Wave-particle duality and the superposition of quantum mechanical states furnish quantum mechanics with unique features which distinguishes it from classical mechanics and give it the apparently counter-intuition interpretation. The two principles are responsible for the observation of the interference effects of quantum particles such as electrons, atoms and molecules. Visibility is a measure of the wave nature and can be though of as a "normalized" coherence quantifier. Reduction in the visibility arises from dephasing (decoherence): a process in which the relative phases get partially or totally destroyed leading to domination of the particle nature. We calculate the coherence and visibility of an ensemble of a single electron and two electrons on two sites using the density matrix formulation. For such a system of electrons, visibility and predictability (a particle nature measure) follow an oscillatory-complementary temporal evolution and neither of them depends on the single particle energy.
Wave-particle duality and the superposition of quantum mechanical states furnish quantum mechanics with unique features which distinguishes it from classical mechanics and give it the apparently counter-intuition interpretation. The two principles are responsible for the observation of the interference effects of quantum particles such as electrons, atoms and molecules. Visibility is a measure of the wave nature and can be though of as a "normalized" coherence quantifier. Reduction in the visibility arises from dephasing (decoherence): a process in which the relative phases get partially or totally destroyed leading to domination of the particle nature. We calculate the coherence and visibility of an ensemble of a single electron and two electrons on two sites using the density matrix formulation. For such a system of electrons, visibility and predictability (a particle nature measure) follow an oscillatory-complementary temporal evolution and neither of them depends on the single particle energy.
We derive a generalized wave-particle duality relation for arbitrary multipath quantum interference phenomena. Beyond the conventional notion of the wave nature of a quantum system, i.e., the interference fringe visibility, we introduce a quantifier as the normalized quantum coherence, recently defined in the framework of quantum information theory. To witness the particle nature, we quantify the path distinguishability or the which-path information based on unambiguous quantum state discrimination. Then, the Bohr complementarity principle for multipath quantum interference can be stated as a duality relation between the quantum coherence and the path distinguishability. For two-path interference, the quantum coherence is identical to the interference fringe visibility, and the relation reduces to the well-known complementarity relation. The duality relation continues to hold in the case where mixedness is introduced due to possible decoherence effects.
The interference observed for a quanton, traversing more than one path, is believed to characterize its wave nature. Conventionally, the sharpness of interference has been quantified by its visibility or contrast, as defined in optics. Based on this visibility, wave-particle duality relations have been formulated for two-path interference. However, as one generalizes the situation to multi-path interference, it is found that conventional interference visibility is not a good quantifier. A recently introduced measure of quantum coherence has been shown to be a good quantifier of the wave nature. The subject of quantum coherence, in relation to the wave nature of quantons and to interference visibility, is reviewed here. It is argued that coherence can be construed as a more general form of interference visibility, if the visibility is measured in a different manner, and not as contrast. Quanta 2019; 8: 24–35.
One of the cornerstones of quantum physics is the wave nature of matter. It explains experimentally observed effects like interference and diffraction, occurring when an object moves from one place to another along several indistinguishable ways simultaneously. The wave nature disappears when the individual ways are distinguishable. In this case, the particle nature of the object becomes visible. To determine the particle nature quantitatively, the way of the object has to be measured. Here, large progress has been made recently with new techniques, enabling one to investigate single moving atoms in a controlled manner. Two examples are discussed in the following two sections. The first experiment describes an atom interferometer, where the way of the atom is entangled with its internal state. This allows one to explore the origin of wave-particle duality and perform a quantitative test of this fundamental principle. The second experiment reports on the observation of an atom-photon molecule, a bound state between an atom and a single photon. A fascinating aspect of this system is that it makes possible to monitor the motion of a single neutral atom in real time.
