Preparation of macroscopically distinguishable superpositions of circular or linear oscillatory states of a bidimensionally trapped ion

A simple scheme for the generation of two different classes of bidimensiona l vibrational Schrodinger cat-like states of an isotropically trapped ion i s presented. We show that by appropriately adjusting an easily controllable parameter having a clear physical meaning, the states prepared by our proc edure are quantum superpositions of either vibrational axial angular moment um eigenstates or Fock states along two orthogonal directions.