A textbook interpretation of quantum physics is that quantum objects can be described in a particle or a wave picture, depending on the operations and measurements performed. Beyond this widely held believe, we demonstrate in this contribution that neither the wave nor the particle description is sufficient to predict the outcomes of quantum-optical experiments. To show this, we derive correlation-based criteria that have to be satisfied when either particles or waves are fed into our interferometer. Using squeezed light, it is then confirmed that measured correlations are incompatible with either picture. Thus, within one single experiment, it is proven that neither a wave nor a particle model explains the observed phenomena. Moreover, we formulate a relation of wave and particle representations to two incompatible notions of quantum coherence, a recently discovered resource for quantum information processing.For such an information-theoretic interpretation of our method, we certify the nonclassicality of coherent states - the quantum counterpart to classical waves - in the particle picture, complementing the known fact that photon states are nonclassical in the typically applied wave picture.
A textbook interpretation of quantum physics is that quantum objects can be described in a particle or a wave picture, depending on the operations and measurements performed. Beyond this widely held believe, we demonstrate in this contribution that neither the wave nor the particle description is sufficient to predict the outcomes of quantum-optical experiments. To show this, we derive correlation-based criteria that have to be satisfied when either particles or waves are fed into our interferometer. Using squeezed light, it is then confirmed that measured correlations are incompatible with either picture. Thus, within one single experiment, it is proven that neither a wave nor a particle model explains the observed phenomena. Moreover, we formulate a relation of wave and particle representations to two incompatible notions of quantum coherence, a recently discovered resource for quantum information processing.For such an information-theoretic interpretation of our method, we certify the nonclassicality of coherent states - the quantum counterpart to classical waves - in the particle picture, complementing the known fact that photon states are nonclassical in the typically applied wave picture.
A single photon exhibits wave-particle duality in the Young's double-slit interferometer. The duality characterized by an interference visibility and a which-path information has trade-off relation known as complementarity. These quantities are related to the first-order coherence, and the interference is based on the phase correlation between lights coming from two arms. However according to quantum optics theory, such a simple wave-particle picture is not enough to understand the nature because the theory showed an importance of higher-order coherence in the sense of both interference and statistical distribution of photons. Second-order intensity correlation is especially crucial to reveal distinctive quantum features of photons with no classical analogue. Here, in an intensity interferometric scenario as represented by the Hong-Ou-Mandel interferometer, we discuss a wave-particle duality of light based on a which-path information and a quantity characterizing a magnitude of the intensity interferometric effect. We show, for classical light, the two quantities obey the complementary principle similar to the case of the double-slit experiment, but do not for nonclassical light. The nonclassical light such as photons at two arms is allowed to show larger which-path information and intensity interference simultaneously beyond the complementary relation. Moreover, the violation reveals a new nonclassical nature of light although both of the above two quantities seem to be understandable classically, which is never found from a consideration of only one side of wave-particle duality.
Publisher Summary Wave-particle duality means that a quantum object can exhibit either wave or particle properties, depending on the experimental situation. The wave nature gives rise to interference phenomena, whereas knowledge about the path taken by the object testifies to its particle nature. It is impossible to observe wave and particle properties simultaneously. Atom interferometry addresses fundamental aspects of the quantum theory of measurement in real experiments. This chapter discusses the loss of interference fringes in a which-way experiment need not be due to the Heisenberg's uncertainty relation. It demonstrates how interference can be restored by erasing the which-way information. The chapter investigated a new regime, where only incomplete which-way information is available. This allowed studying the continuous transition between wave and particle pictures and to test wave-particle duality in a quantitative manner. Future experimental investigations in this field focuses on the investigation of decoherence effects to study the transition between quantum and classical physics, leading to a more detailed understanding of the processes underlying the collapse of the wave function.
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.
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.
The wave-particle duality is a fundamental property of the nature. At the same time, it is one of the greatest mysteries of modern physics. This gave rise to a whole direction in quantum physics - the interpretation of quantum mechanics. The Wiener experiments demonstrating the wave-particle duality of light are discussed. It is shown that almost all interpretations of quantum mechanics allow explaining the double-slit experiments, but are powerless to explain the Wiener experiments. The reason of the paradox, associated with the wave-particle duality is analyzed. The quantum theory consists of two independent parts: (i) the dynamic equations describing the behavior of a quantum object (for example, the Schrodinger or Maxwell equations), and (ii) the Born’s rule, the relation between the wave function and the probability of finding the particle at a given point. It is shown that precisely the Born’s rule results in paradox in explaining the wave-particle duality. In order to eliminate this paradox, we propose a new rational interpretation of the wave-particle duality and associated new rule, connecting the corpuscular and wave properties of quantum objects. It is shown that this new rational interpretation of the wave-particle duality allows using the classic images of particle and wave in explaining the quantum mechanical and optical phenomena, does not result in paradox in explaining the doubleslit experiments and Wiener experiments, and does not contradict to the modern quantum mechanical concepts. It is shown that the Born’s rule follows immediately from proposed new rules as an approximation.
As has become evident from historical studies, science does not proceed in the coherent and predictable way that basic science texts would have us believe. I will argue that an excellent counter-example is an episode from the historical development of quantum mechanics in which the incompatibility of the particle and the wave representations of the electron and light were destined to be encompassed by two mathematically equivalent, but conceptually quite different theories. I shall argue that the appearance of two such different, yet equivalent, quantum theories was not surprising at all and I claim even predictable. As Einstein himself wrote in 1909: ‘It is my opinion that the next phase in the development of theoretical physics will bring us a theory of light that can be interpreted as a kind of fusion of the wave and the [particle] theory.’ Certainly, the interpretative content of Werner Heisenberg's and Erwin Schrödinger's theories could not have been more different. By mid-1926, the theoretical foundations had been laid for a scientific and emotional battleground between the particle and the wave. I suggest that an important element in the debate was not the incompatibility itself but actually coming to terms with ambiguity in science. For, in the end, ambiguous and vague interpretations of the same phenomena became part of science, where science was supposed to give a clear and unambiguous description of nature.