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Journal of Physics B Atomic Molecular and Optical Physics

Experimental Bell violations with classical, non-entangled optical fields

J. Gonzales, P. Sánchez, Diego Barberena, Yonny Yugra, Rafael Caballero, F. De Zela

Published Dec 13, 2017• 3 citations

Abstract

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.

DOI: 10.1088/1361-6455/aaa185

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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.

Abstract In this paper, we report an experimental activity suitable for undergraduate students that makes them question their ideas about locality and realism. The experiment here reported complements previous educational approaches to Bell inequalities, since the usually called S function, that quantifies correlations, is mapped by measuring it for different detection angles. The students themselves worked in a pre-aligned setup that allowed them to test and violate the Clauser–Horne–Shimony–Holt–Bell inequality for two distant photons entangled in polarization.

In analogy with quantum optics it is possible to impose nonseparability between different degrees of freedom of an optical beam. The resulting correlations between these degrees of freedom can be investigated with correlations functions traditionally employed in quantum mechanics, such as the well-known Clauser-Horne-Shimony-Holt (CHSH) correlation function. In this paper we present results achieving a maximal violation of Tsirelson's bound on CHSH correlations between spatial and polarization degrees of freedom of classical (Maxwell) fields. We describe the theoretical method, based on the realization of a nonunitary gate, and then proceed to its experimental implementation carried out with classical optical techniques. Our approach relies on the realization at the level of classical Maxwell fields of a so-called POVM (positive operator valued measure) which is traditionally discussed in the realm of quantum physics.

The growing recognition that entanglement is not exclusively a quantum property, and does not even originate with Schrödinger's famous remark about it [Proc. Camb. Phil. Soc. 31, 555 (1935)], prompts examination of its role in marking the quantum-classical boundary. We have done this by subjecting correlations of classical optical fields to new Bell-analysis experiments, and report here values of the Bell parameter greater than

{\cal B} = 2.54

. This is many standard deviations outside the limit

{\cal B} = 2

established by the Clauser-Horne-Shimony-Holt (CHSH) Bell inequality [Phys. Rev. Lett. 23, 880 (1969)], in agreement with our theoretical classical prediction, and not far from the Tsirelson limit

{\cal B} = 2.828...

. These results cast a new light on the standard quantum-classical boundary description, and suggest a reinterpretation of it.

We demonstrate hybrid entanglement of photon pairs via the experimental violation of a Bell inequality with two different degrees of freedom (DOF), namely, the path (linear momentum) of one photon and the polarization of the other photon. Hybrid entangled photon pairs are created by spontaneous parametric down conversion and coherent polarization to path conversion for one photon. For that photon, path superposition is analyzed, and polarization superposition for its twin photon. The correlations between these two measurements give an

S

parameter of $S=2.653\ifmmode\pm\else\textpm\fi{}0.027$ in a Clauser-Horne-Shimony-Holt inequality and thus violate local realism for two different DOF by more than 24 standard deviations. This experimentally supports the idea that entanglement is a fundamental concept which is indifferent to the specific physical realization of Hilbert space.