What can we hope about output tracking of bilinear quantum systems?
Abstract
We consider a non-resonant bilinear Schrödinger equation with discrete spectrum driven by a scalar control. We prove that this system can approximately track any given trajectory, up to the phase of the coordinates, with arbitrary small controls. The result is valid both for bounded and unbounded Schrödinger operators. The method used relies on finite-dimensional control techniques applied to Lie groups.