Semi-conical eigenvalue intersections and the ensemble controllability problem for quantum systems

Nicolas Augier (1, 2) , Ugo Boscain (3, 4, 2) , Mario Sigalotti (4, 2)

1 CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique
2 CaGE - Control And GEometry
3 CNRS - Centre National de la Recherche Scientifique
4 LJLL (UMR_7598) - Laboratoire Jacques-Louis Lions

We study one-parametric perturbations of finite dimensional real Hamiltonians depending on two controls, and we show that generically in the space of Hamiltonians, conical intersections of eigenvalues can degenerate into semi-conical intersections of eigenvalues. Then, through the use of normal forms, we study the problem of ensemble controllability between the eigenstates of a generic Hamiltonian.

Mots clés: Ensemble control; adiabatic approximation; quantum control; conical intersections of eigenvalues; normal forms

Domaines: Optimisation et contrôle [math.OC]; Physique mathématique [math-ph]

Nicolas Augier, Ugo Boscain, Mario Sigalotti. Semi-conical eigenvalue intersections and the ensemble controllability problem for quantum systems. Mathematical Control and Related Fields, 2020, 10, pp.877-911. ⟨10.3934/mcrf.2020023⟩. ⟨hal-02277653⟩