Spin Correlations of Strongly Interacting Massive Fermion Pairs as a Test of Bell’s Inequality

We report the results of the first-time test of the local hidden variable theories (Bell-Clauser-Horne-Shimony-Holt) involving strongly interacting pairs of massive spin $1/2$ hadrons from the decay of short-lived ($\tau <{10}^{-21}\sec $) ${}^2\mathrm{He}$ spin-singlet state, populated in the nuclear reaction ${}^2\mathrm{H}+{}^1\mathrm{H}\to {}^2\mathrm{He}+n$. The novel features of this experiment are (a) the use of an “event-ready” detector of nearly 100% efficiency to prepare an unbiased sample and (b) a focal-plane polarimeter of full $2\pi \mathrm{sr}$ acceptance with a random “post selection” of the reference axes. The spin-correlation function is deduced to be $S_{\exp }(\pi /4)=2.83\pm {0.24}_{\mathrm{stat}}\pm {0.07}_{\mathrm{sys}}$. This result is in agreement with nonlocal quantum mechanical prediction and it violates the Bell-CHSH inequality of $|S|\le 2$ at a confidence level of 99.3%.

Figure 1

A schematic diagram of the experimental layout. Deuterons interact with protons in liquid hydrogen (${}^1\mathrm{H}$) target. The proton pairs (${}^2\mathrm{He}$) are momentum selected by SMART spectrometer, which are subsequently tracked by the “event-ready” detector (MWDC1 and HOD1). The spin analysis of the protons was then achieved by the EPOL polarimeter, where graphite block is the analyzer and the MWDC2, MWDC3, HOD2, and HOD3 are correlation detectors.

Figure 2

The missing energy of two protons ($E_{\mathrm{rel}}$) in the ${}^1\mathrm{H}(d,{}^2\mathrm{He})$ reaction. Events in the green shaded area ($|E_x(\mathrm{MeV})|<1\mathrm{MeV}$) are selected for further analyses. The inset shows the relative kinetic energies ($E_{\mathrm{rel}}$) of the events in green shaded area. Proton pairs $E_{\mathrm{rel}}<1\mathrm{MeV}$ (pink histogram) are finally selected for correlation analyses. Suppression of the events at high measured $E_{\mathrm{rel}}$ is mainly due to the finite momentum and angular acceptances of SMART.

Figure 3

A conceptual view of the spin-correlation measurements by EPOL (Fig. 1). Correlated proton pairs are scattered by a pair of spin-analyzer targets (graphite block). In each polarimeter, scattered protons are detected with detector $L$ or $R$. ${\overrightarrow{n}}^{(i)}$ ($i=1$, 2) denotes the normal of the scattering plane of each polarimeter. The role of the left-right detectors for both protons is served by the MWDC2, MWDC3 and HOD2, HOD3 assembly shown in Fig. 1. The inset shows virtual sectors of angular ranges $8°\le \theta \le 20°$ and $\Delta \varphi =134°$, used in the polarization analyses. The angles are with respect to reference axes ${\overrightarrow{n}}^{(i)}$ ($i=1$, 2).

Figure 4

Plot of the spin-correlation function $S(\Phi )$ vs $\Phi$. Solid circles are the experimental result $S_{\exp }(\Phi )$ derived from the same data set. Each error shown as blue shaded area is correlated. See text for details.