We analyse the possibility of control for a coupled system of Schrödinger equations on the whole real line for the harmonic oscillator modeling a single trapped ion. In fact the coupling is due to the control which acts as a potential and which is performed by three monochromatic waves which can be switched on and off, only one of them being active at each time. By taking the frequency of these waves large enough, we show that this sytem can be approximated by a much simpler one, the so-called Law-Eberly system, for which we can give an explicit control satisfying all requirements. This enables us to prove approximate controllability for the original system in the natural (L2)2 norms and also in much stronger norms. This work has been done in collaboration with Sylvain Ervedoza.