Enhancing Heralding Efficiency and Biphoton Rate in Type-I Spontaneous Parametric Down-Conversion

The nonlinear optical process of spontaneous parametric down-conversion (SPDC) is widely studied for applications in quantum information science due to its ability to produce two photons that can be entangled in many degrees of freedom. For applications in quantum communication, two metrics of this process are particularly important: heralding efficiency and total joint rate. Here, we derive expressions for both quantities for a variety of different beam geometries and frequencies. We pay specific attention to the spectrum of both biphotons and individual photons. We reveal the underlying mechanisms responsible for the spectral shape and show they differ for different geometries and frequencies. We then use these spectra to calculate heralding efficiency and joint count rate and examine how each of these metrics changes with different geometries, frequencies, spectral filtering, and beam parameters. Interestingly, we find very high heralding efficiencies are achievable for collinear geometries without spectral filtering, while noncollinear geometries require spectral filtering to achieve the same values. We also find that the spectrum is narrower for nondegenerate SPDC than for degenerate SPDC, leading to lower joint count rates and higher heralding efficiency in the former. In addition to the theory, we verify selected predictions with experimental results.