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arXiv:1910.02679 · Physical Review A

Photon-counting distribution for arrays of single-photon detectors

Mattias Jönsson, Gunnar G. Bjork

Published Jan 15, 2020• 14 citations
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Abstract

We derive a computationally efficient expression of the photon-counting distribution for a uniformly illuminated array of single-photon detectors. The expression takes the number of single detectors, their quantum efficiency, and their dark count rate into account. Using this distribution we compute the error of the array detector by comparing the output to that of an ideal detector. We conclude from the error analysis that the quantum efficiency must be very high in order for the detector to resolve a handful of photons with high probability. Furthermore, we conclude that in the worst-case scenario the required array size scales quadratically with the number of photons that should be resolved. We also simulate a temporal array and investigate how large the error is for different parameters, and we compute the optimal size of the array that yields the smallest error.

DOI
10.1103/physreva.101.013815

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We derive a computationally efficient expression of the photon-counting distribution for a uniformly illuminated array of single-photon detectors. The expression takes the number of single detectors, their quantum efficiency, and their dark count rate into account. Using this distribution we compute the error of the array detector by comparing the output to that of an ideal detector. We conclude from the error analysis that the quantum efficiency must be very high in order for the detector to resolve a handful of photons with high probability. Furthermore, we conclude that in the worst-case scenario the required array size scales quadratically with the number of photons that should be resolved. We also simulate a temporal array and investigate how large the error is for different parameters, and we compute the optimal size of the array that yields the smallest error.
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The study on photon counting statistics is of fundamental importance in quantum optics. We theoretically analyzed the imperfect detection of an arbitrary quantum state. We derived photon counting formulae for six typical quantum states (i.e., Fock, coherent, squeeze-vacuum, thermal, odd and even coherent states) with finite quantum efficiencies and dark counts based on multiple on/off detector arrays. We applied the formulae to the simulation of multiphoton number detections and obtained both the simulated and ideal photon number distributions of each state. A comparison between the results by using the fidelity and relative entropy was carried out to evaluate the detection scheme and help select detectors for different quantum states.
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Common methods to achieve photon number resolution rely on fast on-off single-photon detectors in conjunction with temporal or spatial mode multiplexing. Yet, these methods suffer from an inherent trade-off between the efficiency of photon number discrimination and photon detection rate. Here, we introduce a method of photon number resolving detection that overcomes these limitations by replacing mode multiplexing with coherent absorption of a single optical mode in a distributed detector array. Distributed coherent absorption ensures complete and uniform absorption of light among the constituent detectors, enabling fast and efficient photon number resolution. As a proof-of-concept, we consider the case of a distributed array of superconducting nanowire single-photon detectors with realistic parameters and show that deterministic absorption and arbitrarily high photon number discrimination efficiency can be achieved by increasing the number of detectors in the array. Photon number resolution without optical mode multiplication provides a simple yet effective method to discriminate an arbitrary number of photons in large arrays of on-off detectors or in smaller arrays of mode multiplexed detectors.
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Detectors capable of resolving the number of photons are essential in many applications, ranging from classic photonics to quantum optics and quantum communication. In particular, photon-number-resolving detectors based on arrays of superconducting nanostrips can offer a high detection efficiency, a low dark count rate and a recovery time of a few nanoseconds. In this work, we use a detector of this kind for the unbiased generation of random numbers by following two different methods based on the detection of photons. In the former, we exploit the property that the light is equally distributed on each strip of the entire detector, whereas in the latter we exploit the fact that, for a high average number of photons, the parity of the Poissonian distribution of the number of photons emitted by the laser tends to be zero. In addition, since these two methods are independent, it is possible to use them at the same time.