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Chinese Physics B

Wave–particle duality in a Raman atom interferometer

Aiai Jia, Jun Jie Yang, Shuhua Yan, Qingqing Hu, Yukun Luo, Shi‐Yao Zhu

Published Aug 1, 2015• 1 citation
Publisher

Abstract

We theoretically investigate the wave–particle duality based on a Raman atom interferometer, via the interaction between the atom and Raman laser, which is similar to the optical Mach–Zehnder interferometer. The wave and which-way information are stored in the atomic internal states. For the φ − π − π /2 type of atom interferometer, we find that the visibility ( V ) and predictability ( P ) still satisfy the duality relation, P 2 + V 2 ≤ 1.

DOI
10.1088/1674-1056/24/8/080302

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The wave–particle duality of a single particle with an n-dimensional internal degree of freedom is re-examined theoretically in a Mach–Zehnder interferometer. The famous duality relation D2+V2≤ 1 is always valid in this situation, where D is the distinguishability and V is the visibility. However, the sum of the particle information and the wave information,D2+V2, can be smaller than one for the input of a pure state if this initial pure state includes the internal degree of freedom of the particle, while the quantity D2+V2is always equal to one when the internal degree of freedom of the particle is excluded.
The wave—particle duality of a single particle with an n-dimensional internal degree of freedom is re-examined theoretically in a Mach—Zehnder interferometer. The famous duality relation D 2 + V 2 ≤ 1 is always valid in this situation, where D is the distinguishability and V is the visibility. However, the sum of the particle information and the wave information, can be smaller than one for the input of a pure state if this initial pure state includes the internal degree of freedom of the particle, while the quantity D 2 + V 2 is always equal to one when the internal degree of freedom of the particle is excluded.
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.
A distinct method to show a quantum object behaving both as wave and as particle is proposed and described in some detail. We make a systematic analysis using the elementary methodology of quantum mechanics upon Young's two-slit interferometer and the Mach—Zehnder two-arm interferometer with the focus placed on how to measure the interference pattern (wave nature) and the which-way information (particle nature) of quantum objects. We design several schemes to simultaneously acquire the which-way information for an individual quantum object and the high-contrast interference pattern for an ensemble of these quantum objects by placing two sets of measurement instruments that are well separated in space and whose perturbation of each other is negligibly small within the interferometer at the same time. Yet, improper arrangement and cooperation of these two sets of measurement instruments in the interferometer would lead to failure of simultaneous observation of wave and particle behaviors. The internal freedoms of quantum objects could be harnessed to probe both the which-way information and the interference pattern for the center-of-mass motion. That quantum objects can behave beyond the wave—particle duality and the complementarity principle would stimulate new conceptual examination and exploration of quantum theory at a deeper level.