Experimental Test of Local Hidden-Variable Theories

We have measured the linear polarization correlation between the two photons from the $7{}_{}{}^3{}_{}{}^{}S_1^{}{}_{}{}^{}\to 6{}_{}{}^3{}_{}{}^{}P_1^{}{}_{}{}^{}\to 6{}_{}{}^1{}_{}{}^{}S_0^{}{}_{}{}^{}$ cascade of ${\mathrm{Hg}}^{200}$. The results were used to evaluate Freedman's version of the Bell inequality, $\delta <~0$. Our result is ${\delta }_{\exp }=+0.046\mathrm{}\pm 0.014$, in clear violation of the inequality and in excellent agreement with the quantum mechanical prediction, ${\delta }_{\mathrm{QM}}=+0.044\mathrm{}\pm 0.007$. An important feature of the experiment was the explicit measurement of the initial density matrix for the cascading atoms.