Approximate controllability of the Schrödinger equation with a polarizability term

Nabile Boussaid (1) , Marco Caponigro (2) , Thomas Chambrion (3, 4)

1 LMB - Laboratoire de Mathématiques de Besançon (UMR 6623)
2 M2N - Modélisation mathématique et numérique
3 CORIDA - Robust control of infinite dimensional systems and applications
4 IECN - Institut Élie Cartan de Nancy

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.

Domaines: Optimisation et contrôle [math.OC]

Nabile Boussaid, Marco Caponigro, Thomas Chambrion. Approximate controllability of the Schrödinger equation with a polarizability term. CDC - The 51st IEEE Conference on Decision and Control - 2012, Dec 2012, Maui, Hawaii, United States. pp.3024-3029. ⟨hal-00784881⟩