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arXiv:2311.13515 · New Journal of Physics

Photon number resolving detection with a single-photon detector and adaptive storage loop

Nicholas M. Sullivan, Boris Braverman, Jeremy Upham, Robert W. Boyd

Published Apr 1, 2024• 8 citations
arXivHTMLPDF

Abstract

Abstract Photon number resolving (PNR) measurements are beneficial or even necessary for many applications in quantum optics. Unfortunately, PNR detectors are usually large, slow, expensive, and difficult to operate. However, if the input signal is multiplexed, photon ‘click’ detectors, that lack an intrinsic PNR capability, can still be used to realize photon number resolution. Here, we investigate the operation of a single click detector, together with a storage line with tunable outcoupling. Using adaptive feedback to adjust the storage outcoupling rate, the dynamic range of the detector can in certain situations be extended by up to an order of magnitude relative to a purely passive setup. An adaptive approach can thus allow for photon number variance below the quantum shot noise limit under a wider range of conditions than using a passive multiplexing approach. This can enable applications in quantum enhanced metrology and quantum computing.

DOI
10.1088/1367-2630/ad3be5

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Abstract Photon number resolving (PNR) measurements are beneficial or even necessary for many applications in quantum optics. Unfortunately, PNR detectors are usually large, slow, expensive, and difficult to operate. However, if the input signal is multiplexed, photon ‘click’ detectors, that lack an intrinsic PNR capability, can still be used to realize photon number resolution. Here, we investigate the operation of a single click detector, together with a storage line with tunable outcoupling. Using adaptive feedback to adjust the storage outcoupling rate, the dynamic range of the detector can in certain situations be extended by up to an order of magnitude relative to a purely passive setup. An adaptive approach can thus allow for photon number variance below the quantum shot noise limit under a wider range of conditions than using a passive multiplexing approach. This can enable applications in quantum enhanced metrology and quantum computing.
We analyze the performance of photon-number-resolving (PNR) detectors and introduce a figure of merit for the accuracy of such detectors. This figure of merit is the (worst-case) probability that the photon-number-resolving detector correctly predicts the input photon number. Simulations of various PNR detectors based on multiplexed single-photon ``click detectors'' is performed. We conclude that the required quantum efficiency is very high in order to achieve even moderate (up to a handful) photon resolution, we derive the required quantum efficiency as a function of the the maximal photon number one wants to resolve, and we show that the number of click detectors required grows quadratically with the maximal number of photons resolvable.
Standard linear optical detectors have a maximum sensitivity in the few hundreds of photons range, limited by amplifier noise. On the other hand, single photon detectors, which are the most sensitive detectors, are strongly nonlinear: One or more photons result in the same output signal. Photon number resolving (PNR) detectors, which have the ability to discriminate the number of photons in a weak optical pulse, are of great importance in the field of quantum information processing and quantum cryptography. Moreover, a PNR detector with large dynamic range can cover the gap between these two detection modes. Such detectors are greatly desirable not only in quantum information science and technology, but also in any application dealing with low light levels. In this work, we propose a novel approach to photon number resolving detectors based on spatial multiplexing of nanowire superconducting single-photon detectors. In the proposed approach, N superconducting nanowires, each connected in parallel to an integrated resistor, are connected in series. Photon absorption in a nanowire switches its bias current to the parallel resistor, forming a voltage pulse across it. The sum of these voltages, proportional to the number of absorbed photons, is measured at the output. The use of a cryogenic preamplifier with high input impedance for the read-out increases the linearity, the signal to noise ratio, and the speed. With this combination, we expect to be able to count up to few tens of photons with high fidelity, excellent timing resolution, and very high sensitivity in the telecommunication wavelength range.
Abstract Photon statistics of an optical field can be used for quantum optical sensing in low light level scenarios free of bulky optical components. However, photon-number-resolving detection to unravel the photon statistics is challenging. Here, we propose a novel detection approach, that we call ‘photon discerning’, which uses adaptive photon thresholding for photon statistical estimation without recording exact photon numbers. Our photon discerner is motivated by the field of neural networks where tunable thresholds have proven efficient for information extraction in machine learning tasks. The photon discerner maximizes Fisher information per photon by iteratively choosing the optimal threshold in real-time to approach the shot noise limit. Our proposed scheme of adaptive photon thresholding leads to unique remote-sensing applications of quantum degree of linear polarization camera and quantum LiDAR. We investigate optimal thresholds and show that the optimal photon threshold can be counter-intuitive (not equal to 1) even for weak signals (mean photon number much less than 1), due to the photon bunching effect. We also put forth a superconducting nanowire realization of the photon discerner which can be experimentally implemented in the near-term. We show that the adaptivity of our photon discerner enables it to beat realistic photon-number-resolving detectors with limited photon-number resolution in certain applications. Our work suggests a new class of detectors for information-theory driven, compact, and learning-based quantum optical sensing.
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.
Photon-number-resolving (PNR) detectors are essential for photonic quantum computing, where a single measurement outcome must reliably herald a specific quantum state. However, detector fidelity is conventionally evaluated using ensemble-averaged statistics obtained from many measurements, which can remain high even when individual photon-number assignments are frequently misidentified. Here we introduce a universal single-shot fidelity that directly quantifies the probability of correctly identifying a photon number in a single measurement. The framework combines an efficiency-based POVM with a resolution-driven confusion matrix derived from the detector response, allowing photon loss and photon-number misidentification to be treated separately and then recombined into a single operational metric. This distinction reveals two fundamentally different limitations. Detection-efficiency loss represents an unrecoverable hardware constraint, whereas resolution-driven misidentification can be reduced by introducing a rejection region, trading generation rate for confidence. Because the metric is defined independently of detector architecture, it enables direct comparison between energy-resolving detectors such as transition-edge sensors and multiplexed click-based detectors on the same footing. Applying the framework to calibration data from three distinct detector architectures, we demonstrate quantitative comparison across photon-number regimes relevant to both discrete-variable and continuous-variable photonic quantum computing. The resulting benchmark provides a common operational metric for evaluating photon-number-resolving detectors and connecting detector performance to photonic quantum-computing requirements.