Abstract: We investigate single- and multi-photon detection regimes of superconducting nanowire detectors embedded in silicon nitride nanophotonic circuits. At near-infrared wavelengths, simultaneous detection of up to three photons is observed for 120 nm wide nanowires biased far from the critical current, while narrow nanowires below 100 nm provide efficient single photon detection. A theoretical model is proposed to determine the different detection regimes and to calculate the corresponding internal quantum efficiency. The predicted saturation of the internal quantum efficiency in the single photon regime agrees well with plateau behavior observed at high bias currents.
W. H. P. Pernice acknowledges support by the DFG Grant Nos. PE 1832/1-1 and PE 1832/1-2 and the Helmholtz society through Grant No. HIRG-0005. The Ph.D. education of O. Kahl is embedded in the Karlsruhe School of Optics and Photonics (KSOP). G. N. Goltsman acknowledges support by Russian Federation President Grant HШ-1918.2014.2 and Ministry of Education and Science of the Russian Federation Contract No.: RFMEFI58614X0007. A. Korneev acknowledges support by Statement Task No. 3.1846.2014/k. V. Kovalyuk acknowledges support by Statement Task No. 2327. We also acknowledge support by the Deutsche Forschungsgemeinschaft (DFG) and the State of Baden-Württemberg through the DFG-Center for Functional Nanostructures (CFN) within subproject A6.4. We thank S. Kühn and S. Diewald for the help with device fabrication as well as B. Voronov and A. Shishkin for help with NbN thin film deposition and A. Semenov for helpful discussion about the detection mechanism of nanowire SSPD's.
The authors declare no competing financial interests.

Abstract: Nanophotonic circuitry and superconducting nanowires have been successfully combined for detecting single photons, propagating in an integrated photonic circuit, with high efficiency and low noise and timing uncertainty. Waveguide-integrated superconducting nanowire single-photon detectors (SNSPDs) can nowadays be engineered to achieve subnanosecond recovery times and can potentially be adopted for applications requiring Gcps count rates. However, particular attention shall be paid to such an extreme count rate regime since artifacts in the detector functionality emerge. In particular, a count-rate dependent detection efficiency has been encountered that can compromise the accuracy of quantum detector tomography experiments. Here, we investigate the response of waveguide-integrated SNSPDs at high photon flux and identify the presence of parasitic currents due to the accumulation of charge in the readout electronics to cause the above-mentioned artifact in the detection efficiency. Our approach allows us to determine the maximum photon count rate at which the detector can be operated without adverse effects. Our findings are particularly important to avoid artifacts when applying SNSPDs for quantum tomography.
We acknowledge support through ERC Consolidator Grant No. 724707 and from the Deutsche Forschungsgemeinschaft through Project No. PE 1832/5-1,2, as well as funding by the Volkswagen Foundation. This project has received funding from the European Union's Horizon 2020 research and innovation program under the Marie Skłodowska-Curie Grant Agreement No. 675745. V.K. and G.G. acknowledge support from the Russian Science Foundation Project No. 16-12-00045 (NbN film deposition and testing). A.V. acknowledges support from the Karlsruhe School of Optics and Photonics (KSOP).

Abstract: A calculation error was made in the original publication of this letter. The error was in the calculation of the noise equivalent power (NEP) values for the avalanche photodiode detector (APD) and the superconducting single photon detector (SSPD), the incorrect values were plotted on the right axis in Fig. 1(b). The correct NEP values were calculated with the same equation reported in the original letter and the revised Fig. 1(b) is shown below. The other conclusions of the paper remain unaltered.