The mode-mode entanglement between trapped ions and cavity fields is
investigated in the dispersive regime. We show how a simple initial preparation
of Gaussian coherent states and a postselection may be used to generate
motional non-local mesoscopic states (NLMS) involving ions in different traps.
We also present a study of the entanglement induced by dynamical Stark-shifts
considering a cluster of N-trapped ions. In this case, all entanglement is due
to the dependence of the Stark-shifts on the ions' state of motion manifested
as a cross-Kerr interaction between each ion and the field.Comment: 10 pages, 5 figures, corrected typo