Bell test for the free motion of material particles

We present a scheme to establish non-classical correlations in the motion of two macroscopically separated massive particles without resorting to entanglement in their internal degrees of freedom. It is based on the dissociation of a diatomic molecule with two temporally separated Feshbach pulses generating a motional state of two counter-propagating atoms that is capable of violating a Bell inequality by means of correlated single particle interferometry. We evaluate the influence of dispersion on the Bell correlation, showing it to be important but manageable in a proposed experimental setup. The latter employs a molecular BEC of fermionic Lithium atoms, uses laser-guided atom interferometry, and seems to be within the reach of present-day technology.