Generation of Schrodinger cats and entangled coherent states in the motion of a trapped ion by a dispersive interaction

A proposal for realizing one- and two-mode degenerate Raman coupled models, of the type proposed by Knight [Phys. Ser. T 12, 51 (1986)] in the context of quantum optics, for the motion of a trapped two-level lan, is presented. The interaction has a dispersive effect on the vibrational motion of the ion. For the one-mode case, an initial vibrational coherent state evolves into superpositions of coherent states (Schrodinger-cat states) correlated with thr internal states: of the ion. In the two-mode case, with initial coherent states in each mode, entanglements of coherent states between the modes correlated with the internal ionic states an obtained. Detection of such starts is briefly discussed.