Proposal for demonstrating a Bell inequality violation using condensate collisions

We propose and theoretically simulate an experiment for demonstrating a Bell inequality violation for massive particles in the matter-wave regime. The proposal is based on realizing an atom-optics analog of the Rarity-Tapster optical experiment: We use entangled atom pairs produced via atomic four-wave mixing in the collision of two dilute-gas Bose-Einstein condensates of metastable helium. This can be regarded as an extension of a recent successful experimental demonstration of violation of the Cauchy-Schwartz inequality in the same process [1]; the extension to a Bell-test is realized via an additional application of a sequence of two laser-induced Bragg pulses acting as a mirror ($\pi$-pulse) and a 50:50 beam splitter ($\pi/2$-pulse). The Bragg pulses implement a two-particle interferometry on the underlying Bell-state involving two pairs of correlated atoms with equal but opposite momenta. The collision dynamics and the sequence of Bragg pulses is simulated using a stochastic (positive-$P$) formulation of the Bogoliubov approach, and we predict the value of the CSHS-Bell parameter $S\simeq2.5$, showing a clear violation of the CSHS-Bell inequality bounded classically by $S\leq2$.\\[4pt] [1] K.V. Kheruntsyan \emph{et al.}, Phys. Rev. Lett. \textbf{108}, 260401 (2012).