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

Abstract

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 does not optimize the rate of successfully heralded photons, and derive the coupling condition needed to do so, as well as the condition needed to maximize the rate of coincidence counts. Optimizing these rates has a considerable negative effect on the heralding efficiency.Heralded single photons are an important resource both for optical quantum information processing, and for fundamental investigations of nonlinear quantum optics at the single photon level. There is particular interest in developing monolithically integrated sources of heralded single photons, which would enable their use in an onchip optical setting. Several such implementations have recently been demonstrated using spontaneous four-wave mixing (SFWM) in integrated microresonators [1][2][3][4].In typical implementations each photon of a generated pair is emitted into one of two distinct optical modes: a heralding mode (HM) carries a herald photon, the presence of which then indicates the existence of a single photon in an output mode (OM). These modes might correspond to the signal and idler fields generated by SFWM in a microresonator [1,3,5], or to the two outputs of a degenerate photon pair splitter [2]. By discarding experimental runs in which no heralding photon is detected in the HM, the experimenter effectively post-selects on those runs in which a single photon is present in the OM. In an ideal device, detection of an HM photon would guarantee the existence of an OM photon. In practice, even assuming perfect detection efficiency, photon losses within the photon pair source lead to events in which the herald photon is detected but the OM photon is lost. After detecting the herald, the OM mode cannot therefore be represented as the desired pure state ρ OM = |1 1|, but rather ρ OM = P vac |0 0| + P 1 |1 1|, where P vac corresponds to the probability of losing the OM photon given the successful generation of a photon pair and subsequent detection of the HM photon, and P 1 = 1 − P vac . The existence of this vacuum probability degrades the utility of the heralding device: if P vac is significant the very purpose of the herald is compromised. Note that this narrative neglects the effects of spectral correlation between the signal and idler photons, which would lead to the * zachary.vernon@utoronto.ca one-photon state itself being expressed not as |1 1|, but as a mixture of states involving a photon at different frequencie...

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