Non-classical states of motion in an ion trap

We show that a single two-level ion trapped in a harmonic potential and laser cooled at the node of a standing wave can be described by the damped Jaynes-Cummings Model, in the appropriate limits. We propose a scheme for the preparation of Fock states of motion of the trapped ion based on the observation of quantum jumps. We also present a scheme for preparing squeezed states of motion based on the multichromatic excitation of the ion.