Preparation and light-mediated distribution of motional state entanglement- art. no. 012304

We describe and analyze numerically schemes (i) for entangling orthogonal m otional modes of one or a few harmonically trapped atoms or ions and (ii) f or transferring the entanglement from one of these local modes to a distant trapped atom (or atoms) via a light-mediated quantum-state transfer proced ure proposed in previous work [A.S. Parkins and H.J. Kimble, J. Opt. B: Qua ntum Semiclass. Opt. 1, 496 (1999)]. Possibilities arising from these schem es include the generation of an Einstein-Podolsky-Rosen state in the positi ons and momenta of distantly separated trapped atoms and the preparation of delocalized mesoscopic vibrational states.