Approximate controllability of the Schrödinger Equation with a polarizability term in higher Sobolev norms

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 IECL - Institut Élie Cartan de Lorraine

This analysis is concerned with the controllability of quantum systems in the case where the standard dipolar approximation, involving the permanent dipole moment of the system, is corrected with a polarizability term, involving the field induced dipole moment. Sufficient conditions for approximate controllability are given. For transfers between eigenstates of the free Hamiltonian, the control laws are explicitly given. The results apply also for unbounded or non-regular potentials.

Mots clés: bilinear control; polarizability; Schrödinger Equation; Approximate controllability

Domaines: Equations aux dérivées partielles [math.AP]; Optimisation et contrôle [math.OC]

Nabile Boussaid, Marco Caponigro, Thomas Chambrion. Approximate controllability of the Schrödinger Equation with a polarizability term in higher Sobolev norms. 2014. ⟨hal-01006178⟩