Preparation of Motional Mesoscopic Superpositions of Squeezed Coherent States of N Trapped Ions

A scheme is proposed to generate arbitrary, discretesuperpostions of squeezed coherent states of the squeezed center of mass of$N$ trapped ions along a straight line in phase space.The scheme is based on aresonant bichromatic excitation of each trapped ion that generatesdisplacement and squeezing in the vibrational motion conditioned to eachinternal state. In this paper, we also show that such a method can beused for the engineering of motional quantum states.