F. Soto-Eguibar

We present the dynamics of a single harmonically trapped ion interacting with a laser, considering a linear combination of two eigenstates of the system as the initial state. The conditions on the physical parameters that allow for the evolution of the system are discussed. We are able to obtain analytical results even though no approximations are realized and are able to show Rabi oscillations for such initial states.

We provide an explicit expression for the second-order perturbative solution of a single trapped-ion interacting with a laser field in the strong excitation regime. From the perturbative analytical solution, based on a matrix method and a final normalization of the perturbed solutions, we show that the probability to find the ion in its excited state fits well with former results.