One of the milestones of quantum mechanics is Bohr's complementarity principle. It states that a single quantum can exhibit a particlelike $or$ a wavelike behavior, but never both at the same time. These are mutually exclusive and complementary aspects of the quantum system. This means that we need distinct experimental arrangements in order to measure the particle or the wave nature of a physical system. One of the most known representations of this principle is the single-photon Mach-Zehnder interferometer. When the interferometer is closed an interference pattern is observed (wave aspect of the quantum) while if it is open, the quantum behaves like a particle. Here, using a molecular quantum information processor and employing nuclear magnetic resonant (NMR) techniques, we analyze the quantum version of this principle by means of an interferometer that is in a quantum superposition of being closed and open, and confirm that we can indeed measure both aspects of the system with the same experimental apparatus. More specifically, we observe with a single apparatus the interference between the particle and the wave aspects of a quantum system.
One of the milestones of quantum mechanics is Bohr's complementarity principle. It states that a single quantum can exhibit a particlelike or a wavelike behavior, but never both at the same time. These are mutually exclusive and complementary aspects of the quantum system. This means that we need distinct experimental arrangements in order to measure the particle or the wave nature of a physical system. One of the most known representations of this principle is the single-photon Mach-Zehnder interferometer. When the interferometer is closed an interference pattern is observed (wave aspect of the quantum) while if it is open, the quantum behaves like a particle. Here, using a molecular quantum information processor and employing nuclear magnetic resonant (NMR) techniques, we analyze the quantum version of this principle by means of an interferometer that is in a quantum superposition of being closed and open, and confirm that we can indeed measure both aspects of the system with the same experimental apparatus. More specifically, we observe with a single apparatus the interference between the particle and the wave aspects of a quantum system.
An experimental test of the quantum complementarity principle based on single neutral atoms trapped in a blue detuned bottle trap was here performed. A Ramsey interferometer was used to assess the wavelike behavior or particlelike behavior with second $\ensuremath{\pi}/2$ rotation on or off. The wavelike behavior or particlelike behavior is characterized by the visibility V of the interference or the predictability P of which-path information, respectively. The measured results fulfill the complementarity relation ${P}^{2}+{V}^{2}\ensuremath{\le}1$. Imbalance losses were deliberately introduced to the system and we find the complementarity relation is then formally ``violated.'' All the experimental results can be completely explained theoretically by quantum mechanics without considering the interference between wave and particle behaviors. This observation complements existing information concerning Bohr's complementarity principle based on wave-particle duality of a massive quantum system.
A distinct method to show a quantum object behaving both as wave and as particle is proposed and described in some detail. We make a systematic analysis using the elementary methodology of quantum mechanics upon Young's two-slit interferometer and the Mach—Zehnder two-arm interferometer with the focus placed on how to measure the interference pattern (wave nature) and the which-way information (particle nature) of quantum objects. We design several schemes to simultaneously acquire the which-way information for an individual quantum object and the high-contrast interference pattern for an ensemble of these quantum objects by placing two sets of measurement instruments that are well separated in space and whose perturbation of each other is negligibly small within the interferometer at the same time. Yet, improper arrangement and cooperation of these two sets of measurement instruments in the interferometer would lead to failure of simultaneous observation of wave and particle behaviors. The internal freedoms of quantum objects could be harnessed to probe both the which-way information and the interference pattern for the center-of-mass motion. That quantum objects can behave beyond the wave—particle duality and the complementarity principle would stimulate new conceptual examination and exploration of quantum theory at a deeper level.
Some recent works have introduced a quantum twist to the concept of complementarity, exemplified by a setup in which the which-way detector is in a superposition of being present and absent. It has been argued that such experiments allow measurement of particle-like and wave-like behavior at the same time. Here, we derive an inequality which puts a bound on the visibility of interference and the amount of which-way information that one can obtain, in the context of such modified experiments. As the wave aspect can only be revealed by an ensemble of detections, we argue that, in such experiments, a single detection can contribute only to one subensemble, corresponding to either wave aspect or particle aspect. This way, each detected particle behaves either as particle or as wave, never both, and Bohr's complementarity is fully respected.
