  We consider a quantum particle in a 1D interval submitted to a potential. The
evolution of this particle is controlled using an external electric field.
Taking into account the so-called polarizability term in the model (quadratic
with respect to the control), we prove global exact controllability in a
suitable space for arbitrary potential and arbitrary dipole moment. This term
is relevant both from the mathematical and physical points of view. The proof
uses tools from the bilinear setting and a perturbation argument.
