Mesoscopic entanglement via a three-well Bose-Hubbard system and comparison with an optical beamsplitter

We compare and contrast the entangling properties of a three-well Bose-Hubbard model and an optical beamsplitter. The coupling between the different modes is linear in both cases, and we may identify two output modes. Obvious differences are that our Bose-Hubbard model, with only the middle well initially occupied, does not have a vacuum input port, there is no equivalent of a collisional, χ(3) nonlinearity with the beamsplitter, and the results of the Bose-Hubbard model are time dependent. In the non-interacting case, we obtain analytic solutions and show that, like a beamsplitter, the Bose-Hubbard system will not produce entanglement for classical initial states. With nonlinear collisional interactions added, we show that entanglement exists, but that its detection depends on the measures used. In no case did we find a degree of entanglement sufficient to display either the presence of the Einstein-Podolsky-Rosen paradox or the existence of Bell violations.