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arXiv:2202.08042 · Physical Review A

Information Extraction in Photon Counting Experiments

Timon Schapeler, Tim J. Bartley

Published Jan 1, 2022• 2 citations
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Abstract

We demonstrate a comparison of different multiplexing architectures based on quantum detector tomography. Using the purity of their measurement outcomes, we gain insight into the photon-number-resolving ability of the devices. Further, we calculate the information each measurement outcome can extract from a Hilbert space with given dimension. Our work confirms that more multiplexing outcomes enable higher photon-number-resolving ability; however, the splitting between those outcomes must be optimized as well. Published by the American Physical Society 2022

DOI
10.1103/physreva.106.013701

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We demonstrate a comparison of different multiplexing architectures based on quantum detector tomography. Using the purity of their measurement outcomes, we gain insight into the photon-number-resolving ability of the devices. Further, we calculate the information each measurement outcome can extract from a Hilbert space with given dimension. Our work confirms that more multiplexing outcomes enable higher photon-number-resolving ability; however, the splitting between those outcomes must be optimized as well. Published by the American Physical Society 2022
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The ability to discriminate the number of photons in a radiation field has a critical role in the implementation of quantum optical technologies. True photon-number-resolving detectors are rare and complex devices, while a quasi-photon-number-resolving detector (qPNRD) is a practical alternative for real-world applications. Our qPNRD is composed of a fiber demultiplexer and individual non-photon-number-resolving detectors. We perform quantum tomography on our qPNRD based on the positive operator-valued measure and extend the analysis using the Bayesian formalism to uncover how the measurement influences knowledge of the measured photon probability distribution.
Photon counting is a cornerstone of quantum optics. Here, we demonstrate precisely counting from 0 to over 9000 photons, beating the Poisson noise limit by at least 4.1 dB4.1~\mathrm{dB}4.1 dB across this range. We achieve sub-single-photon precision up to 276 photons per pulse. To do so, we multiplex eight intrinsically photon-number-resolving superconducting nanowire single-photon detectors across 128 temporal modes. We use a model-informed characterization of each of the 1024 detection bins, for optimal precision. We perform quantum detector tomography to reconstruct the positive operator valued measures (POVMs) of the complete device, which consists of 1.38⋅1081.38\cdot10^81.38⋅108 matrix elements. At the repetition rate of our experiment of 80 kHz80~\mathrm{kHz}80 kHz, we can precisely count photons corresponding to an optical power of approximately 71 pW71~\mathrm{pW}71 pW, bridging the gap from single-photon measurements to high-sensitivity optical power meters. A photon-number-resolving detector of this size, and the tools used to analyze it, will become increasingly important to characterize large quantum states, as well as tasks in precision metrology and optical power standards.
Although some non-trivial photon number resolving detectors exist, it may still be convenient to discriminate photon number states with the method of multiplexed detection. Multiplexing can be performed with paths in real space, with paths in time, and in principle with any degree of freedom that has a sufficient number of eigenstates and that can be coupled to the photon number. Previous works have addressed the probabilities involved in these measurements with Monte Carlo simulations, or by restricting the number of detectors to powers of 2, or without including quantum efficiency or noise. In this work we find an analytical expression of the detection probabilities for any number of input photons and any number of on/off photon detectors with a quantum efficiency 0%≤η≤100%0\%\leqη\leq100\%0%≤η≤100% and a false count probability ε≥0\varepsilon\geq0ε≥0. This allows us to retrodict the number of photons that we had at the input in the least unbiased way possible. We conclude our work with some examples.
Photon number resolving detectors are the ultimate measurement of quantum optics, which is the reason why developing the technology is getting significant attention in recent years. With this arises the question of how to evaluate the performance of the detectors. We suggest that performance of a photon number detector can be evaluated by comparing it to a multiplex of on-off detectors in a practical scenario: conditional preparation of a photon number state. Here, both the quality of the prepared state and the probability of the preparation are limited by the number of on-off detectors in the multiplex, which allows us to set benchmarks that can be achieved or surpassed by the photon number resolving detectors.