In this contribution we investigate the interaction of a single ion in a trap with laser beams. Our approach, based on unitary transformating the Hamiltonian, allows its exact diagonalization without performing the Lamb-Dicke approximation. We obtain a transformed Jaynes-Cummings type Hamiltonian, and we demonstrate the existence of super-revivals in that system.Comment: 8 pages, 2 figures, in RevTex. To appear in Phys.Rev. A 59 (01 March 1999

We have found that, in the intensity-dependent Jaynes-Cummings model, a field initially prepared in a statistical mixture of two coherent states, |α and | − α , evolves toward a pure state. We have also shown that an even-coherent state turns periodically a into rotated odd-coherent state during the evolution.

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We extend the approach of Ref. [3] for preparing superposition states of a cavity field interacting with a superconducting charge qubit. We study effects of the nonlinearity on the creation of such states. We show that the main contribution of nonlinear effects is to shorten the time necessary to build the superposition.