Approximate solutions for the ion-laser interaction in the high intensity regime: matrix method perturbative analysis

Abstract

This work provides an explicit expression for the second-order perturbative solution of a single trapped ion at the high intensity regime. Unlike other perturbative schemes, where the ion-laser dynamics has been explored using unitary transformations and the Lamb-Dicke regime, this analysis relies instead on a direct perturbation method, that may be implemented in simple manner and works especially well without resorting to additional approximations. Based on a matrix method and a final normalization of the perturbed solutions, the second-order perturbative analysis supply the probability to find the ion in its excited state; the resulting perturbative solution renders a high accuracy, comparable to the one based on the small rotation approximation.