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Physical Review Letters

Experimental Investigation of a Polarization Correlation Anomaly

John F. Clauser

Published May 24, 1976• 304 citations
Publisher

Abstract

An experiment was performed to search for the anomalous two-photon polarization correlation observed earlier by Holt and Pipkin using a cascade of atomic mercury. The experiment is a sensitive test of various aspects of the foundations of quantum mechanics. Although the present experimental arrangement differed only slightly from theirs, the anomalous results were not observed.

DOI
10.1103/physrevlett.36.1223

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An experiment was performed to search for the anomalous two-photon polarization correlation observed earlier by Holt and Pipkin using a cascade of atomic mercury. The experiment is a sensitive test of various aspects of the foundations of quantum mechanics. Although the present experimental arrangement differed only slightly from theirs, the anomalous results were not observed.
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.
We analyze anomalies in data to test the violation of Bell's inequality for the EPR-Bohm experiment. We found that the experimental correlations for photon polarization have an intriguing property. In the experimental data there are visible non-negligible deviations of probabilities $P_{++}^{\rm{exp}}(α, β), P_{+-}^{\rm{exp}}(α, β), P_{-+}^{\rm{exp}}(α, β), P_{--}^{\rm{exp}}(α, β) $ from the predictions of quantum mechanics, namely, P++(α,β)=P−−(α,β)=1/2cos⁡2(α−β)P_{++}(α, β)=P_{--}(α, β)= {1/2}\cos^2(α-β)P++​(α,β)=P−−​(α,β)=1/2cos2(α−β) and P+−=P−+(α,β)=1/2sin⁡2(α−β).P_{+-}=P_{-+}(α, β)={1/2}\sin^2(α-β).P+−​=P−+​(α,β)=1/2sin2(α−β). However, in some mysterious way those deviations compensate each other and finally the correlation Eexp(α,β)=P++exp(α,β)−P+−exp(α,β)−P−+exp(α,β)+P−−exp(α,β)E^{\rm{exp}}(α, β)= P_{++}^{\rm{exp}}(α, β)- P_{+-}^{\rm{exp}}(α, β)- P_{-+}^{\rm{exp}}(α, β)+ P_{--}^{\rm{exp}}(α, β)Eexp(α,β)=P++exp​(α,β)−P+−exp​(α,β)−P−+exp​(α,β)+P−−exp​(α,β) is in the complete agreement with the QM-prediction, namely, E(α,β)=P++(α,β)−P+−(α,β)−P−+(α,β)+P−−(α,β)=cos⁡2(α−β).E(α, β)= P_{++}(α, β)- P_{+-}(α, β)- P_{-+}(α, β)+ P_{--}(α, β)= \cos 2(α-β).E(α,β)=P++​(α,β)−P+−​(α,β)−P−+​(α,β)+P−−​(α,β)=cos2(α−β). Therefore such anomalies play no role in the Bell's inequality framework. Nevertheless, other linear combinations of experimental probabilities do not have such a compensation property. There can be found non-negligible deviations from predictions of quantum mechanics. Thus neither classical nor quantum model can pass the whole family of statistical tests given by all possible linear combinations of the EPR-Bohm probabilities. Does it mean that both models are wrong?
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.
The Paper first summarizes fundamental aspects and results of the quantum electrodynamical theory of the two-photon radiationfromthe decay of the metastable 2 2 S 1/2 atomic hydrogen state. After a brief description of the second improved Stirling two-photon coincidence experiment polarization correlations of the two-photon decay are described in which both two or three linear polarizers are applied in order to test predictions of such correlations based upon quantum mechanics and local realistic theories (i.e., Einstein-Podolsky-Rosen type experiments). It is particularly noticeable that the three-polarizer coincidence measurement provided the largest difference (about 40%) between the Bell limits of local realistic theories and quantum mechanics so far. Apart from confirming in addition the correlations of right-right and left-left circularly polarized two-photon correlations a new type of coherence analysis of the two-photon radiation has been carried out experimentally and theoretically. A result of it is the measured coherence time of τ coh = 1.2 · 10 −15 s and coherence length of l coh = c · τ coh = 350 nm of the two-photon emission. By applying a theoretical model of the two-photon radiation linked to cascade transitions the coherence length can be estimated to l coh ≈ 100 nm in agreement by order of magnitude with the experimental data.