We tested wave-particle duality with the ensemble-averaged spin states of 13 C nuclei in 13 CHCl 3 using the spin states of 1 H nuclei as the path marker. It turns out that wave-particle duality holds when one merely measures the probability density of quantum states, and that wave- and particle-like behaviour is simultaneously observed when measuring populations and coherences in a single nuclear magnetic resonance experiment. The effects of path-marking schemes and the causes of the appearance and disappearance of wave behaviour are analysed.
We tested wave-particle duality with the ensemble-averaged spin states of 13 C nuclei in 13 CHCl 3 using the spin states of 1 H nuclei as the path marker. It turns out that wave-particle duality holds when one merely measures the probability density of quantum states, and that wave- and particle-like behaviour is simultaneously observed when measuring populations and coherences in a single nuclear magnetic resonance experiment. The effects of path-marking schemes and the causes of the appearance and disappearance of wave behaviour are analysed.
We have tested complementarity for the ensemble-averaged spin states of nuclei 13C in the molecule of 13CHCl3 by the use of the spin states of another nuclei 1H as the path marker. It turns out that the wave-particle duality holds when one merely measures the probability density of quantum states, and that the wave- and particle-like behavior is simultaneously observed with the help of measuring populations and coherence in a single nuclear magnetic resonance(NMR) experiment. Effects of path-marking schemes and causes of the appearance and disappearance of the wave behavior are analysed.
We have experimentally demonstrated the interferometric complementarity, which relates the distinguishability D quantifying the amount of which-way (WW) information to the fringe visibility V characterizing the wave feature of a quantum entity, in a bulk ensemble by nuclear magnetic resonance (NMR) techniques. We are primarily concerned about the intermediate cases: partial fringe visibility and incomplete WW information. We propose a quantitative measure of D by an alternative geometric strategy and investigate the relation between D and entanglement. By measuring D and V independently, it turns out that the duality relation D 2 + V 2 = 1 holds for pure quantum states of the markers.
We have experimentally demonstrated the interferometric complementarity, which relates the distinguishability D quantifying the amount of which-way (WW) information to the fringe visibility V characterizing the wave feature of a quantum entity, in a bulk ensemble by Nuclear Magnetic Resonance (NMR) techniques. We primarily concern on the intermediate cases: partial fringe visibility and incomplete WW information. We define D by an alternative formalism and investigate the relation between D and entanglement. By measuring D and V independently, it turns out that the duality relation D 2 + V 2 = 1 holds for pure quantum states of the markers.
Abstract Quantum coherence stemming from the superposition behaviour of a particle beyond the classical realm, serves as one of the most fundamental features in quantum mechanics. The wave-particle duality phenomenon, which shares the same origin, has a strong relationship with quantum coherence. Recently, an elegant relation between quantum coherence and path information has been theoretically derived. Here, we experimentally test such new duality by l1-norm measure and the minimum-error state discrimination. We prepare three classes of two-photon states encoded in polarisation degree of freedom, with one photon serving as the target and the other photon as the detector. We observe that wave-particle-like complementarity and Bagan’s equality, defined by the duality relation between coherence and path information, is well satisfied. Our results may shed new light on the original nature of wave-particle duality and on the applications of quantum coherence as a fundamental resource in quantum technologies.
We analyze an interferometric complementarity between one- and two-particle interference in the general case: Vi2+V122≤1(i=1, 2), and further examine the relation among one-particle interference visibility Vi, two-particle interference visibility V12 and the predication Pi of the path of a single particle. An equality Vi2+V122+Pi2=1(i=1, 2) is achieved for any pure two-particle source, which implies the condition of the complementarity relation to reach the upper bound and its relation to another interferometric complementarity between path information and interference visibility of a single particle. Meanwhile, the relationships of the complementarities and the entanglement E of the composite system are also investigated. Using nuclear magnetic resonance techniques, the two-particle interferometric complementarity was experimentally tested with the ensemble-averaged spin states, including two extreme cases and an intermediate case.
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.