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