Realization of quantum Wheeler's delayed-choice experiment

Journal name:
Nature Photonics
Year published:
Published online


Light is believed to exhibit wave–particle duality1 depending on the detecting devices, according to Bohr's complementarity principle2, as has been demonstrated by the ‘delayed-choice experiment’ with classical detecting devices3, 4, 5, 6, 7, 8, 9. A recent proposal10 suggests that the detecting device can also occupy a quantum state, and a quantum version of the delayed-choice experiment can be performed. Here, we experimentally realize the quantum delayed-choice experiment and observe the wave–particle morphing phenomenon of a single photon. We also illustrate, for the first time, the behaviour of the quantum wave–particle superposition state of a single photon. We find that the quantum wave–particle superposition state is distinct from the classical mixture state because of quantum interference between the wave and particle states. Our work reveals the deep relationship between the complementarity principle and the superposition principle, and it may be helpful in furthering understanding of the behaviour of light.

At a glance


  1. Logic diagrams of the classical and quantum delayed-choice experiments.
    Figure 1: Logic diagrams of the classical and quantum delayed-choice experiments.

    a,b, The classical (a) and quantum (b) experiments. The first H (Hadamard) gate corresponds to the splitting of the two paths, after which a ϕ phase is added. The second H gate corresponds to the detecting device, which is controlled by an ancilla. The set-ups differ in the following way. In a, the ancilla |polright fence = sin α|Vright fence + cos α|Hright fence is first detected on the basis of {|Hright fence,|Vright fence}to generate a series of random numbers, p, and these numbers are used to control the second H gate. In b, the ancilla |polright fence is directly used to control the second H gate, placing the gate in a quantum-superposition state of producing and not producing interference fringes. QRNG represents a quantum random number generator.

  2. Experimental set-up.
    Figure 2: Experimental set-up.

    The set-up includes four parts: single photons generated by the SAQD (not shown), the opened (closed) MZI (quartz, BD1, BD3, HWP1 (HWP2), BD4), the quantum-control apparatus (α, BD2, particle layer, wave layer, BD5), and the detection apparatus (movable polarizer, APDs and the counter and time analyser, which are not shown). Note: the arrows are used to represent the photon polarizations, and the HWPs are not shown; ‘Layer’ in the lower figure represents a detailed sketch of the particle and wave layers.

  3. Probabilities of finding a photon in path 1.
    Figure 3: Probabilities of finding a photon in path 1.

    From a to h, α = jπ/8 (j = 0 to 7). The red symbols are the results of the classical wave–particle mixture, and the blue symbols the quantum superposition. The lines show the corresponding theoretical fit.

  4. Three quantities (centre, visibility and ratio) derived from Fig. 3.
    Figure 4: Three quantities (centre, visibility and ratio) derived from Fig. 3.

    a, ‘Centre’ is the average of the maximum and minimum probabilities. b, ‘Visibility’ is the ratio of the oscillation amplitude to the sum of the maximum and minimum probabilities. c, ‘Ratio’ indicates the ratio of the rise period to the total period. The larger symbols are experimental results and the smaller symbols the theoretical simulation results.


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  1. Key Laboratory of Quantum Information, University of Science and Technology of China, CAS, Hefei, 230026, China

    • Jian-Shun Tang,
    • Yu-Long Li,
    • Xiao-Ye Xu,
    • Guo-Yong Xiang,
    • Chuan-Feng Li &
    • Guang-Can Guo


C-F.L. and J-S.T. planned and designed the experiments. J-S.T., Y-L.L. and G-Y.X. implemented the experiments. G-C.G., J-S.T. and X-Y.X. carried out the theoretical analysis and developed the interpretation. C-F.L. and J-S.T. wrote the paper and all authors discussed its contents. C-F.L. supervised the project.

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