Skip to main content

Thank you for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

Boson bunching is not maximized by indistinguishable particles

Nature Photonics volume 17, pages 702–709 (2023)Cite this article

Subjects

Abstract

Boson bunching is among the most remarkable features of quantum physics. A celebrated example in optics is the Hong–Ou–Mandel effect, where the bunching of two photons arises from a destructive quantum interference between the trajectories where they both either cross a beamsplitter or are reflected. This effect takes its roots in the indistinguishability of identical photons. Hence, it is generally admitted—and experimentally verified—that bunching vanishes as soon as photons can be distinguished, for example, when they occupy distinct time bins or have different polarizations. Here we disprove this alleged straightforward link between indistinguishability and bunching by exploiting a recent finding in the theory of matrix permanents. We exhibit a family of optical circuits such that the bunching of photons into two modes can be substantially boosted by making them partially distinguishable via an appropriate polarization pattern. This boosting effect is already visible in a seven-photon interferometric process, making the observation of this phenomenon within reach of current photonic technology. This unexpected behaviour questions our understanding of multiparticle interference in the grey zone between indistinguishable bosons and classical particles.

This is a preview of subscription content, access via your institution

Access options

Rent or buy this article

Prices vary by article type

from$1.95

to$39.95

Learn more

Prices may be subject to local taxes which are calculated during checkout

Fig. 1: Interferometric set-up.
Fig. 2: Boosted two-mode bunching.
Fig. 3: Photon-number distribution at the output of the circuit achieving boosted two-mode bunching.
Fig. 4: Perturbation effects on boosted two-mode bunching.
Fig. 5: Mechanism at the origin of boosted bunching.
Fig. 6: Bunching violation ratio Rn as a function of n.

Similar content being viewed by others

Data availability

The data supporting the study and figures are available upon request. We acknowledge A. Franzen’s ComponentLibrary for use in making the figures.

Code availability

The project relies on the packages PERMANENTS.JL (https://github.com/benoitseron/Permanents.jl) and BOSONSAMPLING.JL (https://github.com/benoitseron/BosonSampling.jl)48. The source code used for generating the figures and the data of this paper is available on GitHub and the data from OSF (https://osf.io/ex63z/).

References

  1. Wootters, W. K. & Zurek, W. H. Complementarity in the double-slit experiment: quantum nonseparability and a quantitative statement of Bohr’s principle. Phys. Rev. D 19, 473–484 (1979).

    Article  Google Scholar 

  2. Greenberger, D. M. & Yasin, A. Simultaneous wave and particle knowledge in a neutron interferometer. Phys. Lett. A 128, 391–394 (1988).

    Article  ADS  Google Scholar 

  3. Mandel, L. Coherence and indistinguishability. Opt. Lett. 16, 1882–1883 (1991).

    Article  ADS  Google Scholar 

  4. Feynman, R. P., Leighton, R. B. & Sands, M. The Feynman Lectures on Physics (Addison-Wesley, 1963).

  5. Hong, C.-K., Ou, Z.-Y. & Mandel, L. Measurement of subpicosecond time intervals between two photons by interference. Phys. Rev. Lett. 59, 2044–2046 (1987).

    Article  ADS  Google Scholar 

  6. Gerry, C., Knight, P. & Knight, P. L. Introductory Quantum Optics (Cambridge Univ. Press, 2005).

  7. Spagnolo, N. et al. General rules for bosonic bunching in multimode interferometers. Phys. Rev. Lett. 111, 130503 (2013).

    Article  ADS  Google Scholar 

  8. Shchesnovich, V. Universality of generalized bunching and efficient assessment of boson sampling. Phys. Rev. Lett. 116, 123601 (2016).

    Article  ADS  Google Scholar 

  9. Carolan, J. et al. On the experimental verification of quantum complexity in linear optics. Nat. Photon. 8, 621–626 (2014).

    Article  ADS  Google Scholar 

  10. Bapat, R. B. & Sunder, V. S. On majorization and Schur products. Linear Algebra Appl. 72, 107–117 (1985).

    Article  MathSciNet  MATH  Google Scholar 

  11. Drury, S. A counterexample to a question of Bapat and Sunder. Electron. J. Linear Algebra 31, 69–70 (2016).

    Article  MathSciNet  MATH  Google Scholar 

  12. Shchesnovich, V. S. The permanent-on-top conjecture is false. Linear Algebra Appl. 490, 196–201 (2016).

    Article  MathSciNet  MATH  Google Scholar 

  13. Tichy, M. C. Sampling of partially distinguishable bosons and the relation to the multidimensional permanent. Phys. Rev. A 91, 022316 (2015).

