Kinetic inductance and jitter dependence of intrinsic photon-number resolution in superconducting nanowire single-photon detectors

Photon-number resolution (PNR) is crucial in quantum information technology. Time-resolved measurements applied to superconducting nanowire single-photon detectors (SNSPDs) have recently demonstrated intrinsic PNR capabilities, complementing their superior efficiency, speed, and timing precision. Using waveguide-integrated SNSPDs, we investigate the impact of nanowire kinetic inductance and system jitter on intrinsic PNR, identifying the trade-off between intrinsic PNR and detector speed. Increasing the kinetic inductance from 165 nH to 872 nH enhances the PNR quality by 12%, 31%, and 23% for the first three photon numbers but reduces the maximum count rate from 165 Mcps to 19 Mcps.