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Physical Review Letters

Experimental Test of Local Hidden-Variable Theories

Edward S. Fry, Randall C. Thompson

Published Aug 23, 1976• 405 citations
Publisher

Abstract

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 ${\mathrm{Hg}}^{200}$. 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.

DOI
10.1103/physrevlett.37.465

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We have measured the linear polarization correlation between the two photons from the 73S1\ensuremath→63P1\ensuremath→61S07^{3}S_{1}\ensuremath{\rightarrow}6^{3}P_{1}\ensuremath{\rightarrow}6^{1}S_{0}73S1​\ensuremath→63P1​\ensuremath→61S0​ cascade of Hg200{\mathrm{Hg}}^{200}Hg200. The results were used to evaluate Freedman's version of the Bell inequality, \ensuremathδ< 0\ensuremath{\delta}<~0\ensuremathδ< 0. Our result is \ensuremathδexp=+0.046\ifmmode±\else\textpm\fi0.014{\ensuremath{\delta}}_{\mathrm{exp}}=+0.046\ifmmode\pm\else\textpm\fi{}0.014\ensuremathδexp​=+0.046\ifmmode±\else\textpm\fi0.014, in clear violation of the inequality and in excellent agreement with the quantum mechanical prediction, \ensuremathδQM=+0.044\ifmmode±\else\textpm\fi0.007{\ensuremath{\delta}}_{\mathrm{QM}}=+0.044\ifmmode\pm\else\textpm\fi{}0.007\ensuremathδQM​=+0.044\ifmmode±\else\textpm\fi0.007. An important feature of the experiment was the explicit measurement of the initial density matrix for the cascading atoms.
We have measured the linear polarization correlation of the photons emitted in a radiative atomic cascade of calcium. A high-efficiency source provided an improved statistical accuracy and an ability to perform new tests. Our results, in excellent agreement with the quantum mechanical predictions, strongly violate the generalized Bell's inequalities, and rule out the whole class of realistic local theories. No significant change in results was observed with source-polarizer separations of up to 6.5 m.
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.
A family of theories called "deterministic local hidden variable theories" (DLHV) is characterized and their consequences are investigated for an experimentally realistic situation. An experiment on the polarization correlation of optical photon pairs emitted in certain atomic cascades is proposed as a test of the family of DLHV theories. The model-independent hidden variable predictions applicable to the realistic experimental arrangement are obtained by a generalization of a previous theorem of Bell. Quantum mechanical predictions for the same experimental situation are calculated for two cases: a J = 0 + J = 1 + J = 0 and a J = 1 + J = 1 + J = 0 electric dipole cascade. For both cascades, it is shown that the quantum mechanical and the DLHV predictions are in sufficient disagreement for an actual experimental test to be possible. Restrictions on detector solid angle and polarizer efficiency, necessary to obtain a decisive experiment, are explicitly given. The Einstein, Podolsky, and Rosen argument for the existence of a DLHV theory is reviewed.
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.