Abstract
The laser field interacting with single trapped ion in a carrier excitation frame in the presence of an external field is investigated. Detailed analytical expressions are given, taking into account carrier excitation configurations. We study the evolution of the population inversion, fidelity, ion-field entanglement, Fisher information and the geometric phase. The results indicate the influence of the external field on the information quantities to describe some physical phenomena. The relation between the population inversion, fidelity, von Neumann entropy, Fisher information, and geometric phase are explored during the time evolution.