Extracting photon-number information from superconducting nanowire single-photon detectors traces via mean-derivative projection

Photon-number-resolved detection with superconducting nanowire single-photon detectors (SNSPDs) attracts increasing interest, often focusing on the rising edge of the electrical signal as the main source of photon-number-resolving information. It remains unclear whether additional photon-number information is contained in the rest of the detector response and how this can be optimally extracted and interpreted. In this work, we combine principal component analysis (PCA) with readout at relatively low sampling rates to explore the photon-number-resolving capabilities of SNSPDs. We find that the information of the photon number is captured by a single principal component that closely resembles the time derivative of the average response trace. Using the time derivative of the average response trace provides an agnostic method to obtain the photon number from SNSPD traces without the necessity of performing PCA, making this method simple and quick to calibrate. As an auxiliary diagnostic, we use a distinguishability metric based on the Bhattacharyya coefficient [ , 401 (1946)] to quantify and compare the photon-number-resolving capabilities of different detector systems. Our analysis and interpretation of the principal components imply that photon-number resolution in SNSPDs can be achieved with moderate hardware requirements in terms of both sample rate (5 GS s − 1 ) and analog bandwidth (3 GHz) and could be implemented in a field-programmable gate array, giving a highly scalable solution for real-time photon counting.