A simple scheme for the generation of two different classes of bidimensional vibrational Schrödinger cat-like states of an isotropically trapped ion is presented. We show that by appropriately adjusting an easily controllable parameter having a clear physical meaning, the states prepared by our procedure are quantum superpositions of either vibrational axial angular momentum eigenstates or Fock states along two orthogonal directions.
Maniscalco, S., Messina, A., & Napoli, A. (2000). Preparation of macroscopically distinguishable superpositions of circular or linear oscillatory states of a bidimensionally trapped ion. Journal of Modern Optics, 47(12), 2113-2126. https://doi.org/10.1080/09500340008235134