Quantum wave–particle superposition in a delayed-choice experiment

Abstract

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. The quantum-delayed choice experiment is implemented with multiple entangled photons under Einstein’s locality condition. The wave–particle quantum superposition is realized by controlling the relative phase between the wave and particle states.