Abstract
We consider a dispersive effective coupling between the internal energy electronic levels of an ion in a trap with its own center-of-mass motion. By using a procedure similar to the Ramsey oscillatory method, a quantum nondemolition experiment of the center-of-mass vibration population number is proposed. A procedure to generate squeezed states and Schrödinger-cat-like states that are superpositions of squeezed states is also suggested.