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Modern Physics Letters B

A construction method of the wave–particle entanglement state of the particle system

Tingwei Zhou

Published Sep 13, 2023• 0 citations
Publisher

Abstract

Entanglement of the wave–particle duality of particles has attracted enormous attention as one of fundamental feature of quantum mechanics. Herein, we systematically studied the wave–particle entanglement of the particle system composed of N particles. The results indicate that the particle system has the wave–particle entanglement after the interaction, when the wave function of any one of the system can be obtained by using same basis vectors before the interaction. Moreover, a construction method of the wave–particle entanglement state is found for the particle system. Finally, the photons can show the wave–particle entanglement in the previous experimental work, which was further confirmed by the construction method. The results provide a new understanding for the entanglement of the wave–particle duality.

DOI
10.1142/s0217984924500076

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Entanglement of the wave–particle duality of particles has attracted enormous attention as one of fundamental feature of quantum mechanics. Herein, we systematically studied the wave–particle entanglement of the particle system composed of N particles. The results indicate that the particle system has the wave–particle entanglement after the interaction, when the wave function of any one of the system can be obtained by using same basis vectors before the interaction. Moreover, a construction method of the wave–particle entanglement state is found for the particle system. Finally, the photons can show the wave–particle entanglement in the previous experimental work, which was further confirmed by the construction method. The results provide a new understanding for the entanglement of the wave–particle duality.
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 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.
When observed, a quantum system exhibits either wave-like or particle-like properties, depending on how it is measured. However, this duality is affected by the entanglement of the system with its quantum memory, raising a fundamental question: how are wave-particle duality and entanglement related? Here, we broaden the scope of wave-particle duality to include entanglement, introduce universal conservation laws for the wave-particle-entanglement triad, and perform demonstrations on silicon-integrated nanophotonic quantum chips. Our experiments not only mark the first confirmation of universal conservation laws but also highlight the potential of integrated photonics for exploring complex quantum phenomena in high-dimensional systems.
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.
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.