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Physical Review A

Using the Pauli exclusion principle to exhibit local-realism violations in overlapping interferometers

Bernard Yurke, David Stoler

Published Mar 1, 1993• 12 citations
Publisher

Abstract

Recently Hardy has exhibited a striking new violation of local realism that occurs in a pair of interferometers that have been interconnected so that knowledge about the path chosen by a particle in one interferometer conveys some information about the path or paths chosen by the particle in the other interferometer. It has been demonstrated that particle annihilation and a two-photon interference effect can be exploited to give rise to this local realism violation. Here we show that in the case of fermion interferometers the Pauli exclusion principle can be exploited to give rise to this effect.

DOI
10.1103/physreva.47.1704

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Recently Hardy has exhibited a striking new violation of local realism that occurs in a pair of interferometers that have been interconnected so that knowledge about the path chosen by a particle in one interferometer conveys some information about the path or paths chosen by the particle in the other interferometer. It has been demonstrated that particle annihilation and a two-photon interference effect can be exploited to give rise to this local realism violation. Here we show that in the case of fermion interferometers the Pauli exclusion principle can be exploited to give rise to this effect.
A pair of interferometers can be coupled by allowing one path from each to overlap such that if the particles meet in this overlap region, they annihilate. It was shown by one of us over 30 years ago that such annihilation-coupled interferometers can exhibit apparently paradoxical behavior. More recently, Bose et al. [Phys. Rev. Lett. 119, 240401 (2017)] and Marletto et al. [Phys. Rev. Lett. 119, 240402 (2017)] have considered a pair of interferometers that are phase coupled (where the coupling is through gravitational interaction). In this case one path from each interferometer undergoes a phase-coupling interaction. We show that these phase-coupled interferometers exhibit the same apparent paradox as the annihilation-coupled interferometers, though in a curiously dual manner.
We show that it is, in principle, possible to perform local-realism violating experiments of the Hardy type in which only position and momentum measurements are made on two particles emanating from a common source. In the optical domain, homodyne detection of the in-phase and out-of-phase amplitude components of an electromagnetic field is analogous to position and momentum measurement. Hence, local realism violations of the Hardy type are possible in optical systems employing only homodyne detection.
Quantum systems in Fock states do not have a phase. When two or more Bose-Einstein condensates are sent into interferometers, they nevertheless acquire a relative phase under the effect of quantum measurements. The usual explanation relies on spontaneous symmetry breaking, where phases are ascribed to all condensates and treated as unknown classical quantities. However, this image is not always sufficient: when all particles are measured, quantum mechanics predicts probabilities that are sometimes in contradiction with it, as illustrated by quantum violations of local realism. In this letter, we show that interferometers can be used to demonstrate a large variety of violations with an arbitrarily large number of particles. With two independent condensates, we find violations of the BCHSH inequalities, as well as new N-body Hardy impossibilities. With three condensates, we obtain new GHZ (Greenberger, Horne and Zeilinger) type contradictions.
Quantum systems in Fock states do not have a phase. When two or more Bose-Einstein condensates are sent into interferometers, they nevertheless acquire a relative phase under the effect of quantum measurements. The usual explanation relies on spontaneous symmetry breaking, where phases are ascribed to all condensates and treated as unknown classical quantities. However, this image is not always sufficient: when all particles are measured, quantum mechanics predicts probabilities that are sometimes in contradiction with it, as illustrated by quantum violations of local realism. In this Rapid communication, we show that interferometers can be used to demonstrate a large variety of violations with an arbitrarily large number of particles. With two independent condensates, we find violations of the Bell-Clauser-Horne-Shimony-Holt inequalities, as well as NNN-body Hardy impossibilities. With three condensates, we obtain Greenberger-Horne-Zeilinger-type contradictions.
We analyze the interference of individual photons in two overlapping Mach–Zehnder interferometers joined via a common beam splitter. We show how two kinds of interference effects—single-photon Mach–Zehnder interference and two-photon Hong–Ou–Mandel interference—interfere with one another, partially canceling each other out. This configuration illustrates how quantum effects can combine nontrivially and, moreover, emphasizes that quantum interference happens at measurement. This work can serve as a bridge to more advanced quantum mechanical concepts, such as testing the predictions of quantum mechanics vs local realism.