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

Abstract

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.

► References

[1] M. D. Eisaman, J. Fan, A. Migdall, and S. V. Polyakov. Invited review article: Single-photon sources and detectors. Review of Scientific Instruments, 82 (7): 071101, 2011. 10.1063/​1.3610677.
https:/​/​doi.org/​10.1063/​1.3610677

[2] Sarah Thomas and Pascale Senellart. The race for the ideal single-photon source is on. Nature Nanotechnology, 16 (4): 367–368, 2021. 10.1038/​s41565-021-00851-1.
https:/​/​doi.org/​10.1038/​s41565-021-00851-1

[3] Nicolas Sangouard and Hugo Zbinden. What are single photons good for? Journal of Modern Optics, 59 (17): 1458–1464, 2012. 10.1080/​09500340.2012.687500.
https:/​/​doi.org/​10.1080/​09500340.2012.687500

[4] Pieter Kok, W. J. Munro, Kae Nemoto, T. C. Ralph, Jonathan P. Dowling, and G. J. Milburn. Linear optical quantum computing with photonic qubits. Rev. Mod. Phys., 79: 135–174, Jan 2007. 10.1103/​RevModPhys.79.135.
https:/​/​doi.org/​10.1103/​RevModPhys.79.135

[5] Christopher J. Chunnilall, Ivo Pietro Degiovanni, Stefan Kück, Ingmar Müller, and Alastair G. Sinclair. Metrology of single-photon sources and detectors: a review. Optical Engineering, 53 (8): 081910–081910, July 2014. 10.1117/​1.oe.53.8.081910.
https:/​/​doi.org/​10.1117/​1.oe.53.8.081910

[6] Stefan Kück. Single photon sources for absolute radiometry – a review about the current state of the art. Measurement: Sensors, 18: 100219, 2021. ISSN 2665-9174. 10.1016/​j.measen.2021.100219.
https:/​/​doi.org/​10.1016/​j.measen.2021.100219

[7] D. F. Walls and Gerard J. Milburn. Quantum Optics. Springer, Berlin, Heidelberg, 2 edition, 2008. ISBN 978-3-540-28574-8. 10.1007/​978-3-540-28574-8.
https:/​/​doi.org/​10.1007/​978-3-540-28574-8

[8] Miroslav Ježek, Ivo Straka, Michal Mičuda, Miloslav Dušek, Jaromír Fiurášek, and Radim Filip. Experimental test of the quantum non-gaussian character of a heralded single-photon state. Phys. Rev. Lett., 107: 213602, Nov 2011. 10.1103/​PhysRevLett.107.213602.
https:/​/​doi.org/​10.1103/​PhysRevLett.107.213602

[9] Ana Predojević, Miroslav Ježek, Tobias Huber, Harishankar Jayakumar, Thomas Kauten, Glenn S. Solomon, Radim Filip, and Gregor Weihs. Efficiency vs. multi-photon contribution test for quantum dots. Opt. Express, 2014. 10.1364/​OE.22.004789.
https:/​/​doi.org/​10.1364/​OE.22.004789

[10] Ivo Straka, Ana Predojević, Tobias Huber, LukášLachman, Lorenz Butschek, Martina Miková, Michal Mičuda, Glenn S. Solomon, Gregor Weihs, Miroslav Ježek, and Radim Filip. Quantum non-gaussian depth of single-photon states. Phys. Rev. Lett., 113: 223603, Nov 2014. 10.1103/​PhysRevLett.113.223603.
https:/​/​doi.org/​10.1103/​PhysRevLett.113.223603

[11] Anatole Kenfack and Karol Życzkowski. Negativity of the wigner function as an indicator of non-classicality. Journal of Optics B: Quantum and Semiclassical Optics, 6 (10): 396, 2004. 10.1088/​1464-4266/​6/​10/​003.
https:/​/​doi.org/​10.1088/​1464-4266/​6/​10/​003

[12] Alan Migdall, Sergey V Polyakov, Jingyun Fan, and Joshua C Bienfang. Single-photon generation and detection: physics and applications. Academic Press, 2013. ISBN 978-0-12-387695-9.

[13] Katiúscia N Cassemiro, Kaisa Laiho, and Christine Silberhorn. Accessing the purity of a single photon by the width of the hong–ou–mandel interference. New Journal of Physics, 12 (11): 113052, 2010. 10.1088/​1367-2630/​12/​11/​113052.
https:/​/​doi.org/​10.1088/​1367-2630/​12/​11/​113052

[14] Kevin Zielnicki, Karina Garay-Palmett, Daniel Cruz-Delgado, Hector Cruz-Ramirez, Michael F. O'Boyle, Bin Fang, Virginia O. Lorenz, Alfred B. U'Ren, and Paul G. Kwiat. Joint spectral characterization of photon-pair sources. Journal of Modern Optics, 65 (10): 1141–1160, Jun 2018. 10.1080/​09500340.2018.1437228.
https:/​/​doi.org/​10.1080/​09500340.2018.1437228

