  Superconducting nanowire single-photon detectors have emerged as a promising
technology for quantum metrology from the mid-infrared to ultra-violet
frequencies. Despite the recent experimental successes, a predictive model to
describe the detection event in these detectors is needed to optimize the
detection metrics. Here, we propose a probabilistic criterion for single-photon
detection based on single-vortex (flux quanta) crossing the width of the
nanowire. Our model makes a connection between the dark-counts and
photon-counts near the detection threshold. The finite-difference calculations
demonstrate that a change in the bias current distribution as a result of the
photon absorption significantly increases the probability of single-vortex
crossing even if the vortex potential barrier has not vanished completely. We
estimate the instrument response function and show that the timing uncertainty
of this vortex tunneling process corresponds to a fundamental limit in timing
jitter of the click event. We demonstrate a trade-space between this intrinsic
(quantum) timing jitter, quantum efficiency, and dark count rate in TaN, WSi,
and NbN superconducting nanowires at different experimental conditions. Our
detection model can also explain the experimental observation of exponential
decrease in the quantum efficiency of SNSPDs at lower energies. This leads to a
pulse-width dependency in the quantum efficiency, and it can be further used as
an experimental test to compare across different detection models.
