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arXiv:1908.04552 · Journal of Physics Communications

Wave-particle duality in single-photon entanglement

Wei Li, Shengmei Zhao

Published Apr 29, 2021• 2 citations
arXivHTMLPDF

Abstract

Abstract Single-photon entanglement, the entanglement between vacuum state and single-photon state, is essentially the entanglement of particle characteristics. Wave-particle duality indicates that wave property and particle property could coexist. Can we find evidence of wave-behavior entanglement in single-photon entanglement? Here, based on the construction of Bell-like inequality in wave space, we propose a method to verify the wave-particle duality in single-photon entanglement. First, we define the wave state in two-dimensional space relative to the photon number state, and propose a method to measure the wave state. The strong violation of Bell’s inequality based on the joint measurement of wave states indicates the existence of single-photon entanglement, and the wave is the conjugate variable of the particle. Wave state entanglement obtained from Fourier transform of single photon entanglement and the corresponding measurement protocols will provide us with more information-carrying schemes in the field of quantum information. The difference in the representation in photon-number space and wave space implies the wave-particle duality of single photon entanglement.

DOI
10.1088/2399-6528/abfd15

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Abstract Single-photon entanglement, the entanglement between vacuum state and single-photon state, is essentially the entanglement of particle characteristics. Wave-particle duality indicates that wave property and particle property could coexist. Can we find evidence of wave-behavior entanglement in single-photon entanglement? Here, based on the construction of Bell-like inequality in wave space, we propose a method to verify the wave-particle duality in single-photon entanglement. First, we define the wave state in two-dimensional space relative to the photon number state, and propose a method to measure the wave state. The strong violation of Bell’s inequality based on the joint measurement of wave states indicates the existence of single-photon entanglement, and the wave is the conjugate variable of the particle. Wave state entanglement obtained from Fourier transform of single photon entanglement and the corresponding measurement protocols will provide us with more information-carrying schemes in the field of quantum information. The difference in the representation in photon-number space and wave space implies the wave-particle duality of single photon entanglement.
Wave-particle duality and entanglement are two fundamental characteristics of quantum mechanics. All previous works on experimental investigations in wave-particle properties of single photons (or single particles in general) showed that a well-defined interferometer setting determines a well-defined property of single photons. Here we take a conceptual step forward and control the wave-particle property of single photons with a Bell state. By doing so, we experimentally test the complementarity principle in a scenario in which the setting of the interferometer is not defined at any instance of the experiment, not even in principle. To achieve this goal, we establish the three-photon entangled state, i.e., the entanglement between a single photon and a two-photon Bell state, send the photon of interest SSS into a quantum Mach-Zehnder interferometer (MZI), in which the output beam splitter of the MZI is controlled by the quantum state of the second photon CCC, which is entangled with a third photon AAA. Therefore, the individual quantum state of photon CCC is undefined, which implements the undefined settings of the MZI for photon SSS. This is realized by using three cascaded phase-stable interferometers for three photons. There is typically no well-defined setting of the MZI and thus the very formulation of the wave-particle objectivity from local hidden variable models becomes internally inconsistent.
Wave-particle duality is the most fundamental description of the nature of a quantum object, which behaves like a classical particle or wave depending on the measurement apparatus. On the other hand, entanglement represents nonclassical correlations of composite quantum systems, being also a key resource in quantum information. Despite the very recent observations of wave-particle superposition and entanglement, whether these two fundamental traits of quantum mechanics can emerge simultaneously remains an open issue. Here we introduce and experimentally realize a scheme that deterministically generates entanglement between the wave and particle states of two photons. The elementary tool allowing this achievement is a scalable single-photon setup which can be in principle extended to generate multiphoton wave-particle entanglement. Our study reveals that photons can be entangled in their dual wave-particle behavior and opens the way to potential applications in quantum information protocols exploiting the wave-particle degrees of freedom to encode qubits.Here the authors experimentally realize a scheme that deterministically generates entanglement between the wave and particle states of two photons using a scalable all-optical scheme. They achieve this result by first showing generation of controllable single-photon wave-particle superposition states.
Abstract The Mach–Zehnder interferometer experiment described earlier shows why and how quantum mechanics is different from classical mechanics. A photon sent through a beam splitter behaves like a particle when it is observed by only one of the two detectors. When two beam splitters are used, the photon “interferes with itself” and behaves like a wave. This is the so-called wave-particle duality of quantum mechanics which leads to quantum entanglement. This chapter discusses quantum superpositions when two or more particles are present. Understanding and analysing entanglement is one of the most interesting directions in the field of quantum information. First, a historical background of quantum entanglement is given, followed by a discussion on Bell's inequalities, separable states that do not violate Bell's inequalities, pure states that violate Bell's inequalities, mixed states that do not violate Bell's inequalities, and entanglement in second quantisation.
Abstract Complementarity or wave-particle duality has been the basis of quantum mechanics over the last century. Since the Hanbury Brown and Twiss experiments in 1956, the particle nature of single photons has been intensively studied for various quantum phenomena such as anticorrelation and Bell inequality violation. Regarding the fundamental question on quantumness or nonclassicality, however, no clear answer exists for what quantum entanglement should be and how to generate it. Here, we experimentally demonstrate the secrete of quantumness using the wave nature of single photons.
The wave-particle duality has been said to contain the entire mystery of quantum mechanics. Many delayed-choice experiments have been performed to further understand the wave-particle duality. Here, we reveal some flaws in the known interference theories by comparing the theoretical predictions with the experimental facts and show that the presence of media is a necessary condition for interference of single photons, a photon interferes with other photon via microscopic particles in the interface of media, and the wave-like property of a photon originates from interaction between the photon and media; the particle property is the inherent characteristic of a photon, and the wave-like behavior of a photon always accompanies the particle behavior; the coherent time of single photons cannot be longer than the lifetime of the polarized states of the microscopic particles. Interference of single photons is interpreted properly, and the conundrum of the wave-particle duality is well solved.
The first- and second-order wave-particle dualities for two-photon states are investigated in a Mach-Zehnder interferometer. These duality relations are experimentally tested through two-photon pure states and two-photon mixed states. The experimental results are in full agreement with the theoretical predictions. The optical fields exhibiting the same first-order particlelike and wavelike behaviors may carry entirely different second-order duality information, which implies that the higher-order duality relations are a useful tool for analyzing the wave-particle duality for multiphoton states.