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arXiv:2007.16048 · Optics Express

Quantum detector tomography of a 2×2 multi-pixel array of superconducting nanowire single photon detectors

Timon Schapeler, Jan Philipp Höpker, Tim J. Bartley

Published Sep 18, 2020• 26 citations
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Abstract

We demonstrate quantum detector tomography of a commercial 2×2 array of superconducting nanowire single photon detectors. We show that detector-specific figures of merit including efficiency, dark-count and cross-talk probabilities can be directly extracted, without recourse to the underlying detector physics. These figures of merit are directly identified from just four elements of the reconstructed positive operator valued measure (POVM) of the device. We show that the values for efficiency and dark-count probability extracted by detector tomography show excellent agreement with independent measurements of these quantities, and we provide an intuitive operational definition for cross-talk probability. Finally, we show that parameters required for the reconstruction must be carefully chosen to avoid oversmoothing the data.

DOI
10.1364/oe.404285

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We demonstrate quantum detector tomography of a commercial 2×2 array of superconducting nanowire single photon detectors. We show that detector-specific figures of merit including efficiency, dark-count and cross-talk probabilities can be directly extracted, without recourse to the underlying detector physics. These figures of merit are directly identified from just four elements of the reconstructed positive operator valued measure (POVM) of the device. We show that the values for efficiency and dark-count probability extracted by detector tomography show excellent agreement with independent measurements of these quantities, and we provide an intuitive operational definition for cross-talk probability. Finally, we show that parameters required for the reconstruction must be carefully chosen to avoid oversmoothing the data.
Abstract We demonstrate and verify quantum detector tomography of a superconducting nanowire single-photon detector (SNSPD) in a multiplexing scheme which permits measurement of up to 71 000 photons per input pulse. We reconstruct the positive operator valued measure (POVM) of this device in the low photon-number regime, and use the extracted parameters to show the POVMs spanning the whole dynamic range of the device. We verify this by finding the mean photon number of a bright state. Our work shows that a reliable quantum description of large-scale SNSPD devices is possible, and should be applicable to other multiplexing configurations.
Abstract Though photon-number-resolving (PNR) detectors based on multiplexed threshold elements are key tools for quantum optics and quantum information, yet accurate calibration of their response in the presence of imperfections remains challenging. Here we develop a model for a four-channel PNR detector designed as a superconducting nanowire single-photon detector (SNSPD) array, allowing for unequal channel transmission coefficients and dark counts. Closed-form expressions for the click probabilities and transfer-matrix elements are obtained for coherent-state probes, and a numerical study quantifies the range of channel imbalance where the commonly used equal-channel, single-parameter approximation fails. Applying this framework to experimental data from a four-channel PNR SNSPD, we show that direct model-based fits do not reproduce the measured click statistics probably because of inter-channel cross-talks. To overcome this, we implement a hybrid quantum detector tomography scheme that combines a model-based fit to the mean click number with a data-driven reconstruction of the low-photon subspace. The resulting transfer matrix reproduces the experimental click statistics with average fidelity above 99.9% and provides a robust description of the detector in the presence of cross-talks and other non-idealities.
We develop a combinatorial and Bayesian framework to quantify the information gained by increasing the local photon-number resolution of multiplexed detection systems based on superconducting nanowire single-photon detectors (SNSPDs). Motivated by recent studies that attribute photon-number resolving capabilities to a single SNSPD overcoming the typical on/off detection mechanism, we generalize the existing formulation for the binary devices by deriving the probability response tensor of multiplexed systems based on SNSPDs with an arbitrary number of resolvable states. We include finite efficiency through binomial loss convolution and, separately, assess the impact of dark counts. From this response tensor we derive a generalized N-photon detector fidelity, a Bayesian photon-number reconstruction, and the corresponding reconstruction fidelity. We particularize this formulation to study 2-, 3- and 4-state multiplexed systems with different numbers of detectors and show that increasing local photon-number resolution systematically improves both detector fidelity and Bayesian photon-number reconstruction. This substantially relaxes the quadratic scaling between detector number and resolvable photon-number required by purely binary multiplexed arrays. These results provide a quantitative value-of-information assessment for multi-state photon-number-resolving detector arrays.
Superconducting nanowire single-photon detectors (SNSPDs) are widely used in telecom wavelength optical quantum information science applications. Quantum detector tomography allows the positive-operator-valued measure (POVM) of a single-photon detector to be determined. We use an all-fiber telecom wavelength detector tomography test bed to measure detector characteristics with respect to photon flux and polarization, and hence determine the POVM. We study the SNSPD both as a binary detector and in an 8-bin, fiber based, Time-Multiplexed (TM) configuration at repetition rates up to 4 MHz. The corresponding POVMs provide an accurate picture of the photon number resolving capability of the TM-SNSPD.
We report a 16-pixel (4×4) superconducting nanowire single-photon detector (SNSPD) array featuring pixel-level photon-number-resolving capability. This multidimensional sensing is enabled by integrating a compact four-element series nanowire architecture into each spatial pixel, allowing direct discrimination of one to four photons. Under single-mode fiber illumination, the device achieves a total system detection efficiency of 41.5%, given the array geometrical fill factor of 53%. Across all channels, the device exhibits reliable multiphoton discrimination, maintaining minimum readout fidelities of 96%, 89%, 73%, and 77% for one- to four-photon states, respectively. Furthermore, independent channel evaluations reveal low timing jitter and negligible inter-channel crosstalk (<0.1 % ). By implementing differentiating pulse shaping for high-flux operation, a maximum single-channel −3 dB count rate of 984 MHz is achieved, establishing an aggregated array bandwidth potential of 8.9 GHz. This sensing architecture may provide a viable pathway toward high-flux single-photon imaging, offering potential applications in quantum optics and light detection and ranging (LiDAR) systems.