Abstract
A quantum scheme is presented in which a three-level trapped ion interacts with two laser beams in the absence and presence of a classical field. We analyze the impact of the classical field and the Lamb-Dicke parameter (LDP) on the dynamical behavior of an entanglement quantifier, population probabilities and the geometric phase (GP). From the set of LDP values and the classical field, we obtain the time dependence of the GP and population probabilities. The results show that both the time-dependent field and the LDP play an important role in developing the entanglement, fidelity and population probabilities. Robust entangled qudit states are obtained by two elaborated measures which are concurrence and fidelity.