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.

Direct observation of the particle exchange phase of photons

Abstract

Quantum theory stipulates that if two particles are identical in all physical aspects, the allowed states describing the system are either symmetric or antisymmetric with respect to permutations of single-particle states1,2,3,4,5. Experimentally, the symmetry of the states can be inferred indirectly from the fact that neglecting the correct exchange symmetry in the theoretical analysis leads to dramatic discrepancies with the observations6,7,8,9,10,11,12,13. The only way to directly unveil the symmetry of the states for, say, two identical particles is through the interference of the state itself and its physically permuted version, and measuring the phase associated with the permutation process, the so-called particle exchange phase14. Following this idea, we have observed the exchange phase of indistinguishable photons, providing direct evidence of their bosonic character.

This is a preview of subscription content

Access options

Buy article

Get time limited or full article access on ReadCube.

$32.00

All prices are NET prices.

Fig. 1: Conceptual sketch of the interferometer setup.
Fig. 2: Complete interferometer setup.
Fig. 3: Measurement results.

Data availability

The authors declare that the main data supporting the findings of this study are available within the article and its Supplementary Information. Extra data are available from the corresponding authors upon reasonable request.

Code availability

The code that was used to analyse the experimental data is available from the corresponding authors upon reasonable request.

References

  1. Leinaas, J. M. & Myrheim, J. On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37, 1–23 (1977).

    Article  Google Scholar 

  2. Pauli, W. Über den Zusammenhang des Abschlusses der Elektronengruppen im Atom mit der Komplexstruktur der Spektren. Zeitschrift für Physik 31, 765–783 (1925).

    ADS  Article  Google Scholar 

  3. Davis, K. B. et al. Bose-Einstein condensation in a gas of sodium atoms. Phys. Rev. Lett. 75, 3969–3973 (1995).

    ADS  Article  Google Scholar 

  4. Messiah, A. M. L. & Greenberg, O. W. Symmetrization postulate and its experimental foundation. Phys. Rev. 136, B248–B267 (1964).

    ADS  MathSciNet  Article  Google Scholar 

  5. Sakurai, J. J. & Napolitano, J. Modern Quantum Mechanics 2nd edn (Cambridge Univ. Press, 2017).

  6. Hilborn, R. C. & Yuca, C. L. Spectroscopic test of the symmetrization postulate for spin-0 nuclei. Phys. Rev. Lett. 76, 2844–2847 (1996).

    ADS  Article  Google Scholar 

  7. Modugno, G., Inguscio, M. & Tino, G. M. Search for small violations of the symmetrization postulate for spin-0 particles. Phys. Rev. Lett. 81, 4790–4793 (1998).

    ADS  Article  Google Scholar 

  8. English, D., Yashchuk, V. V. & Budker, D. Spectroscopic test of Bose-Einstein statistics for photons. Phys. Rev. Lett. 104, 253604 (2010).

    ADS  Article  Google Scholar 

  9. Ramberg, E. & Snow, G. A. Experimental limit on a small violation of the Pauli principle. Phys. Lett. B 238, 438–441 (1990).

    ADS  Article  Google Scholar 

  10. de Angelis, M., Gagliardi, G., Gianfrani, L. & Tino, G. M. Test of the symmetrization postulate for spin-0 particles. Phys. Rev. Lett. 76, 2840–2843 (1996).

    ADS  Article  Google Scholar 

  11. DeMille, D., Budker, D., Derr, N. & Deveney, E. Search for exchange-antisymmetric two-photon states. Phys. Rev. Lett. 83, 3978–3981 (1999).

    ADS  Article  Google Scholar 

  12. Ospelkaus, S. et al. Quantum-state controlled chemical reactions of ultracold potassium-rubidium molecules. Science 327, 853–857 (2010).

    ADS  Article  Google Scholar 

  13. Levin, K., Fetter, A. L. & Stamper-Kurn, D. M. Ultracold Bosonic and Fermionic Gases 1st edn (Cambridge Univ. Press, 2012).

  14. Roos, C. F., Alberti, A., Meschede, D., Hauke, P. & Häffner, H. Revealing quantum statistics with a pair of distant atoms. Phys. Rev. Lett. 119, 160401 (2017).

    ADS  Article  Google Scholar 

  15. Walmsley, I. Quantum interference beyond the fringe. Science 358, 1001–1002 (2017).

    ADS  MathSciNet  Article  Google Scholar 

  16. 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).

    ADS  Article  Google Scholar 

  17. Perez-Leija, A. et al. Endurance of quantum coherence due to particle indistinguishability in noisy quantum networks. npj Quant. Info. 4, 45 (2018).

    ADS  Article  Google Scholar 

  18. Nosrati, F., Castellini, A., Compagno, G. & Lo Franco, R. Robust entanglement preparation against noise by controlling spatial indistinguishability. npj Quant. Info. 6, 39 (2020).