Bohr's complementarity notion is at the heart of quantum physics. It suggests that quantum systems are observed as waves or particles depending on the type of measurement, i.e., the experimental arrangement, they are subjected to. For instance, sending single photons to an open or closed Mach-Zehnder interferometer (MZI) leads to the observation of particle or wave behaviours, respectively. In 1984, Wheeler proposed a "Gedanken" delayed-choice experiment in which the interferometer configuration is chosen at will by the experimentalist only after the photon has already passed the input beam-splitter (BS_in) of the device. This experiment was realized using a single photon source and showed that Bohr's complementarity notion was still obeyed.It was recently proposed to take Wheeler's experiment one step further by employing an output "quantum beam-splitter" (QBS), i.e.,preparing BS_out in a coherent superposition of being absent and present. This allows choosing the type of measurement, i.e., wave or particle, only after having determined the state of the QBS, which can be (in principle) infinitely delayed.We realized such an experiment by exploiting the resource of entanglement, in this case pairs of polarization entangled photons. The behaviour of one of the paired photons, called the test photon, is analysed using a MZI having a QBS at its output. This QBS is enabled by entanglement and made of a polarization dependent beam-splitter. The other photon, called the corroborative photon, allows determining the state of the QBS, and consequently, which test photon behaviour (wave, particle, or both) is observed.By manipulating the corroborative photon polarization state, we demonstrate a continuous morphing of the test photon from wave to particle behaviour. This refutes simple models of single photons behaving exclusively as waves or particles. The state of the QBS is determined via the measurement of the corroborative photon only after the test photon has already been detected. The space-like separation between the two measurements invalidates local-hidden variable models associated with pre-existing information about the measurement outcomes. In other words, when the test photon is detected, no information is available about the type of measurement it underwent. These results still perfectly obey Bohr's complementarity notion and its extension.
To resolve the challenges (paradoxes) attending the genesis of quantum theory, Niels Bohr in 1927 proposed a generalization of the conceptual framework of classical physics, termed complementarity, which posited pairs of classical concepts that could be manifested only in mutually exclusive experimental arrangements with both needed to embrace the full range of physical experience. In this context particle–wave complementarity has encountered two major obstacles; (1) No formulation of it has commanded a general consensus; and (2) empirical evidence abounds that contradicts the claim of mutual exclusivity of particle and wave properties of quantum objects in a single experiment. These problems are rooted in the unrestricted scope of this claim. It is shown that a restricted version of particle–wave complementarity, here called “which value–interference” complementarity, is consistent with observations, is naturally contained in the mathematical formalism of quantum theory and, in fact, holds in any representation of quantum theory defined by the eigenvectors of a complete set of commuting observables, such as the configuration space position (kinematic) variables or the complementary linear momentum (dynamic) variables. Thus, the which value–interference form of particle–wave complementarity exists within kinematic–dynamic complementarity, a “layered” complementarity, so to speak. It is hoped that a consistent and valid exposition of particle–wave complementarity will be helpful to those who find the framework of complementarity useful and appropriate for some purpose.
Bohr's complementarity principle is of fundamental historic and conceptual importance for quantum mechanics (QM), and states that, with a given experimental apparatus configuration, one can observe either the wave-like or the particle-like character of a quantum system, but not both. However, it was eventually realized that these dual behaviors can both manifest partially in the same experimental setup, and, using ad hoc proposed measures for the wave and particle aspects of the quanton, complementarity relations were proposed limiting how strong these manifestations can be. Recently, a formalism was developed and quantifiers for the particleness and waveness of a quantum system were derived from the mathematical structure of QM entailed in the density matrix's basic properties ($\ensuremath{\rho}\ensuremath{\ge}0, \mathrm{Tr}\ensuremath{\rho}=1$). In this article, using IBM Quantum Experience quantum computers, we perform experimental tests of these complementarity relations applied to a particular class of one-qubit quantum states and also for random quantum states of one, two, and three qubits.