Benchmarking single-photon sources from an auto-correlation measurement

Pavel Sekatski1, Enky Oudot2, Patrik Caspar1, Rob Thew1, and Nicolas Sangouard3

1Department of Applied Physics, University of Geneva, Geneva, Switzerland
2ICFO - Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology, 08860 Castelldefels (Barcelona), Spain
3Université Paris-Saclay, CEA, CNRS, Institut de physique théorique, 91191, Gif-sur-Yvette, France

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Here we argue that the probability that a given source produces exactly a single photon is a natural quantity to benchmark single-photon sources as it certifies the absence of multi-photon components and quantifies the efficiency simultaneously. Moreover, this probability can be bounded simply from an auto-correlation measurement — a balanced beam splitter and two photon detectors. Such a bound gives access to various non-classicality witnesses that can be used to certify and quantify Wigner-negativity, in addition to non-Gaussianity and P-negativity of the state produced by the source. We provide tools that can be used in practice to account for an imperfect beam splitter, non-identical and non-unit detection efficiencies, dark counts and other imperfections, take finite statistical effects into account without assuming that identical states are produced in all rounds, and optionally allow one to remove the detector inefficiencies from the analysis. We demonstrate the use of the proposed benchmark, non-classicality witness and measure using a heralded single-photon source based on spontaneous parametric down-conversion. We report on an average probability that a single photon is produced $\geq 55\%$ and an average measure of the Wigner negativity $\geq 0.004$ with a confidence level of $1-10^{-10}$.

Single-photon sources are crucial for various quantum technologies. The performance of these sources is usually quantified by the efficiency and the absence of multi-photon components. However both aspects are captured by the probability that a source produces a single photon, which naturally benchmarks the capability of the single-photon source to do what its name suggests.

Considering various levels of assumptions about the detection setup, we show that this single-photon probability can be lower-bounded from the usual auto-correlation measurement — a balanced beam splitter and two single-photon detectors. Furthermore, if additional information on the mode-purity of the source is available, the single-photon probability can be related to a measure of non-classically of the state prepared by the source — the negativity of the Wigner quasi-probability distribution associated to the produced state.

Finally, we demonstrate the practicality of the proposed benchmark and non-classically measure using a heralded single-photon source based on spontaneous parametric down-conversion.

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[2] Martin Esmann, Stephen C. Wein, and Carlos Antón‐Solanas, "Solid‐State Single‐Photon Sources: Recent Advances for Novel Quantum Materials", Advanced Functional Materials 2315936 (2024).

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