Appears in collection : Quantum control and feedback: foundations and applications

Joint work with Marco Caponigro.

In this talk we show that under generic (and reasonably explicit) conditions, a controlled bilinear Schrödinger equation with discrete-spectrum drift is exactly controllable in projections on any finite sum of eigenspaces. The proof of this result is based on rigorous decoupling estimates between finite-dimensional reductions and the complete infinite-dimensional dynamics, coupled with finite-dimensional Lie-algebraic control techniques and classical topological arguments issuing from degree theory.