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Wave-particle duality epitomizes the counterintuitive character of quantum physics. A striking illustration is the quantum delay-choice experiment, which is based on Wheelers 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 in particular 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 187-m-long two-photon Hong-Ou-Mandel interferometer. The third photon is sent 141m away from the interferometers and remotely prepares a two-photon quantum gate according to independent active choices under Einstein locality conditions. We have realized 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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Complementarity, that is the ability of a quantum object to behave either as a particle or as a wave, is one of the most intriguing features of quantum mechanics. An exemplary Gedanken experiment, emphasizing such a measurement-dependent nature, was suggested by Wheeler using single photons. The subtleness of the idea lies in the fact that the output beam-splitter of a Mach-Zehnder interferometer is put in or removed after a photon has already entered the interferometer, thus performing a delayed test of the wave-particle complementary behavior. Recently, it was proposed that using a quantum analogue of the output beam-splitter would permit carrying out this type of test after the detection of the photon and observing wave-particle superposition. In this paper we describe an experimental demonstration of these predictions using another extraordinary property of quantum systems, entanglement. We use a pair of polarization entangled photons composed of one photon whose nature (wave or particle) is tested, and of a corroborative photon that allows determining which one, or both, of these two aspects is being tested. This corroborative photon infers the presence or absence of the beam-splitter and until it is measured, the beam-splitter is in a superposition of these two states, making it a quantum beam-splitter. When the quantum beam-splitter is in the state present or absent, the interferometer reveals the wave or particle nature of the test photon, respectively. Furthermore, by manipulating the corroborative photon, we can continuously morph, via entanglement, the test photon from wave to particle behavior even after it was detected. This result underlines the fact that a simple vision of light as a classical wave or a particle is inadequate.
Wheelers delayed-choice experiment investigates the indeterminacy of wave-particle duality and the role played by the measurement apparatus in quantum theory. Due to the inconsistency with classical physics, it has been generally believed that it is not possible to reproduce the delayed-choice experiment using a hidden variable theory. Recently, it was shown that this assumption was incorrect, and in fact Wheelers delayed-choice experiment can be explained by a causal two dimensional hidden-variable theory [R. Chaves, G. B. Lemos, and J. Pienaar, Phys. Rev. Lett. 120, 190401 (2018)]. Here, we carry out an experiment of a device-independent delayed-choice experiment using photon states that are space-like separated, and demonstrate a loophole-free version of the delayed-choice protocol that is consistent with quantum theory but inconsistent with any causal two-dimensional hidden variable theory. This salvages Wheelers thought experiment and shows that causality can be used to test quantum theory in a complementary way to the Bell and Leggett-Garg tests.
Famous double-slit or double-path experiments, implemented in a Youngs or Mach-Zehnder interferometer, have confirmed the dual nature of quantum matter, When a stream of photons, neutrons, atoms, or molecules, passes through two slits, either wave-like interference fringes build up on a screen, or particle-like which-path distribution can be ascertained. These quantum objects exhibit both wave and particle properties but exclusively, depending on the way they are measured. In an equivalent Mach-Zehnder configuration, the object displays either wave or particle nature in the presence or absence of a beamsplitter, respectively, that represents the choice of which-measurement. Wheeler further proposed a gedanken experiment, in which the choice of which-measurement is delayed, i.e. determined after the object has already entered the interferometer, so as to exclude the possibility of predicting which-measurement it will confront. The delayed-choice experiments have enabled significant demonstrations of genuine two-path duality of different quantum objects. Recently, a quantum controlled version of delayed-choice was proposed by Ionicioiu and Terno, by introducing a quantum-controlled beamsplitter that is in a coherent superposition of presence and absence. It represents a controllable experiment platform that can not only reveal wave and particle characters, but also their superposition. Moreover, a quantitative description of two-slit duality relation was initialized in Wootters and Zureks seminal work and formalized by Greenberger,et. al. as D2+V2<=1, where D is the distinguishability of whichpath information, and V is the contrast visibility of interference. In this regard, getting which-path information exclusively reduces the interference visibility, and vice versa. This double-path duality relation has been tested in pioneer experiments and recently in delayed-choice measurements.
We propose a scheme feasible with current technology to implement a quantum delayed-choice experiment in the realm of cavity QED. Our scheme uses two-level atoms interacting on and off resonantly with a single mode of a high Q cavity. At the end of the protocol, the state of the cavity returns to its ground state, allowing new sequential operations. The particle and wave behavior, which are verified in a single experimental setup, are postselected after the atomic states are selectively detected.
Nowadays the most intriguing features of wave particle complementarity of single photon is exemplified by the famous Wheelers delayed choice experiment in linear optics, nuclear magnetic resonance and integrated photonic device systems. Studying the wave particle behavior in light and matter interaction at single photon level is challenging and interesting, which gives how single photons complement in light and matter interaction. Here, we demonstrate a Wheelers delayed choice experiment in an interface of light and atomic memory, in which the cold atomic memory makes the heralded single photon divided into a superposition of atomic collective excitation and leaked pulse, thus acting as memory beam splitters. We observe the morphing behavior between particle and wave of a heralded single photon by changing the relative proportion of quantum random number generator, the second memory efficiency, and the relative storage time of two memories. The reported results exhibit the complementarity behavior of single photon under the interface of light atom interaction.
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