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Physical Review Research

Quantum duality: A source point of view

Xiao‐Feng Qian, G. S. Agarwal

Published Feb 4, 2020• 29 citations
Publisher

Abstract

Two-path interference is the dominant scenario of studying and testing quantum duality. It is an equivalent process of regenerating a single quantum particle by a two-center source. The authors show that the intrinsic properties of such a two-center source unexpectedly controls the generated quantum particle's wave-particle duality coherence through a compact Pythagorean relation

DOI
10.1103/physrevresearch.2.012031

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Two-path interference is the dominant scenario of studying and testing quantum duality. It is an equivalent process of regenerating a single quantum particle by a two-center source. The authors show that the intrinsic properties of such a two-center source unexpectedly controls the generated quantum particle's wave-particle duality coherence through a compact Pythagorean relation
We study wave-particle duality by exploring for the first time effects of a quantum object's source. A single photon emitted from a pair of nonlocally entangled two-level atoms is specifically analyzed. Surprisingly, duality is found to be a conditional phenomenon depending on the photon's atomic source. It can be tuned maximum, medium, and even minimum (completely absent) by the atomic state purity through an exact quadratic relation that can be called Duality Pythagorean Theorem. The analysis shows a new way of investigating duality by accounting how the single quantum object is created. The result sheds a new light on the fundamental understanding of the completeness of wave-particle duality, and can be tested in various practical physical systems.
The wave-particle duality of quantum objects has been a center concept in quantum mechanics since its birth. For the two-path or two-slit experiment, the dual nature of quantum matter has been well studied in various systems. To rule out the interpretation of quanta knowing the measurement setting it will be confronted, Wheeler proposed the famous delayed-choice gedanken experiment [1] , which is an ideal platform to test the intrinsic characters of wave-particle duality. However, all these experiments to date have been focused on the two-path case.
To test the principle of complementarity and wave-particle duality quantitatively, we need a quantum composite system that can be controlled by experimental parameters. Here, we demonstrate that a double-path interferometer consisting of two parametric downconversion crystals seeded by coherent idler fields, where the generated coherent signal photons are used for quantum interference and the conjugate idler fields are used for which-path detectors with controllable fidelity, is useful for elucidating the quantitative complementarity. We show that the source purity μsμ_sμs​ is tightly bounded by the entanglement measure EEE by the relation μs=1−E2μ_s=\sqrt{1-E^2 }μs​=1−E2​ and the visibility VVV and detector fidelity FFF determine the coherence of the quantons, i.e., C=V∣F∣C = V|F|C=V∣F∣. The quantitative complementarity of the double-path interferometer we developed recently is explained in terms of the quanton-detector entanglement or quanton source purity that are expressed as functions of injected seed photon numbers. We further suggest that the experimental scheme utilizing two stimulated parametric downconversion processes is an ideal tool for investigating and understanding wave-particle duality and complementarity quantitatively.
The wave-particle duality that manifests in the Young's double-slit interferometry satisfying the well known Englert-Greenberger-Yasin inequality has recently been shown to obey a universal triality relation involving coherence, predictability and rather surprisingly entanglement. In the present work, we explicitly demonstrate the persistence of the triality relation in the quantum induced coherence interferometer and the classical configuration recovers the well known duality inequality. Furthermore, we explore the origin of coherence and entanglement, in the induced coherence interferometer, and means to control them. We show that path indistinguishability (or intrinsic indistinguishability of the sources) in our setup plays a complementary role in influencing both interference and entanglement. We bring out manifestly the nature of coherence in both classical and quantum versions of induced coherence interferometers.
The wave-particle duality is the main point of demarcation between quantum and classical physics, and is the quintessential mystery of quantum mechanics. Young's two-slit interference experiment is the arch prototype of actual and gedanken experiments used as a testing ground of this duality. Quantum mechanics predicts that any detector capable of determining the path taken by a particle through one or the other of a two-slit plate will destroy the interference pattern. We will examine both the experimental and theoretical attempts to test this assertion, including a new kind of experiment, and to grasp the underlying truth behind this mystery from the earliest days to the present. Where positions differ, the views of both sides are presented in a balanced approach.
The concepts of geometric phase and wave-particle duality are interlinked to several fundamental phenomena in quantum physics, but their mutual relationship still forms an uncharted open problem. Here we address this question by studying the geometric phase of a photon in double-slit interference. We especially discover a general complementarity relation for the photon that connects the geometric phase it exhibits in the observation plane and the which-path information it encases at the two slits. The relation can be seen as quantifying wave-particle duality of the photon via the geometric phase, thus corroborating a foundational link between two ubiquitous notions in quantum physics research.