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Physical Review A

Amplification and the wave-particle duality

R. C. Swanson, John L. Carlsten

Published Mar 1, 1993• 0 citations
Publisher

Abstract

By utilizing amplifiers in a modified interferometer, both particlelike and wavelike characteristics of single input photons are analyzed theoretically. Quantum theory predicts that proposed measurements on the amplified field will indicate that the single input photon exhibits extremes of both wavelike and particlelike characteristics. The evidence for wavelike behavior is fringe visibility at the output of the interferometer. Anticorrelation between the outputs of the two legs of the interferometer provides the evidence for particlelike behavior. Although quantum noise degrades both the particle-sensitive and the wave-sensitive measurement, no trade-off between the wavelike and the particlelike characteristics takes place. Complementarity, however, is maintained by the quantum noise added during amplification.

DOI
10.1103/physreva.47.2211

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By utilizing amplifiers in a modified interferometer, both particlelike and wavelike characteristics of single input photons are analyzed theoretically. Quantum theory predicts that proposed measurements on the amplified field will indicate that the single input photon exhibits extremes of both wavelike and particlelike characteristics. The evidence for wavelike behavior is fringe visibility at the output of the interferometer. Anticorrelation between the outputs of the two legs of the interferometer provides the evidence for particlelike behavior. Although quantum noise degrades both the particle-sensitive and the wave-sensitive measurement, no trade-off between the wavelike and the particlelike characteristics takes place. Complementarity, however, is maintained by the quantum noise added during amplification.
One of the milestones of quantum mechanics is Bohr's complementarity principle. It states that a single quantum can exhibit a particlelike ororor a wavelike behavior, but never both at the same time. These are mutually exclusive and complementary aspects of the quantum system. This means that we need distinct experimental arrangements in order to measure the particle or the wave nature of a physical system. One of the most known representations of this principle is the single-photon Mach-Zehnder interferometer. When the interferometer is closed an interference pattern is observed (wave aspect of the quantum) while if it is open, the quantum behaves like a particle. Here, using a molecular quantum information processor and employing nuclear magnetic resonant (NMR) techniques, we analyze the quantum version of this principle by means of an interferometer that is in a quantum superposition of being closed and open, and confirm that we can indeed measure both aspects of the system with the same experimental apparatus. More specifically, we observe with a single apparatus the interference between the particle and the wave aspects of a quantum system.
The complementarity of a single photon's particlelike and wavelike behaviors can be described by the inequality ${D}^{2}+{V}^{2}\ensuremath{\le}1$, with DDD being the path distinguishability and VVV being the fringe visibility. In this paper, we generalize this duality relation to the multiphoton case, where two concepts, higher-order distinguishability and higher-order fringe visibility, are introduced to quantify the higher-order particlelike and wavelike behaviors of multiphotons.
We present a study of the relation between wave-particle duality and quantum uncertainty in a two-path interferometer and derive equalities and inequalities involving the visibility (representing wave-like behavior), the predictability (representing particle-like behavior), and their variances. We experimentally demonstrate that, for a single photon in a Mach-Zehnder interferometer, these quantities are related via an equation that connects both duality and uncertainty. This relation holds for the single-photon source prepared either in a pure state or a mixed state.
A single photon exhibits wave-particle duality in the Young's double-slit interferometer. The duality character-ized by an interference visibilityVVVas the wave-like property and a which-path informationDDDas the particle-like property has tradeoff relationD2+V2≤1D^{2}+V^{2}\leq 1D2+V2≤1known 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.
One of the most remarkable features of quantum physics is that attributes of quantum objects, such as the wavelike and particlelike behaviors of single photons, can be complementary in the sense that they are equally real but cannot be observed simultaneously. Quantum measurements, serving as windows providing views into the abstract edifice of quantum theory, are basic tools for manifesting the intrinsic behaviors of quantum objects. However, a quantitative formulation of complementarity that highlights its manifestations in general measurement scenarios remains elusive. Here we develop a general framework for demonstrating quantum complementarity in the form of information exclusion relations (IERs), which incorporates the wave-particle duality relations as particular examples. Moreover, we explore the applications of our theory in entanglement detection and elucidate that our IERs lead to an extended form of entropic uncertainty relations, providing insights into the connection between quantum complementarity and the preparation uncertainty.
One of the most puzzling consequences of interpreting quantum mechanics in terms of concepts borrowed from classical physics, is the so-called wave-particle duality. Usually, wave-particle duality is illustrated in terms of complementarity between path distinguishability and fringe visibility in interference experiments. In this work, we instead propose a new type of complementarity, that between the continuous nature of waves and the discrete character of particles. Using the probabilistic methods of quantum field theory, we show that the simultaneous measurement of the wave amplitude and the number of photons in the same beam of light is, under certain circumstances, prohibited by the laws of quantum mechanics. Our results suggest that the concept of “interferometric duality'' could be eventually replaced by the more general one of “continuous-discrete duality''.