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.
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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.
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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.
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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.
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Supplementary Information
Supplementary Figs. 1–5 and discussion.
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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
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DOI: https://doi.org/10.1038/s41566-021-00818-7
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