    Article  ADS  Google Scholar 

  14. Shchesnovich, V. Partial indistinguishability theory for multiphoton experiments in multiport devices. Phys. Rev. A 91, 013844 (2015).

    Article  ADS  MathSciNet  Google Scholar 

  15. Dittel, C. et al. Totally destructive interference for permutation-symmetric many-particle states. Phys. Rev. A 97, 062116 (2018).

    Article  ADS  Google Scholar 

  16. Zhang, F. Matrix Theory: Basic Results and Techniques (Springer, 2011).

  17. Shchesnovich, V. Tight bound on the trace distance between a realistic device with partially indistinguishable bosons and the ideal bosonsampling. Phys. Rev. A 91, 063842 (2015).

    Article  ADS  MathSciNet  Google Scholar 

  18. Schur, I. Über endliche Gruppen und hermitesche Formen. Math. Zeitschrift 1, 184–207 (1918).

    Article  MathSciNet  MATH  Google Scholar 

  19. Oppenheim, A. Inequalities connected with definite hermitian forms. J. Lond. Math. Soc. 1, 114–119 (1930).

  20. Gloub, G. H. & Van Loan, C. F. Matrix Computations 3rd edn (Johns Hopkins Univ. Press, 1996).

  21. Flamini, F., Spagnolo, N. & Sciarrino, F. Photonic quantum information processing: a review. Rep. Prog. Phys. 82, 016001 (2018).

    Article  ADS  Google Scholar 

  22. Pelucchi, E. et al. The potential and global outlook of integrated photonics for quantum technologies. Nat. Rev. Phys 4, 194–208 (2021).

    Article  Google Scholar 

  23. Wang, H. et al. Toward scalable boson sampling with photon loss. Phys. Rev. Lett. 120, 230502 (2018).

    Article  ADS  Google Scholar 

  24. Wang, H. et al. Boson sampling with 20 input photons and a 60-mode interferometer in a 1014-dimensional Hilbert space. Phys. Rev. Lett. 123, 250503 (2019).

    Article  ADS  Google Scholar 

  25. Wang, J., Sciarrino, F., Laing, A. & Thompson, M. G. Integrated photonic quantum technologies. Nat. Photon. 14, 273–284 (2020).

    Article  ADS  Google Scholar 

  26. Hoch, F. et al. Reconfigurable continuously-coupled 3D photonic circuit for Boson Sampling experiments. npj Quantum Inf. 8, 55 (2022).

  27. Carolan, J. et al. Universal linear optics. Science 349, 711–716 (2015).

    Article  MathSciNet  MATH  Google Scholar 

  28. Crespi, A. et al. Suppression law of quantum states in a 3D photonic fast Fourier transform chip. Nat. Commun. 7, 10469 (2016).

    Article  ADS  Google Scholar 

  29. Jönsson, M. & Björk, G. Evaluating the performance of photon-number-resolving detectors. Phys. Rev. A 99, 043822 (2019).

    Article  ADS  Google Scholar 

  30. Provazník, J., Lachman, L., Filip, R. & Marek, P. Benchmarking photon number resolving detectors. Opt. Express 28, 14839–14849 (2020).

    Article  ADS  Google Scholar 

  31. Cheng, R. et al. A 100-pixel photon-number-resolving detector unveiling photon statistics. Nat. Photon. 17, 112–119 (2023).

  32. Pryde, G. J. & White, A. G. Creation of maximally entangled photon-number states using optical fiber multiports. Phys. Rev. A 68, 052315 (2003).

    Article  ADS  Google Scholar 

  33. Tichy, M. C. et al. Four-photon indistinguishability transition. Phys. Rev. A 83, 062111 (2011).

    Article  ADS  Google Scholar 

  34. Ra, Y.-S. et al. Nonmonotonic quantum-to-classical transition in multiparticle interference. Proc. Natl Acad. Sci. USA 110, 1227–1231 (2013).

