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arXiv:2510.00714 · APL Quantum

Practical considerations for assignment of photon numbers with SNSPDs

Timon Schapeler, Isabell Mischke, Fabian Schlue, Michael Stefszky, Benjamin Brecht, Christine Silberhorn, Tim J. Bartley

Published Jan 2, 2026• 2 citations
arXivHTMLPDF

Abstract

Superconducting nanowire single-photon detectors (SNSPDs) can enable photon-number resolution (PNR) based on accurate measurements of the detector’s response time to few-photon optical pulses. In this work, we investigate the impact of the optical pulse shape and duration on the accuracy of this method. We find that Gaussian temporal pulse shapes yield cleaner arrival-time histograms and, thus, more accurate PNR, compared to bandpass-filtered pulses of equal bandwidth. For low system jitter and an optical pulse duration comparable to the other jitter contributions, photon numbers can be discriminated in our system with a commercial SNSPD. At 60 ps optical pulse duration, photon-number discrimination is significantly reduced. Furthermore, we highlight the importance of using the correct arrival-time histogram model when analyzing photon-number assignment. Using exponentially modified Gaussian distributions, instead of the commonly used Gaussian distributions, we can more accurately determine photon-number misidentification probabilities. Finally, we reconstruct the positive operator-valued measures of the detector, revealing sharp features that indicate the intrinsic PNR capabilities.

DOI
10.1063/5.0304127

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Superconducting nanowire single-photon detectors (SNSPDs) can enable photon-number resolution (PNR) based on accurate measurements of the detector’s response time to few-photon optical pulses. In this work, we investigate the impact of the optical pulse shape and duration on the accuracy of this method. We find that Gaussian temporal pulse shapes yield cleaner arrival-time histograms and, thus, more accurate PNR, compared to bandpass-filtered pulses of equal bandwidth. For low system jitter and an optical pulse duration comparable to the other jitter contributions, photon numbers can be discriminated in our system with a commercial SNSPD. At 60 ps optical pulse duration, photon-number discrimination is significantly reduced. Furthermore, we highlight the importance of using the correct arrival-time histogram model when analyzing photon-number assignment. Using exponentially modified Gaussian distributions, instead of the commonly used Gaussian distributions, we can more accurately determine photon-number misidentification probabilities. Finally, we reconstruct the positive operator-valued measures of the detector, revealing sharp features that indicate the intrinsic PNR capabilities.
Abstract We experimentally demonstrate high-fidelity detection of 0, 1- and 2-photon states in a commercial superconducting nanowire single photon detector (SNSPD) under 20 MHz pulsed coherent illumination. The arrival of a different number of photons induces distinct temporal dynamics in the disruption of the superconducting state of the detector. Therefore, specific features emerge in the arrival-time histograms, that we show are directly correlated with the photon-number state. We show that, across a broad range of time-averaged light intensities, the probabilities of detecting 1- and 2 + -photon events collapse onto the Poisson distribution of coherent light. We identify the voltage detection threshold as a critical factor for photon number resolving (PNR) capabilities. Even under demanding conditions of high repetition rate illumination, we found that a high trigger level significantly enhances total detection fidelity, achieving 0.920 and 0.845 for 1-photon and for 2-photon events. These results correspond to remarkably low conditional misidentification probabilities, 0.000 02 and 0.0013, describing the classification error among detected 1- and 2-photon events. We identify an inherent 39 ps latency difference between single- and multi-photon detection events. We show that the measured 2-photon conditional misidentification probability corresponds to the one of a multiplexed PNR detector with 730 pixels. We believe that our findings provide a framework for developing high/fidelity spatially multiplexed SNSPD by exploiting the intrinsic PNR capabilities of individual constituting elements.
The ability to resolve photon numbers is crucial in quantum information science and technology, driving the development of detectors with intrinsic photon-number resolving (PNR) capabilities. Although transition edge sensors represent the state-of-the-art in PNR performance, superconducting nanowire single-photon detectors (SNSPDs) offer superior efficiency, speed, noise reduction, and timing precision. Directly inferring photon numbers, however, has only recently become feasible due to advances in readout technology. Despite this, photon-number discrimination remains constrained by the nanowire's electrical properties and readout jitter. In this work, we employ waveguide-integrated SNSPDs and time-resolved measurements to explore how the nanowire kinetic inductance and system jitter affect PNR capabilities. By analyzing the latency time of the photon detection, we can resolve changes in the rising edge of the detection pulse. We find that lower jitter as well as increased kinetic inductance enhances the pulse separation for different photon numbers and improves the PNR capability. Enhancing the kinetic inductance from 165 nH to 872 nH improves PNR quality by 12%, 31% and 23% over the first three photon numbers, though at the cost of reducing the detector's count rate from 165 Mcps to 19 Mcps. Our findings highlight the trade-off between PNR resolution and detector speed.
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.
Photon-number-resolving (PNR) detectors are essential components of photonic quantum technologies. However, conventional single-channel edge-triggered readout struggles to resolve the photon number nnn in real time or to characterize how timing jitter depends on nnn. In this work, we use a dual-trigger method on a three-pixel series-connected superconducting nanowire single-photon detector (SNSPD) that triggers on both the rising and falling edges of the detection pulse. By doing so, we preserve the precise arrival time of the detection event while mapping the photon number onto the time interval between the rising and falling edges, allowing clear separation of the events. Using this technique, we assign each detection event to n=1,2,n = 1, 2,n=1,2, or 3 photons with 99 %99\,\%99% posterior confidence across all three classes. The timing jitter decreases as nnn increases, reaching values below 41 ps41\, \text{ps}41ps for n≥2n \geq 2n≥2. Comparing edge-triggering with constant-fraction discrimination (CFD) for arrival-time extraction, we find that CFD yields lower jitter for single-photon events and a nearly constant mean arrival time. Altogether, our results establish dual-triggering as a robust, low-latency readout scheme for PNR detectors, while revealing a photon-number dependence of the timing jitter relevant to timing precision achievable in heralded photonic quantum applications.
Photon number resolving (PNR) is an important capacity for detectors working in quantum and classical applications. Although a conventional superconducting nanowire single-photon detector (SNSPD) is not a PNR detector, by arranging nanowires in a series array and multiplexing photons over space, such series PNR-SNSPD can gain quasi-PNR capacity. However, the accuracy and maximum resolved photon number are both limited by the signal-to-noise ratio (SNR) of the output pulses. Here, we introduce a matched filter, which is an optimal filter in terms of SNR. Experimentally, the normalized spacing between pulse amplitudes from adjacent photon number detections increased by a maximum factor of 2.1 after the matched filter. Combining with a cryogenic amplifier to increase SNR further, such spacing increased by a maximum factor of 5.3. In contrast to a low pass filter, the matched filter gave better SNRs while maintaining low timing jitters. The minimum timing jitter of 55 ps was obtained experimentally. Our results suggest that the matched filter is a useful tool for improving the performance of the series PNR-SNSPD. The maximum resolved photon number can be expected to reach 65 or even larger.
Photon-number-resolving (PNR) detectors are a key enabling technology in photonic quantum information processing. Here, we demonstrate the PNR capacity of conventional superconducting nanowire single-photon detectors by performing ultra-high-resolution time-tagging of the detector-generated electrical pulses. This method provides a viable approach for PNR with high detection efficiency and a high operational repetition rate. We present the implementation of such a PNR detector in the telecom C-band and its characterization by measuring the photon-number statistics of coherent light with tunable intensity. Additionally, we demonstrate the capabilities of the detection method by measuring photon-number correlations of non-classical states.