Fano Fluctuations In Superconducting-Nanowire Single-Photon Detectors

Because of their universal nature, Fano fluctuations are expected to influence the response of superconductingnanowire single-photon detectors (SNSPDs). We predict that photon counting rate (PCR) as a function of bias current (I-B) in SNSPDs is described by an integral over a transverse coordinate-dependent complementary error function. Fano fluctuations in the amount of energy deposited into the electronic system contribute to the finite width of this error function Delta IB. The local response of an SNSPD can also affect this width: the location of the initial photon absorption site across the width of the wire can impact the probability of vortex-antivortex unbinding and vortex entry from the edges. In narrow-nanowire SNSPDs, the local responses are uniform, and Fano fluctuations dominate Delta IB. We demonstrate good agreement between theory and experiments for a series of bath temperatures and photon energies in narrow-wire WSi SNSPDs. In a wide-nanowire device, the strong local dependence will introduce a finite width to the PCR curve, but with sharp cusps. We show how Fano fluctuations can smooth these features to produce theoretical curves that bettermatch experimental data. We also show that the time-resolved hotspot relaxation curves predicted by Fano fluctuations match the previously measured Lorentzian shapes (except for their tails) over the entire range of bias currents investigated experimentally.