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Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields

Proposed atomic cascade experimental test of symmetric local hidden-variables theories

Emilio Santos

Published Jul 15, 1987• 5 citations
Publisher

Abstract

The proposal is made of replacing the usual auxiliary assumptions needed for the derivation of testable Bell inequalities by an assumption resting only on symmetry considerations. It is shown that reliable atomic cascade tests of symmetric local hidden-variables theories should combine high statistics, cascades of type 0\ensuremath{\rightarrow}1\ensuremath{\rightarrow}0, and calcite polarizers. The three conditions have been achieved in experiments already performed, but never before simultaneously.

DOI
10.1103/physrevd.36.636

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Europhysics Letters (EPL)•Mar 1, 1987•2 citations
The proposal is made of replacing the usual auxiliary assumptions needed for the derivation of testable Bell inequalities by an assumption resting only on symmetry considerations. It is shown that reliable atomic cascade tests of symmetric local hidden-variables theories should combine high statistics, cascades of type 0\ensuremath{\rightarrow}1\ensuremath{\rightarrow}0, and calcite polarizers. The three conditions have been achieved in experiments already performed, but never before simultaneously.
Bell's inequalities cannot be violated in atomic-cascade experiments, even with ideal apparatus, due to the three-body character of the atomic decay. Here we propose a new experiment that would block this loophole by means of a suitable selection of an ensemble of photon pairs. A threshold value for the quantum efficiency is found which may allow the discrimination between quantum mechanics and local-hidden-variables theories. Experimental requirements for performing such a test are discussed.
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.
We have measured the linear polarization correlation between the two photons from the $7^{3}S_{1}\ensuremath{\rightarrow}6^{3}P_{1}\ensuremath{\rightarrow}6^{1}S_{0}$ cascade of Hg200{\mathrm{Hg}}^{200}Hg200. The results were used to evaluate Freedman's version of the Bell inequality, $\ensuremath{\delta}<~0$. Our result is ${\ensuremath{\delta}}_{\mathrm{exp}}=+0.046\ifmmode\pm\else\textpm\fi{}0.014$, in clear violation of the inequality and in excellent agreement with the quantum mechanical prediction, ${\ensuremath{\delta}}_{\mathrm{QM}}=+0.044\ifmmode\pm\else\textpm\fi{}0.007$. An important feature of the experiment was the explicit measurement of the initial density matrix for the cascading atoms.