Wheeler's delayed-choice gedanken experiment with a single atom

Journal name:
Nature Physics
Year published:
Published online
Corrected online

The wave–particle dual nature of light and matter and the fact that the choice of measurement determines which one of these two seemingly incompatible behaviours we observe are examples of the counterintuitive features of quantum mechanics. They are illustrated by Wheelers famous ‘delayed-choice experiment1, recently demonstrated in a single-photon experiment2. Here, we use a single ultracold metastable helium atom in a Mach–Zehnder interferometer to create an atomic analogue of Wheelers original proposal. Our experiment confirms Bohrs view that it does not make sense to ascribe the wave or particle behaviour to a massive particle before the measurement takes place1. This result is encouraging for current work towards entanglement and Bells theorem tests in macroscopic systems of massive particles3.

At a glance


  1. Schematics of Wheeler[rsquor]s delayed-choice experiments.
    Figure 1: Schematics of Wheelers delayed-choice experiments.

    a, Optical version of Wheelers delayed-choice experiment. b, Atomic version of Wheelers experiment, where the physical beamsplitters and mirrors are now replaced with optical Bragg pulses. A quantum random number generator (QRNG) is used to decide whether the last beamsplitting pulse is either implemented or not. The random number is triggered and chosen after the π-pulse (mirror pulse), thereby ensuring that the atom has no prior knowledge of how it will be detected when it enters the interferometer.

  2. Spatial and temporal locations of the output ports of the interferometer, showing the well-resolved detection locations.
    Figure 2: Spatial and temporal locations of the output ports of the interferometer, showing the well-resolved detection locations.

    Blue data represent the counts observed at the |0right fence output port, whereas red data represent the |1right fence port. The atoms reaching port |1right fence arrive at a slightly latter time than those in port |0right fence due to the momentum kick they receive from the Bragg pulses.

  3. Wheeler[rsquor]s delayed-choice experiment with massive bodies.
    Figure 3: Wheelers delayed-choice experiment with massive bodies.

    Blue squares represent the open configuration and red dots represent the closed configuration of the interferometer. The inset shows the result when a large number of atoms ~1,000 are used, in such case the error bars (1 s.d.) are smaller than the data symbols used. The result shown in the main figure is produced using a single atom, with each point being the cumulative result of a few thousand runs of the experiment and the error bars representing the statistical spread of the data. The solid lines are fits to the data, with the closed configuration fitting well to a sinusoidal form with a visibility of 0.98 ± 0.05. A linear fit to the open configuration has a slight slope due to imperfections in our Bragg pulses.

  4. Second-order correlation function of atoms arriving at the output ports of our interferometer as a function of the delay between experimental runs.
    Figure 4: Second-order correlation function of atoms arriving at the output ports of our interferometer as a function of the delay between experimental runs.

    Here the delay is in units of the cycle time of the experiment, where tcycle = 35 s.

Change history

Corrected online 03 June 2015
In the version of this Letter originally published, a sentence in the text describing the points in Fig. 3 was incorrect and should have read: 'The distinction between the removal (blue points) and application (red points) of the mixing π/2 pulse is very clear, as the former is ~50% irrespective of the phase ϕ, while the latter shows the expected sinusoidal dependence on ϕ, typical of a Mach–Zehnder interferometer.' This has now been corrected in all versions of the Letter.


