Non-Gaussian states represent a powerful resource for quantum information
protocols in the continuous variables regime. Cat states, in particular, have
been produced in the motional degree of freedom of trapped ions by controlled
displacements dependent on the ionic internal state. An alternative method
harnesses the Kerr nonlinearity naturally existent in this kind of system. We
present detailed calculations confirming its feasibility for typical
experimental conditions. Additionally, this method permits the generation of
complex non-Gaussian states with negative Wigner functions. Especially,
superpositions of many coherent states are achieved at a fraction of the time
necessary to produce the cat state.Comment: 6 pages, 5 figure
