Quantum wave–particle superposition in a delayed-choice experiment


Wave–particle duality epitomizes the counterintuitive character of quantum physics. A striking illustration is the quantum delayed-choice experiment, which is based on Wheeler’s classic delayed-choice gedanken experiment, but with the addition of a quantum-controlled device enabling wave-to-particle transitions. Here, we realize a quantum delayed-choice experiment in which we control the wave and the particle states of photons and particularly the phase between them, thus directly establishing the created quantum nature of the wave–particle. We generate three-photon entangled states and inject one photon into a Mach–Zehnder interferometer embedded in a 186-m-long two-photon Hong–Ou–Mandel interferometer. The third photon is sent 141 m away from the interferometers and remotely prepares a two-photon quantum gate according to independent active choices under Einstein locality conditions. We realize transitions between wave and particle states in both classical and quantum scenarios, and therefore tests of the complementarity principle that go fundamentally beyond earlier implementations.

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Fig. 1: The evolution of delayed-choice experiments.
Fig. 2: Experimental configuration.
Fig. 3: Continuous transitions between particle and wave states in both classical and quantum scenarios.
Fig. 4: Witnessing the wave–particle quantum superpositions.

Data availability

The data that support the plots within this paper and other findings of this study are available from the corresponding author upon reasonable request.


  1. 1.

    Bohr, N. The quantum postulate and the recent development of atomic theory. Nature 121, 580–590 (1928).

  2. 2.

    Wheeler, J. A. in Mathematical Foundations of Quantum Theory (ed. Marlow, A. R.) 9–48 (Academic Press, 1978).

  3. 3.

    Wheeler, J. A. & Zurek, W. H. Quantum Theory and Measurement (Princeton University Press, 1984).

  4. 4.

    Alley, C. O., Jakubowicz, O. G. & Wickes, W. C. Results of the delayed-random-choice quantum mechanics experiment with light quanta. In Proceedings of the 2nd International Symposium on Foundations of Quantum Mechanics, 36 (Physical Society of Japan, 1986).

  5. 5.

    Hellmuth, T., Walther, H., Zajonc, A. & Schleich, W. Delayed-choice experiments in quantum interference. Phys. Rev. A 35, 2532–2541 (1987).

  6. 6.

    Baldzuhn, J., Mohler, E. & Martienssen, W. A wave–particle delayed-choice experiment with a single-photon state. Z. Phys. B 77, 347–352 (1989).

  7. 7.

    Jacques, V. et al. Experimental realization of Wheeler’s delayed-choice gedanken experiment. Science 315, 966–968 (2007).

  8. 8.

    Manning, A. G., Khakimov, R. I., Dall, R. G. & Truscott, A. G. Wheeler’s delayed-choice gedanken experiment with a single atom. Nat. Phys. 11, 539–542 (2015).

  9. 9.

    Shadbolt, P., Mathews, J. C. F., Laing, A. & O’Brien, J. L. Testing foundations of quantum mechanics with photons. Nat. Phys. 10, 278–286 (2014).

  10. 10.

    Ma, X.-S., Kofler, J. & Zeilinger, A. Delayed-choice gedanken experiments and their realizations. Rev. Mod. Phys. 88, 015005 (2016).

  11. 11.

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

  12. 12.

    Jaeger, G., Shimony, A. & Vaidman, L. Two interferometric complementarities. Phys. Rev. A 51, 54–67 (1995).

  13. 13.

    Englert, B.-G. Fringe visibility and which-way information: an inequality. Phys. Rev. Lett. 77, 2154–2157 (1996).

  14. 14.

    Ionicioiu, R. & Terno, D. R. Proposal for a quantum delayed-choice experiment. Phys. Rev. Lett. 107, 230406 (2011).

  15. 15.

    Scully, M. O. & Drühl, K. Quantum eraser: a proposed photon correlation experiment concerning observation and ‘delayed choice’ in quantum mechanics. Phys. Rev. A 25, 2208–2213 (1982).

  16. 16.

    Coles, P. J., Kaniewski, J. & Wehner, S. Equivalence of wave–particle duality to entropic uncertainty. Nat. Commun. 5, 5814 (2014).

  17. 17.

    Rab, A. S. et al. Entanglement of photons in their dual wave-particle nature. Nat. Commun. 8, 915 (2017).

  18. 18.

