Approximate controllability of the Schrödinger equation with a polarizability term

This paper is concerned with the controllability of quantum systems in the case where the standard dipolar approximation, involving the permanent dipole moment of the system, has to be corrected by a so-called polarizability term, involving the field induced dipole moment. Sufficient conditions for controllability between eigenstates of the free Hamiltonian are derived and control laws are explicitly given. As an illustration, the results are applied to the planar rotation of the HCN molecule.