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arXiv:2001.05886 · Journal of Physics B Atomic Molecular and Optical Physics

Bell violations with entangled and non-entangled optical fields

J. Gonzales, P. Sánchez, V. Avalos, F. De Zela

Published Mar 13, 2019• 1 citation
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Abstract

Abstract We report Bell violations with classical light prepared in both entangled and non-entangled polarization-path, binary states. Our results show that violations of constraints such as the Bell–Clauser–Horn–Shimony–Holt inequality do not necessarily falsify local realism. Correlations in the realm of classical statistical optics, which are not of the Bell type, may lead to Bell violations.

DOI
10.1088/1361-6455/ab0f76

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Abstract We report Bell violations with classical light prepared in both entangled and non-entangled polarization-path, binary states. Our results show that violations of constraints such as the Bell–Clauser–Horn–Shimony–Holt inequality do not necessarily falsify local realism. Correlations in the realm of classical statistical optics, which are not of the Bell type, may lead to Bell violations.
Abstract We report experiments in which the Bell parameter S that enters the Clauser–Horne–Shimony–Holt inequality: ∣ S ∣ ≤ 2 , attains values ∣ S ∣ > 2 . In our experiments, we used two spatially separated optical beams, the electric fields of which were correlated to one another. The amount of correlation was quantified by the spectral degree of coherence η ( α , β ) . This quantity measures the correlation between fields that exist at two distant locations and whose respective polarizations are given in terms of angles α and β , which can be set independently from one another. Such a correlation qualifies for the construction of the Bell parameter S . By changing the amount of field correlation, we could cover a range that goes from ∣ S ∣ < 2 to ∣ S ∣ > 2 . Our experimental findings should provide useful material for the ongoing, theoretical discussions about the quantum–classical border.
Bell's theorem revealed the fundamental incompatibility between the predictions of quantum mechanics and local realism. Bell inequality violations have since demonstrated quantum nonlocality using photons and internal states of massive particles, but never using their motional states. Here we report the first Bell inequality violation in the motional states of massive particles. Using momentum-entangled pairs of metastable helium atoms manipulated by matter-wave interferometry, we measure a Clauser-Horne-Shimony-Holt (CHSH) Bell parameter of S=2.52±0.17S = 2.52 \pm 0.17S=2.52±0.17, violating the CHSH-Bell inequality (S≤2S \le 2S≤2). Our work completes a long-standing objective in quantum atom optics by extending Bell tests from internal quantum variables to the external degrees of freedom of massive particles, opening a new regime for exploring quantum nonlocality in matter waves and for investigating the interplay between quantum mechanics and gravity.
Conventional tests of Bell’s inequality rely on entangled photon pairs. Here, we replace entangled pairs with two independent photons of orthogonal polarization, and demonstrate that Bell’s inequality is still violated. Given the inherent local realism of independent photons, this experiment proves that Bell’s inequality cannot falsify the local realism of photons. We thus conjecture that the violation of Bell’s inequality by entangled photon pairs originates from their orthogonal polarizations, rather than the breakdown of local realism. To interpret this unexpected violation with independent photons, we further substitute the two photons with two monochromatic light beams, and calculate the transmittance correlation through polarizers via Malus’s law and Karl Pearson’s correlation formula. We show that this correlation also defies Bell’s inequality. Retracing the derivation of Bell’s inequality reveals its validity is restricted to binary events, which accounts for the observed violation with light beams. Finally, we propose a thought experiment involving gradual attenuation of light intensity down to the single-photon regime, and hypothesize that single-photon transmission through a polarizer does not constitute a binary event. This hypothesis provides a unified interpretation for both our experimental findings and all canonical Bell inequality tests reported to date.
Linearly polarized projections are the tacit means for performing Clauser–Horne–Shimony–Holt (CHSH) Bell-inequality tests using polarization-entangled photon pairs. The inequality is valid for all states on the Poincaré–Bloch sphere, but few laboratory studies have investigated violations with the full sphere. In this article, we explore the experimental verifications of the predicted violations of the CHSH inequality with Bell and non-Bell states with same and different linear and elliptically polarized basis states for each photon. We find that Bell states violate CHSH when using the same basis for both photons, regardless of their ellipticity, whereas they show no violations for photon projections in different bases. We found non-Bell maximally entangled states for which the converse is true.
The assumption of local realism imposes constraints, such as Bell inequalities, on quantities obtained from measurements. In recent years, various tests of local realism have gained popularity in undergraduate laboratories, giving students the exciting opportunity to experimentally contradict this philosophical assumption. The standard test of the CHSH (Clauser–Horne–Shimony–Holt) Bell inequality requires 16 measurements, whereas a test of Freedman's inequality requires only three measurements. The calculations required to test Freedman's inequality are correspondingly simpler and the theory is less abstract. We suggest that students may benefit from testing Freedman's inequality before proceeding to the CHSH inequality and other more complicated experiments. Our measured data violated Freedman's inequality by more than six standard deviations.