Abstract
A theoretical investigation of the interaction between trapped ions and an external laser field beyond the Lamb-Dicke regime taking into account the time-dependent ion-field coupling is reported. At exact resonances the time-dependent ion-field interaction is analytically solvable. We focus on the role of different parameters in the phenomenon of collapses and revivals of the Rabi oscillations. In the case of an initial pure state, we account for a number of interesting phenomena including revivals which are determined by the initial photon-number distribution. Starting with an initial coherent state for the center-of-motion quantized modes, and the ion in. its upper state, we demonstrate the existence of super-revivals. We briefly explain the statistical basis of the measures of mixedness and entanglement. The general results are illustrated using pure and mixed state density matrices of the composite system. Some applications are provided and discussed in detail, bringing to light the feasibility and the wide potentiality of the different forms of the entanglement measures. It is found that the time evolution of the quantum linear entropy systematically captures the corresponding collapse and revival features in the atomic inversion. We also show that the degree of entanglement of the ion-field system, for the initial mixed state, can be completely quantified by the quantum mutual entropy. The analysis shows that the entanglement degree due to the quantum mutual entropy exhibits new features in the time-dependent case.