Design Considerations for High-purity Heralded Single Photon Sources

When building a parametric downconversion photon-pair source with spectrally separable photons, e.g. for making high-purity heralded single photons, two practical issues must be accounted for: the design of the experiment, and its characterization. To address experiment design, we study the impact on spectral separability of realistic (sech shaped and chirped) pump fields, realistic nonlinear crystals with fabrication imperfections, and undesirable PDC generation far from the central PMF peak coming from nonlinearity shaping methods. To address experiment characterization, we study the effect of discretization and spectral range of the measured bi-photon joint spectrum, the difference between inferring separability from the joint spectral amplitude vs. the joint spectral intensity, and advantages of interference experiments for purity characterization over methods based on the joint spectral intensity. This study will be of practical interest to researchers building the next generation of nonlinear sources of separable photon pairs.