate is constrained due to a trade-off between multiphoton events and pair emission rate. Using an efficient and low noise photon-number-resolving superconducting nanowire detector we herald, in real time, a single photon at telecommunication wavelength. We perform a second-order photon correlation
g2(0) measurement of the signal mode conditioned on the measured photon number of the idler mode for various pump powers and demonstrate an improvement of a heralded single-photon source. We develop an analytical model using a phase-space formalism that encompasses all multiphoton effects and relevant imperfections, such as loss and multiple Schmidt modes. We perform a maximum-likelihood fit to test the agreement of the model to the data and extract the best-fit mean photon number $\ensuremath{\mu}$ of the pair source for each pump power. A maximum reduction of $0.118\ifmmode\pm\else\textpm\fi{}0.012$ in the photon
g2(0) correlation function at $\ensuremath{\mu}=0.327\ifmmode\pm\else\textpm\fi{}0.007$ is obtained, indicating a strong suppression of multiphoton emissions. For a fixed ${g}^{2}(0)=7\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3}$, we increase the single pair generation probability by 25%. Our experiment, built using fiber-coupled and off-the-shelf components, delineates a path to engineering ideal sources of single photons.
Heralded single-photon sources (HSPS) intrinsically suffer from multiphoton emission, leading to a trade-off between the source's quality and the heralding rate. A solution to this problem is to use photon-number-resolving (PNR) detectors to filter out the heralding events where more than one photon pair is created. Here, we demonstrate the use of a high-efficiency PNR superconducting nanowire single-photon detector (SNSPD) as a heralding detector for a HSPS. By filtering out higher-order heralding detections, we can reduce the
g(2)(0) of the heralded single photon by
(26.6±0.2)%, or alternatively, for a fixed pump power, increasing the heralding rate by a factor of
1.363±0.004 for a fixed
g(2)(0). Additionally, we use the detector to directly measure the photon-number distribution of a thermal mode and calculate the unheralded
g(2)(0). We show the possibility to perform
g(2)(0) measurements with only one PNR detector, with the results in agreement with those obtained by more common-place techniques which use multiple threshold detectors. Our work shows that efficient PNR SNSPDs can significantly improve the performance of HSPSs and can precisely characterize them, making these detectors a useful tool for a wide range of optical quantum information protocols.