Updating the wave-particle duality Maria C. Bosca e-mail: bosca@ugr.es Departamento de Fisica Atomica, Molecular y Nuclear Universidad de Granada E-18071. Granada Spain The wave-particle-duality, the fundamental component of the new quantum formalism in Bohr’s opinion, must be reformulated by incorporating the results of some experiments accomplished in the last decades of twentieth century. The Bohr´s complementarity principle stated the mutual exclusiveness and joint full completeness of the two (classical) descriptions of quantum systems; after Einstein-Podolsky-Rosen’paper, the wave-particle duality, or wave-particle complementarity, could be expressed by stating that it is impossible to build up an experimental arrangement in which we observe at the same time both corpuscular and wave aspects. In a two-slit experiment, they would correspond, respectively, to the which-way knowledge and the observation of interference pattern. Bohr showed this mutual exclusivity in numerous examples , and linked it to the unavoidable disturbance inherent in any measurement event. In quantum mechanical formalism, the complementarity principle has a clear mathematical expression: two observables are complementary if precise knowledge of one of them implies that all possible outcomes of the other are equally probable; their extension to classical concepts (as wave and particle) is not concerned. In 1991 Scully et al published a variant of the two-slit experiment that incorporates two micromasers cavities and a laser beam to provide which-path information without net momentum transferred during the interaction ; the impossibility of know which slit an atom went through and still observe the interference fringes is preserved by the establishing of quantum correlations between the measuring apparatus and the system being observed. They claimed that complementarity, of which wave-particle duality would be to them a manifestation, is more fundamental than the uncertainty principle . In 1996 B-G. Englert, following an approach originally due to Wooters and Zurek , derived , without making use of Heisenberg’s uncertainty relation, an inequality that quantifies the mutual compatibility relation between fringe visibility and which-way information. The inequality, that they denominated as “interferometric duality”, has the expression D^2 + V^2 ≤ 1, where D stands for the distinguishability of the ways and V for the fringe visibility; both of them are mathematical expressions that can be measured to check experimentally the inequality . Today, it is clear that intermediate particle-wave behaviours exist and, in addition to that, there are single experiments in which both classical wave-like and particle-like behaviours are showed total and simultaneously on an individual system. For instance, in the Bose’s double-prism experiment , tunnelling and perfect anticoincidence were observed in single photon states. Consequently, the meaning of the wave-particle duality must incorporate the simultaneous use of the two classical descriptions in the interpretation of experiments, loosing their original mutual exclusivity , which is incorporated as an extreme case in the new interferometric duality, a continuous quantum concept . The wave-particle duality, therefore, must be formulated as an interpretative addition to quantum mechanics, to which is possible to renounce if any pretension of visualize quantum phenomena in terms of classical concepts and intuitions is abandoned.
Abstract One of the cornerstones of quantum physics is the wave nature of matter. It explains experimentally observed effects like interference and diffraction, occurring when an object moves from one place to another along several indistinguishable ways simultaneously. The wave nature disappears when the individual ways are distinguishable. In this case, the particle nature of the object becomes visible. To determine the particle nature quantitatively, the way of the object has to be measured. Here, large progress has been made recently with new techniques, enabling one to investigate single moving atoms in a controlled manner. Two examples are discussed in the following two sections. The first experiment describes an atom interferometer, where the way of the atom is entangled with its internal state. This allows one to explore the origin of wave‐particle duality and perform a quantitative test of this fundamental principle. The second experiment reports on the observation of an atom‐photon molecule, a bound state between an atom and a single photon. A fascinating aspect of this system is that it makes possible to monitor the motion of a single neutral atom in real time.
Wave-particle duality, a fundamental principle of quantum mechanics, encapsulates the complementary relationship between the wave and particle behaviors of quantum systems. In this paper, we treat quantum coherence and classical distinguishability as complementary resources and uncover a novel duality relation, which is explored through quantum state discrimination under incoherent operations, extending beyond typical interference scenarios. We prove that in an ensemble of mutually orthogonal pure states, the sum of ``co-bits,'' quantifying the coherence preserved under incoherent free operations, and classical bits, representing the distinguishability extracted via quantum state discrimination, is bounded. This coherence-distinguishability duality relation exposes an inherent tradeoff between the simultaneous preservation of a system's quantum coherence (wavelike property) and the extraction of its classical distinguishability (particlelike property). Our findings provide a fresh perspective on wave-particle duality through quantum resource theories, offering complementary insights into manipulating quantum and classical resources, with implications for quantum foundations and quantum technologies.