Fig. 1

a Demonstration of the wave-particle duality using a Mach–Zehnder interferometer. A single photon is first split at the input beam-splitter BS₁, then undergoes a phase shift ϕ and finally is observed at detectors D₁ and D₂. The photon behaves as a wave if the output beam-splitter BS₂ is inserted, or as a particle if BS₂ is removed. In quantum delayed-choice experiments, BS₂ is set in a quantum superposition of being present and absent, and consequently, the photon can simultaneously exhibit its wave and particle nature. b Level structure of the driven NV spin in the electronic ground state. Here we have assumed that the Zeeman splitting between the spin states |±1〉 is eliminated by applying an external field. c Schematic representation of a mechanical quantum delayed-choice experiment with an NV electronic spin and two CNTs. The mechanical vibrations of the CNTs are completely decoupled or coherently coupled, depending, respectively, on whether or not the intermediate spin is in the spin state |0〉, with the dc current I_k through the kth CNT, and the distance d_k between the spin and the kth CNT