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Physical Review A

Single- and two-photon wave-particle superpositions: Theory and experiment

Qing-Feng Xue, Xu-Cai Zhuang, Nguyen Ba An, Deyang Duan, R. Ma, Weiwei Pan, Qinqin Wang, Yunjie Xia, Zhong‐Xiao Man

Published Aug 29, 2023• 2 citations

Abstract

Simultaneous observation of the wave and particle natures of a quantum object under one experimental arrangement represents the latest development regarding wave-particle duality. In this work, we propose a simple scheme using linear-optics devices to observe either the particle nature or wave nature or the wave-particle superposition (WPS) of photons by controlling a relevant classical parameter. Our setup consists of two stages, the preparation and measurement stages, with the latter stage containing an additional classical variable whose value will be given only after the first stage in order to avoid any possible communication between the two stages and thus rule out the classical hidden-variable model. We not only develop the theory but also perform the corresponding experiments. The experimental observations perfectly agree with the theoretical predictions. Our findings are the following. The frequency (wavelength) of both single- and two-photon systems is independent of whether the photon(s) is wavelike or in a WPS state, with the common fact being that the frequency (wavelength) of two photons as a whole entity is twice (half) that of a single photon. As for the interference-pattern visibility, it is always lower in the case of WPS than in the case of a wavelike state for a single photon as well as for two photons. Remarkably, with a given value of the control parameter, the interference visibility in the case of WPS is always higher in the single-photon scenario than in the two-photon one. Although here we are dealing with photons, the obtained results apply equally well to matter particles.

DOI: 10.1103/physreva.108.022223

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Simultaneous observation of the wave and particle natures of a quantum object under one experimental arrangement represents the latest development regarding wave-particle duality. In this work, we propose a simple scheme using linear-optics devices to observe either the particle nature or wave nature or the wave-particle superposition (WPS) of photons by controlling a relevant classical parameter. Our setup consists of two stages, the preparation and measurement stages, with the latter stage containing an additional classical variable whose value will be given only after the first stage in order to avoid any possible communication between the two stages and thus rule out the classical hidden-variable model. We not only develop the theory but also perform the corresponding experiments. The experimental observations perfectly agree with the theoretical predictions. Our findings are the following. The frequency (wavelength) of both single- and two-photon systems is independent of whether the photon(s) is wavelike or in a WPS state, with the common fact being that the frequency (wavelength) of two photons as a whole entity is twice (half) that of a single photon. As for the interference-pattern visibility, it is always lower in the case of WPS than in the case of a wavelike state for a single photon as well as for two photons. Remarkably, with a given value of the control parameter, the interference visibility in the case of WPS is always higher in the single-photon scenario than in the two-photon one. Although here we are dealing with photons, the obtained results apply equally well to matter particles.

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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.

A new scheme with very simple implementations giving obvious experimental results has been demonstrated to reveal the particle and wave duality of light. The scheme demonspates the wave property of light by coherent superposition and the particle property of light by random path selection though a 50/50 beam splitter. Preliminary experiments showed high interference visibility of 99% and the particle nature of light as high as 90% by using a highly attenuated pulsed laser as a single photon source. This scheme displays both the wave and particle nature of light though a simple experimental setup, which makes it a quite promising schem for revealing the property of light.

A single photon exhibits wave-particle duality in the Young's double-slit interferometer. The duality character-ized by an interference visibility

V

as the wave-like property and a which-path information

D

as the particle-like property has tradeoff relation

D^{2}+V^{2}\leq 1

known as complementarity [1]–[3]. There are a lot of studies about the complementary nature of photons from various viewpoints such as delayed-choice experiments, theoretical works related to the uncertainty principle, and so on. More recently, studies have expanded the concept of the wave-particle duality to higher-order interferometric scenarios, in which the input light includes two or more pho-tons [4], [5]. Despite having a long history, all previous studies have been related to phase correlation of optical states, which reason would be why the main focus in the first place is the investigation of the mysterious quantum nature of a photon, including the superposition principle.

Quantum physics, which describes the strange behavior of light and matter at the smallest scales, is one of the most successful descriptions of reality, yet it is notoriously inaccessible. Here we provide an approachable explanation of quantum physics using simple thought experiments. We derive all relevant quantum predictions using minimal mathematics, without introducing the advanced calculations that are typically used to describe quantum physics. We focus on the two key surprises of quantum physics, namely wave-particle duality, a term that was introduced to capture the fact that single quantum particles in some respects behave like waves and in other respects like particles, and entanglement, which applies to two or more quantum particles and brings out the inherent contradiction between quantum physics and seemingly obvious assumptions regarding the nature of reality. Following arguments originally made by John Bell and Lucien Hardy, we show that the so-called local hidden variables are inadequate at explaining the behavior of entangled quantum particles. This means that one either has to give up on hidden variables, i.e., the idea that the outcomes of measurements on quantum particles are determined before an experiment is actually carried out, or one has to relinquish the principle of locality, which requires that no causal influences should be faster than the speed of light and is a cornerstone of Einstein's theory of relativity. Finally, we describe how these remarkable predictions of quantum physics have been confirmed in experiments. We have successfully used the present approach in a course that is open to all undergraduate students at the University of Calgary, without any prerequisites in mathematics or physics.