Generation of Schrödinger cats and entangled coherent states in the motion of a trapped ionby a dispersive interaction

TLDR: In this paper, a degenerate Raman coupled model for the motion of a trapped two-level ion is presented, where an initial vibrational coherent state evolves into superpositions of coherent states correlated with the internal states of the ion.

Abstract: A proposal for realizing one- and two-mode degenerate Raman coupled models, of the type proposed by Knight [Phys. Scr. T 12, 51 (1986)] in the context of quantum optics, for the motion of a trapped two-level ion, 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 (Schr\"odinger-cat states) correlated with the 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 are obtained. Detection of such states is briefly discussed.