Generation of mesoscopic superpositions of two squeezed states of motion for a trapped ion

We propose a scheme to generate mesoscopic superpositions of two squeezed states of motion using a highly anisotropic two-dimensional trap in which the ion's motion is tightly bound in the Y direction. In our scheme, the ion is driven multichromatically by three codirectional laser beams along the X axis, as well as a resonant laser beam along the Y axis. We show that, with the appropriate chosen initial states, the desired states of motion are realized in the X direction when the system reaches its steady state, which is indicated by the extinction of the fluorescence from the ion.