[15] Wassily Hoeffding. Probability Inequalities for Sums of Bounded Random Variables. Journal of the American Statistical Association, 58 (301): 13–30, mar 1963. 10.1080/​01621459.1963.10500830.
https:/​/​doi.org/​10.1080/​01621459.1963.10500830

[16] E. Wigner. On the quantum correction for thermodynamic equilibrium. Phys. Rev., 40: 749–759, Jun 1932. 10.1103/​PhysRev.40.749.
https:/​/​doi.org/​10.1103/​PhysRev.40.749

[17] Werner Vogel and Dirk-Gunnar Welsch. Quantum optics. John Wiley & Sons, 2006. 10.1002/​3527608524.
https:/​/​doi.org/​10.1002/​3527608524

[18] R. L. Hudson. When is the wigner quasi-probability density non-negative? Reports on Mathematical Physics, 6 (2): 249–252, 1974. ISSN 0034-4877. 10.1016/​0034-4877(74)90007-X.
https:/​/​doi.org/​10.1016/​0034-4877(74)90007-X

[19] U. Chabaud, PE. Emeriau, and F. Grosshans. Witnessing wigner negativity. Quantum, 471: 230503, Jun 2021. 10.22331/​q-2021-06-08-471.
https:/​/​doi.org/​10.22331/​q-2021-06-08-471

[20] Antoine Royer. Wigner function as the expectation value of a parity operator. Phys. Rev. A, 15: 449–450, Feb 1977. 10.1103/​PhysRevA.15.449.
https:/​/​doi.org/​10.1103/​PhysRevA.15.449

[21] F. W. J. Olver, A. B. Olde Daalhuis, D. W. Lozier, B. I. Schneider, R. F. Boisvert, C. W. Clark, B. R. Miller, B. V. Saunders, H. S. Cohl, M. A. McClain, and eds. Nist digital library of mathematical functions. http:/​/​dlmf.nist.gov/​, Release 1.1.3 of 2021-09-15.
http:/​/​dlmf.nist.gov/​

[22] M. Munroe, D. Boggavarapu, M. E. Anderson, and M. G. Raymer. Photon-number statistics from the phase-averaged quadrature-field distribution: Theory and ultrafast measurement. Phys. Rev. A, 52: R924–R927, Aug 1995. 10.1103/​PhysRevA.52.R924.
https:/​/​doi.org/​10.1103/​PhysRevA.52.R924

[23] N. Bruno, A. Martin, T. Guerreiro, B. Sanguinetti, and R. T. Thew. Pulsed source of spectrally uncorrelated and indistinguishable photons at telecom wavelengths. Optics Express, 22 (14): 17246, jul 2014. 10.1364/​OE.22.017246.
https:/​/​doi.org/​10.1364/​OE.22.017246

[24] T. Guerreiro, A. Martin, B. Sanguinetti, N. Bruno, H. Zbinden, and R. T. Thew. High efficiency coupling of photon pairs in practice. Optics Express, 21 (23): 27641, nov 2013. 10.1364/​OE.21.027641.
https:/​/​doi.org/​10.1364/​OE.21.027641

[25] Misael Caloz, Matthieu Perrenoud, Claire Autebert, Boris Korzh, Markus Weiss, Christian Schönenberger, Richard J. Warburton, Hugo Zbinden, and Félix Bussières. High-detection efficiency and low-timing jitter with amorphous superconducting nanowire single-photon detectors. Applied Physics Letters, 112 (6), 2018. 10.1063/​1.5010102.
https:/​/​doi.org/​10.1063/​1.5010102

[26] P. Sekatski, E. Oudot, P. Caspar, R.T. Thew, and N. Sangouard. Benchmarking single-photon sources from an auto-correlation measurement [data set]. 2022. 10.5281/​zenodo.7245446.
https:/​/​doi.org/​10.5281/​zenodo.7245446

[27] Marlan O Scully and M Suhail Zubairy. Quantum optics. American Association of Physics Teachers, 1999. 10.1017/​CBO9780511813993.
https:/​/​doi.org/​10.1017/​CBO9780511813993

[28] Pavel Sekatski, N Sangouard, Félix Bussieres, Christoph Clausen, Nicolas Gisin, and Hugo Zbinden. Detector imperfections in photon-pair source characterization. Journal of Physics B: Atomic, Molecular and Optical Physics, 45 (12): 124016, 2012. 10.1088/​0953-4075/​45/​12/​124016.
https:/​/​doi.org/​10.1088/​0953-4075/​45/​12/​124016

[29] A. Dodel, A. Mayinda, E. Oudot, A. Martin, P. Sekatski, J.-D. Bancal, and N. Sangouard. Proposal for witnessing non-classical light with the human eye. Quantum, 1: 7, April 2017. ISSN 2521-327X. 10.22331/​q-2017-04-25-7.
https:/​/​doi.org/​10.22331/​q-2017-04-25-7

Cited by

On Crossref's cited-by service no data on citing works was found (last attempt 2023-02-07 15:19:49). On SAO/NASA ADS no data on citing works was found (last attempt 2023-02-07 15:19:50).