    ADS  Article  Google Scholar 

  19. Castellini, A. et al. Indistinguishability-enabled coherence for quantum metrology. Phys. Rev. A 100, 012308 (2019).

    ADS  MathSciNet  Article  Google Scholar 

  20. Sperling, J., Perez-Leija, A., Busch, K. & Walmsley, I. A. Quantum coherences of indistinguishable particles. Phys. Rev. A 96, 032334 (2017).

    ADS  Article  Google Scholar 

  21. LoFranco, R. & Compagno, G. Indistinguishability of elementary systems as a resource for quantum information processing. Phys. Rev. Lett. 120, 240403 (2018).

    ADS  Article  Google Scholar 

  22. Morris, B. et al. Entanglement between identical particles is a useful and consistent resource. Phys. Rev. X 10, 041012 (2020).

    Google Scholar 

  23. Sun, K. et al. Experimental quantum entanglement and teleportation by tuning remote spatial indistinguishability of independent photons. Opt. Lett. 45, 6410–6413 (2020).

    ADS  Article  Google Scholar 

  24. Barros, M. R. et al. Entangling bosons through particle indistinguishability and spatial overlap. Opt. Express 28, 38083–38092 (2020).

    ADS  Article  Google Scholar 

  25. Mirman, R. Experimental meaning of the concept of identical particles. Il Nuovo Cimento B (1971-1996) 18, 110–122 (1973).

    Google Scholar 

  26. Landshoff, P. & Stapp, H. P. Parastatistics and a unified theory of identical particles. Ann. Phys. 45, 72–92 (1967).

    ADS  Article  Google Scholar 

  27. van Enk, S. J. Exchanging identical particles and topological quantum computing. Preprint at https://arxiv.org/abs/1810.05208 (2018).

  28. Peres, A. Quantum Theory: Concepts and Methods 1st edn (Springer, 2002).

  29. Aharonov, Y. & Anandan, J. Phase change during a cyclic quantum evolution. Phys. Rev. Lett. 58, 1593–1596 (1987).

    ADS  MathSciNet  Article  Google Scholar 

  30. Wang, K., Weimann, S., Nolte, S., Perez-Leija, A. & Szameit, A. Measuring the Aharonov-Anandan phase in multiport photonic systems. Opt. Lett. 41, 1889–1892 (2016).

    ADS  Article  Google Scholar 

  31. Altschul, B. Testing photons’ Bose-Einstein statistics with Compton scattering. Phys. Rev. D 82, 101703 (2010).

    ADS  Article  Google Scholar 

  32. Urban, E. et al. Coherent control of the rotational degree of freedom of a two-ion Coulomb crystal. Phys. Rev. Lett. 123, 133202 (2019).

    ADS  Article  Google Scholar 

  33. Matthiesen, C., Yu, Q., Guo, J., Alonso, A. M. & Häffner, H. Trapping electrons in a room-temperature microwave Paul trap. Phys. Rev. X 11, 011019 (2021).

    Google Scholar 

  34. Sinha, U., Couteau, C., Jennewein, T., Laflamme, R. & Weihs, G. Ruling out multi-order interference in quantum mechanics. Science 329, 418–421 (2010).

    ADS  MathSciNet  Article  Google Scholar 

Download references

Acknowledgements

We thank PicoQuant GmbH for providing the MultiHarp 150. C.M. T.K. and O.B. acknowledge support by the German Research Foundation (DFG) Collaborative Research Center (CRC) SFB 787 project C2 and the German Federal Ministry of Education and Research (BMBF) with the project Q.Link.X. Figures 1 and 2 were created with the freely available 3DOptix optical design tool. We thank the 3DOptix-Team, who kindly allowed the use of their software to produce the figures of the article.

Author information

Authors and Affiliations

Authors

Contributions

A.P.-L., K.T., O.B. and K.B. initiated the study and guided the work. K.T., C.M., T.K., M.S. and J.W. designed the interferometer. M.S., C.M. and T.K. set up the interferometer. C.M. and M.S. performed the optical measurements. C.M. and K.T. analysed and interpreted the experimental data. K.T. and A.P.-L. developed the theory. K.T., C.M. and A.P.-L. wrote the manuscript with input from all co-authors.

Corresponding authors

Correspondence to Konrad Tschernig, Chris Müller or Armando Perez-Leija.

Ethics declarations

Competing interests

The authors declare no competing interests.

Additional information

Peer review informationNature Photonics thanks Dmitry Budker and Rosario Lo Franco for their contribution to the peer review of this work.

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

Supplementary information

Supplementary Information

Supplementary Figs. 1–5 and discussion.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Tschernig, K., Müller, C., Smoor, M. et al. Direct observation of the particle exchange phase of photons. Nat. Photon. 15, 671–675 (2021). https://doi.org/10.1038/s41566-021-00818-7

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1038/s41566-021-00818-7

Further reading

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