We realize fast, efficient and small footprint niobium nitride superconducting nanowire single photon detectors atop of photonic waveguides. By reducing the bias current of the nanowire, in order to break the superconductivity and trigger a detection event, more than one photon needs to be absorbed in a localized section of the wire within a very short time delay (hot-spot relaxation time), making such devices promising also for multiphoton sensing applications. We adopt a near-infrared pump-probe technique in a cryogenic environment to investigate the bias current dependence of the hot-spot relaxation time. A minimum relaxation time of (22 ± 1) ps is obtained when applying a bias current of 50% of the switching current at a bath temperature of 1.7K. Our study reveals a strong increase of the picosecond relaxation time with increasing bias current. We further adopt the same technique for determining the multi-photon detection regimes of the detector, which are in agreement with standard quantum detector tomography. In this context, we introduce a practical model and reconstruction method for determining the detector sensitivity regimes. Our work provides a complete description of the detector working operation in both number photon threshold sensitivity and time-delay sensitivity. The results allow for implementing on-chip measurement architectures for the characterization of weak classical light emitters and fast single photon sources with only one detector, driven at different biasing currents, with a drastic reduction of the time uncertainty limitations of typical correlation measurement systems.
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