    Peruzzo, A., Shadbolt, P., Brunner, N., Popescu, S. & O’Brien, J. L. A quantum delayed-choice experiment. Science 338, 634–637 (2012).

  19. 19.

    Kaiser, F., Coudreau, T., Milman, P., Ostrowsky, D. B. & Tanzilli, S. Entanglement-enabled delayed-choice experiment. Science 338, 637–640 (2012).

  20. 20.

    Tang, J.-S. et al. Realization of quantum Wheeler’s delayed-choice experiment. Nat. Photon. 6, 600–604 (2012).

  21. 21.

    Roy, S. S., Shukla, A. & Mahesh, T. S. NMR implementation of a quantum delayed-choice experiment. Phys. Rev. A 85, 022109 (2012).

  22. 22.

    Auccaise, R. et al. Experimental analysis of the quantum complementarity principle. Phys. Rev. A 85, 032121 (2012).

  23. 23.

    Xin, T., Li, H., Wang, B.-X. & Long, G.-L. Realization of an entanglement-assisted quantum delayed-choice experiment. Phys. Rev. A 92, 022126 (2015).

  24. 24.

    Zheng, S.-B. et al. Quantum delayed-choice experiment with a beam splitter in a quantum superposition. Phys. Rev. Lett. 115, 260403 (2015).

  25. 25.

    Liu, K. et al. A twofold quantum delayed-choice experiment in a superconducting circuit. Sci. Adv. 3, e1603159 (2017).

  26. 26.

    Chaves, R., Lemos, G. B. & Pienaar, J. Causal modeling the delayed-choice experiment. Phys. Rev. Lett. 120, 190401 (2018).

  27. 27.

    Polino, E. et al. Device independent certification of a quantum delayed choice experiment. Preprint at https://arxiv.org/abs/1806.00211 (2018).

  28. 28.

    Huang, H.-L. et al. Compatibility of causal hidden-variable theories with a delayed-choice experiment. Phys. Rev. A 100, 012114 (2019).

  29. 29.

    Yu, S. et al. Realization of a causal-modeled delayed-choice experiment using single photons. Phys. Rev. A 100, 012115 (2019).

  30. 30.

    Ionicioiu, R., Jennewein, T., Mann, R. B. & Terno, D. R. Is wave–particle objectivity compatible with determinism and locality? Nat. Commun. 5, 3997 (2014).

  31. 31.

    Zukowski, M., Zeilinger, A. & Weinfurter, H. Entangling photons radiated by independent pulsed sources. Ann. NY Acad. Sci. 755, 91–102 (1995).

  32. 32.

    Kwiat, P. G. et al. New high-intensity source of polarization-entangled photon pairs. Phys. Rev. Lett. 75, 4337–4341 (1995).

  33. 33.

    Langford, N. K. et al. Demonstration of a simple entangling optical gate and its use in Bell-state analysis. Phys. Rev. Lett. 95, 210504 (2005).

  34. 34.

    Kiesel, N., Schmid, C., Weber, U., Ursin, R. & Weinfurter, H. Linear optics controlled-phase gate made simple. Phys. Rev. Lett. 95, 210505 (2005).

  35. 35.

    Okamoto, R., Hofmann, H. F., Takeuchi, S. & Sasaki, K. Demonstration of an optical quantum controlled-not gate without path interference. Phys. Rev. Lett. 95, 210506 (2005).

  36. 36.

    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).

  37. 37.

    Jacques, V. et al. Delayed-choice test of quantum complementarity with interfering single photons. Phys. Rev. Lett. 100, 220402 (2008).

  38. 38.

    Ma, X.-S. et al. Quantum erasure with causally disconnected choice. Proc. Natl Acad. Sci. USA 110, 1221–1226 (2013).

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We thank J. Kofler and Č. Brukner for helpful discussions, and M. Chen for taking the birds-eye-view photograph of the experiment. This research is supported by the National Key Research and Development Program of China (2017YFA0303700), the National Natural Science Foundation of China (grants nos. 11674170 and 11621091), the National Science Foundation of Jiangsu Province (no. BK20170010), the programme for Innovative Talents and Entrepreneur in Jiangsu and the Fundamental Research Funds for the Central Universities.

Author information

K.W., Q.X. and X.-s.M. designed and performed the experiment. K.W. and X.-s.M. analysed the data. K.W. and X.-s.M. wrote the manuscript with input from all authors. S.Z. and X.-s.M. supervised the project.

Correspondence to Xiao-song Ma.

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