  1. Wheeler, J. A. in Mathematical Foundations of Quantum Theory (ed Marlow, A. R.) (Academic Press, 1978).
  2. Jacques, V. et al. Experimental realization of Wheelers delayed-choice gedanken experiment. Science 315, 966968 (2007).
  3. Bell, J. S. Speakable and Unspeakable in Quantum Mechanics (Cambridge Univ. Press, 1987).
  4. de Broglie, L. Recherches sur la théorie des quanta. Ann. de Phys. 3, 22128 (1925).
  5. Davisson, C. & Germer, L. H. Diffraction of electrons by a crystal of nickel. Phys. Rev. 30, 705740 (1927).
  6. Englert, B-G. Fringe visibility and which-way information: An inequality. Phys. Rev. Lett. 77, 21542157 (1996).
  7. Ma, X., Kofler, J. & Zeilinger, A. Delayed-choice gedanken experiments and their realizations. Preprint at http://arxiv.org/abs/1407.2930v1 (2014).
  8. Hellmuth, T., Walther, H., Zajonc, A. & Schleich, W. Delayed-choice experiments in quantum interference. Phys. Rev. A 35, 25322541 (1987).
  9. Alley, C. O., Jacubowicz, O. G. & Wickes, W. C. in Proceedings of the Second International Symposium on the Foundations of Quantum Mechanics (ed Narani, H.) 3647 (Physics Society of Japan, 1987).
  10. Baldzuhn, J., Mohler, E. & Martienssen, W. A wave-particle delayed-choice experiment with a single-photon state. Z. Phys. 77, 347352 (1989).
  11. Kim, Y-H., Yu, R., Kulik, S. P., Shih, Y. & Scully, M. O. Delayed “choice quantum eraser. Phys. Rev. Lett. 84, 15 (2000).
  12. Ma, X-s. et al. Experimental delayed-choice entanglement swapping. Nature Phys. 8, 479484 (2012).
  13. Andrews, M. R. et al. Observation of interference between two Bose condensates. Science 275, 637641 (1997).
  14. Lawson-Daku, B. J. et al. Delayed choices in atom Stern–Gerlach interferometry. Phys. Rev. A 54, 50425047 (1996).
  15. Kawai, T. et al. Realization of a delayed choice experiment using a multilayer cold neutron pulser. Nucl. Instrum. Methods Phys. Res. A 410, 259263 (1998).
  16. Manning, A. G., Khakimov, R., Dall, R. G. & Truscott, A. G. A single atom source in the picokelvin regime. Phys. Rev. Lett. 113, 130403 (2014).
  17. Martin, P. J., Oldaker, B. G., Miklich, A. H. & Pritchard, D. E. Bragg scattering of atoms from a standing light wave. Phys. Rev. Lett. 60, 515518 (1988).
  18. Cronin, A., Schmiedmayer, J. & Pritchard, D. Optics and interferometry with atoms and molecules. Rev. Mod. Phys. 81, 10511129 (2009).
  19. Vassen, W. et al. Cold and trapped metastable noble gases. Rev. Mod. Phys. 84, 175210 (2012).
  20. Grangier, P., Roger, G. & Aspect, A. Experimental evidence for a photon anticorrelation effect on a beam splitter: A new light on single-photon interferences. Europhys. Lett. 1, 173179 (1986).
  21. Durr, S., Nonn, T. & Rempe, G. Fringe visibility and which-way information in an atom interferometer. Phys. Rev. Lett. 81, 57055709 (1998).
  22. Schwindt, P. D., Kwiat, P. G. & Englert, B-G. Quantitative wave-particle duality and nonerasing quantum erasure. Phys. Rev. A 60, 42854290 (1999).
  23. Jaeger, G., Shimony, A. & Vaidman, L. Two interferometric complementarities. Phys. Rev. A 51, 5467 (1995).
  24. Jacques, V. et al. Delayed-choice test of quantum complementarity with interfering single photons. Phys. Rev. Lett. 100, 220402 (2008).
  25. Dall, R. G. et al. Observation of atomic speckle and Hanbury Brown–Twiss correlations in guided matter waves. Nature Commun. 2, 291 (2011).
  26. Dall, R. G. et al. Ideal n-body correlations with massive particles. Nature Phys. 9, 341344 (2013).
  27. Dall, R. G. & Truscott, A. G. Bose–Einstein condensation of metastable helium in a bi-planar quadrupole Ioffe configuration trap. Opt. Commun. 270, 255261 (2007).
  28. Dedman, C. J., Dall, R. G., Byron, L. J. & Truscott, A. G. Active cancellation of stray magnetic fields in a Bose–Einstein condensation experiment. Rev. Sci. Instrum. 78, 024703 (2007).
  29. Shlyapnikov, G. V., Walraven, J. T. M., Rahmanov, U. M. & Reynolds, M. W. Decay kinetics and Bose condensation in a gas of spin-polarized triplet helium. Phys. Rev. Lett. 73, 32473250 (1994).
  30. Hodgman, S. S. et al. Metastable helium: A new determination of the longest atomic excited-state lifetime. Phys. Rev. Lett. 103, 053002 (2009).

Download references

Author information


  1. Research School of Physics and Engineering, Australian National University, Canberra ACT 0200, Australia

    • A. G. Manning,
    • R. I. Khakimov,
    • R. G. Dall &
    • A. G. Truscott


A.G.M., R.G.D. and A.G.T. conceived the experiment. A.G.M. and R.I.K. performed the experiment and R.I.K. collected the data presented in this Letter. All authors contributed to the conceptual formulation of the physics, the interpretation of the data and writing the manuscript.

Competing financial interests

The authors declare no competing financial interests.

Corresponding author

Correspondence to:

Author details

Additional data