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arXiv:2511.13475 · APS Open Science

Machine learning inspired photon number resolution in superconducting nanowire single-photon detectors

I. S. Kuijf, F. B. Baalbergen, L. Seldenthuis, E. P. L. van Nieuwenburg, M. J. A. de Dood

quant-phphysics.ins-detphysics.opticsSubmitted Nov 17, 2025• Announced Nov 18, 2025• 0 citations
v1 · Nov 17, 2025v2 · Mar 16, 2026v3 · Mar 17, 2026
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Abstract

Photon-number resolved detection with superconducting nanowire single-photon detectors (SNSPDs) attracts increasing interest, but lacks a systematic framework for interpreting and benchmarking this capability. In this work, we combine principal component analysis (PCA) with a new readout technique to explore the photon-number resolving capabilities of SNSPDs and find that the information of the photon number is contained in a single principal component which approximates the time derivative of the average response trace. We introduce a new confidence metric based on the Bhattacharyya coefficient to quantify the photon-number-resolving capabilities of a detector system and show that this metric can be used to compare different 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 GSample/sec) and analog bandwidth (3 GHz) and could be implemented in an FPGA, giving a highly scalable solution for real-time photon counting.

DOI
10.1103/dwth-wjtr

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Since their first demonstration in 2001 [Gol’tsman et al., Appl. Phys. Lett. 79, 705–707 (2001)], superconducting-nanowire single-photon detectors (SNSPDs) have witnessed two decades of great developments. SNSPDs are the detector of choice in most modern quantum optics experiments and are slowly finding their way into other photon-starved fields of optics. Until now, however, in nearly all experiments, SNSPDs were used as “binary” detectors, meaning that they could only distinguish between 0 and >=1 photons, and photon number information was lost. Recent research has demonstrated proof-of-principle photon-number resolution (PNR) SNSPDs counting 2–5 photons. The photon-number-resolving capability is highly demanded in various quantum-optics experiments, including Hong–Ou–Mandel interference, photonic quantum computing, quantum communication, and non-Gaussian quantum state preparation. In particular, PNR detectors at the wavelength range of 850–950 nm are of great interest due to the availability of high-quality semiconductor quantum dots (QDs) [Heindel et al., Adv. Opt. Photonics 15, 613–738 (2023)] and high-performance cesium-based quantum memories [Ma et al., J. Opt. 19, 043001 (2017)]. In this paper, we demonstrate NbTiN-based SNSPDs with >94% system detection efficiency, sub-11 ps timing jitter for one photon, and sub-7 ps for 2 photons. More importantly, our detectors resolve up to 7 photons using conventional cryogenic electric readout circuitry. Through theoretical analysis, we show that the PNR performance of demonstrated detectors can be further improved by enhancing the signal-to-noise ratio and bandwidth of our readout circuitry. Our results are promising for the future of optical quantum computing and quantum communication.
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Many quantum applications will benefit significantly from photon number resolving detection. However, photon number resolving detectors have been largely experimental devices implemented in laboratory settings. Recent advances in superconducting nanowire device fabrication and readout techniques have enabled the implementation of photon number resolution in widely deployable commercial single-photon detection systems. We will discuss progress in implementing photon number resolved detection with commercially produced superconducting nanowire single photon detectors via spatial multiplexing of independently instrumented detector elements and photon number dependent rise-time changes in single-element nanowire devices.
Single-photon detectors based on superconducting nanowires (SNSPDs) are promising technologies with good comprehensive performance, especially their excellent temporal resolution for applications in quantum precision measurements and time-varying ultimate detection. The response time of an SNSPD can be characterized by aspects of hotspot thermal relaxation and electrical relaxation, which are also responsible for the time jitter of the SNSPD. The factors affecting the temporal resolution of an SNSPD, the underlying physical mechanism, the intrinsic limit, and possible optimization methods are reviewed. The poor energy resolution and lack of photon number resolution for conventional SNSPDs can be overcome by using high-impedance readouts, novel device structures, characterization methods and, most importantly, SNSPD arrays, which can simultaneously further improve the temporal resolution. The study of the temporal and photon number resolution of SNSPDs helps reveal the underlying physics and is valuable for their new application in various practical engineering areas.