Dynamical localization in the Paul trap — the influence of the internal structure of the atom

We show that quantum localization occurs in the center-of-mass motion of a two-level ion stored in a Paul trap and interacting with a standing laser field. The variable showing localization is identified to be the vibrational quantum number of a reference Floquet oscillator. The quantum localization length is shown to oscillate as a function of the atom-field detuning with a period given by the secular frequency of the trap. Furthermore, we simulate the effect of spontaneous emission on the system and show that in the limit of far detuning the phenomenon of dynamical localization is not destroyed by decoherence.