No free lunch: the trade-off between heralding rate and efficiency in microresonator-based heralded single photon sources

Generation of heralded single photons has recently been demonstrated using spontaneous four-wave mixing in integrated microresonators. While the results of coincidence measurements on the generated photon pairs from these systems show promise for their utility in heralding applications, such measurements do not reveal all of the effects of photon losses within the resonator. These effects, which include a significant degradation of the heralding efficiency, depend strongly on the relative strengths of the coupling of the ring modes to loss modes and channel modes. We show that the common choice of critical coupling neither optimizes the rate of successfully heralded photons nor coincidences and derives the coupling conditions needed to do so. Optimizing these rates has a considerable negative effect on the heralding efficiency.