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Optics Communications

Proposal for a new test of Bell's inequality in an optical interference experiment

Z. Y. Ou, C.K. Hong, L. Mandeļ

Published Jul 1, 1988• 22 citations
Publisher

Abstract

A new experimental test of Bell's inequality is proposed, that depends on measurements of the two-photon detection probability as a function of position in an interference experiment. Although the experiment also makes use of polarizers, the polarization angles remain fixed and only the detector positions are varied. The proposed experiment differs from most previous tests of Bell's inequality in that the measured quantities are mutually exclusive probabilities.

DOI
10.1016/0030-4018(88)90371-9

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A new experimental test of Bell's inequality is proposed, that depends on measurements of the two-photon detection probability as a function of position in an interference experiment. Although the experiment also makes use of polarizers, the polarization angles remain fixed and only the detector positions are varied. The proposed experiment differs from most previous tests of Bell's inequality in that the measured quantities are mutually exclusive probabilities.
A new experimental test of one form of Bell’s inequality is proposed that involves measurement of the joint probability for the detection of two photons as a function of position. The two photons are produced In the process of spontaneous parametric downconversion of pump photons in a nonlinear medium and are allowed to interfere. Although polarizers are used also, the essential variables are the photon positions, which are orthogonal, unlike most polarization states. The probabilities that enter into the Bell inequality, therefore, relate to mutually exclusive events, unlike those in previous tests of locality.
Experimental tests of Bell's inequality allow to distinguish quantum mechanics from local hidden variable theories. Such tests are performed by measuring correlations of two entangled particles (e.g. polarization of photons or spins of atoms). In order to constitute conclusive evidence, two conditions have to be satisfied. First, strict separation of the measurement events in the sense of special relativity is required ("locality loophole"). Second, almost all entangled pairs have to be detected (for particles in a maximally entangled state the required detector efficiency is 82.8%), which is hard to achieve experimentally ("detection loophole"). By using the recently demonstrated entanglement between single trapped atoms and single photons it becomes possible to entangle two atoms at a large distance via entanglement swapping. Combining the high detection efficiency achieved with atoms with the space-like separation of the atomic state detection events, both loopholes can be closed within the same experiment. In this paper we present estimations based on current experimental achievements which show that such an experiment is feasible in future.
Experimental tests of Bell's inequality allow to distinguish quantum mechanics from local hidden variable theories. Such tests are performed by measuring correlations of two entangled particles (e.g. polarization of photons or spins of atoms). In order to constitute conclusive evidence, two conditions have to be satisfied. First, strict separation of the measurement events in the sense of special relativity is required ("locality loophole"). Second, almost all entangled pairs have to be detected (for particles in a maximally entangled state the required detector efficiency is 82.8%), which is hard to achieve experimentally ("detection loophole"). By using the recently demonstrated entanglement between single trapped atoms and single photons it becomes possible to entangle two atoms at a large distance via entanglement swapping. Combining the high detection efficiency achieved with atoms with the space-like separation of the atomic state detection events, both loopholes can be closed within the same experiment. In this paper we present estimations based on current experimental achievements which show that such an experiment is feasible in future.
In quantum mechanics, quantum entanglement is a physical phenomenon in which quantum particles (such as photons, electrons...) are connected to each other despite the large distances between them.This phenomenon occurs when a pair or group of particles is created in such a way that the quantum state of a particular particle cannot be described independently of other particles, even if there is a large distance between these particles.This research dealt with a computerized theoretical study of John Bell's theory to verify quantum entanglement, which was later tested by the French scientist Alain Aspect on photons of light, and the polarization angles of light were (0.45, 22.5, 67.5)This experiment was conducted and the results were recorded from the virtual interactive quantum entanglement laboratory (VIQEL), which is highly efficient in simulating the equations of quantum mechanics and probability functions, where we obtained accurate results by increasing the number of photonic pairs involved in the experiment and then the results were compared with the results of previous research by other scientists to prove that the main variable, which is the angle of polarization, does not affect the result when its value changes, but its effect lies in the difference in angles in the experiment, which in turn enhances From the theory of quantum entanglement.
As a criterion between quantum mechanics and local hidden-variable theories, the so-called Einstein-Podolsky-Rosen paradox is mainly tested in the form of the statistical correlation between polarizations of photons issuing from a cascade transition. It has been stated more than once that an improved form of the test would make use of polarizers, the orientation of which would change randomly in a time comparable with the time of flight of the two photons; the Bell locality assumption could then be replaced by a weaker assumption also considered by Bell: The Einstein principle of separability. However, to our knowledge, no workable experimental scheme has yet been proposed, and we believe the one described in this paper to be a workable one. After explaining the difference between the Bell locality assumption and the Einstein principle of separability, we briefly discuss the theoretical implications of the modified experiment. The overall scheme of the apparatus we are proposing is described, and the generalized Bell inequalities, modified for our case, are derived. As in previous experiments, supplementary assumptions are made in order to derive experimentally testable inequalities. Finally, we describe the device we intend to use to carry out the proposed scheme.
Most experimental tests of Bell inequalities have involved measurements of correlations between two photons. One of the first definitive experiments involved the linear polarization correlation between two photons in an atomic cascade of 200 Hg. That experiment is discussed in depth in this paper. The form of the initial state density matrix was a critical part of that experiment; and the experimental and theoretical determination of the density matrix, including finite solid-angle effects is discussed. However, all Bell inequality experiments to date have two widely recognized loopholes, detector efficiency and locality. This paper concludes with a very brief description of an experiment that will close both of these loopholes. In contrast to existing experiments with photons, this new test involves spin correlations between the nuclei of two 199 Hg atoms; it is an exact experimental realization of Bohm's version of the Einstein-Podolsky-Rosen gedankenexperiment.