    Article  ADS  Google Scholar 

  35. Tichy, M. C. Interference of identical particles from entanglement to boson-sampling. J. Phys. B 47, 103001 (2014).

  36. Tillmann, M. et al. Generalized multiphoton quantum interference. Phys. Rev. X 5, 041015 (2015).

    Google Scholar 

  37. Turner, P. S. Postselective quantum interference of distinguishable particles. Preprint at https://arxiv.org/abs/1608.05720 (2016).

  38. Jones, A. E. et al. Multiparticle interference of pairwise distinguishable photons. Phys. Rev. Lett. 125, 123603 (2020).

    Article  ADS  Google Scholar 

  39. Menssen, A. J. et al. Distinguishability and many-particle interference. Phys. Rev. Lett. 118, 153603 (2017).

    Article  ADS  Google Scholar 

  40. Shchesnovich, V. & Bezerra, M. Collective phases of identical particles interfering on linear multiports. Phys. Rev. A 98, 033805 (2018).

    Article  ADS  Google Scholar 

  41. Jones, A. E. Distinguishability in Quantum Interference. PhD thesis, Imperial College London (2019).

  42. Zhang, F. An update on a few permanent conjectures. Special Matrices 4, 305–316 (2016).

    Article  MathSciNet  MATH  Google Scholar 

  43. Drury, S. et al. A real counterexample to two inequalities involving permanents. Math. Inequalities Appl. 20, 349–352 (2017).

  44. Clements, W. R., Humphreys, P. C., Metcalf, B. J., Kolthammer, W. S. & Walmsley, I. A. Optimal design for universal multiport interferometers. Optica 3, 1460–1465 (2016).

    Article  ADS  Google Scholar 

  45. Tichy, M. C., Tiersch, M., de Melo, F., Mintert, F. & Buchleitner, A. Zero-transmission law for multiport beam splitters. Phys. Rev. Lett. 104, 220405 (2010).

    Article  ADS  Google Scholar 

  46. Zhang, F. Notes on Hadamard products of matrices. Linear Multilinear Algebra 25, 237–242 (1989).

    Article  MathSciNet  MATH  Google Scholar 

  47. Aaronson, S. & Arkhipov, A. The computational complexity of linear optics. In Proc. Forty-Third Annual ACM Symposium on Theory of Computing 333–342 (ACM, 2011).

  48. Seron, B. & Restivo, A. BosonSampling.jl: a Julia package for quantum multi-photon interferometry. Preprint at https://arxiv.org/abs/2212.09537 (2022).

Download references

Acknowledgements

We thank S. Drury for useful correspondence, as well as F. Flamini and V. Shchesnovich for valuable discussions. B.S. is a Research Fellow and L.N. was a Postdoctoral Researcher of the Fonds de la Recherche Scientifique – FNRS (Belgium). N.J.C. acknowledges support from the Fonds de la Recherche Scientifique – FNRS (Belgium) under grant no. T.0224.18 and by the European Union under project ShoQC within ERA-NET Cofund in Quantum Technologies (QuantERA) programme. L.N. also acknowledges funding from FCT-Fundação para a Ciência e a Tecnologia (Portugal) via project no. CEECINST/00062/2018. This project has also received funding from the European Union’s Horizon 2020 research and innovation programme under Marie Skłodowska-Curie grant agreement no. 956071.

Author information

Authors and Affiliations

  1. Centre for Quantum Information and Communication, Ecole polytechnique de Bruxelles, Université libre de Bruxelles, Brussels, Belgium

    Benoit Seron, Leonardo Novo & Nicolas J. Cerf

  2. International Iberian Nanotechnology Laboratory (INL), Braga, Portugal

    Leonardo Novo

Authors
  1. Benoit Seron
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Leonardo Novo
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Nicolas J. Cerf
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

All authors developed the original concepts, derived the formulae, discussed the results and wrote the paper. B.S. implemented the numerical simulations.

Corresponding author

Correspondence to Nicolas J. Cerf.

Ethics declarations

Competing interests

The authors declare no competing interests.

Peer review

Peer review information

Nature Photonics thanks Lorenzo Marrucci and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

Additional information

Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Supplementary information

Supplementary Information

Supplementary information including one figure.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and Permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Seron, B., Novo, L. & Cerf, N.J. Boson bunching is not maximized by indistinguishable particles. Nat. Photon. 17, 702–709 (2023). https://doi.org/10.1038/s41566-023-01213-0

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1038/s41566-023-01213-0

This article is cited by

Search

Advanced search

Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing