Hamiltonian identification for quantum systems : well posedness and numerical approaches

Claude Le Bris (1, 2) , Mazyar Mirrahimi (3) , Herschel Rabitz (4) , Gabriel Turinici (5)

1 CERMICS - Centre d'Enseignement et de Recherche en Mathématiques et Calcul Scientifique
2 MICMAC - Methods and engineering of multiscale computing from atom to continuum
3 SISYPHE - SIgnals and SYstems in PHysiology & Engineering
4 Department of Chemistry
5 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision

This paper considers the inversion problem related to the manipulation of quantum systems using laser-matter interactions. The focus is on the identification of the field free Hamiltonian and/or the dipole moment of a quantum system. The evolution of the system is given by the Schrödinger equation. The available data are observations as a function of time corresponding to dynamics generated by electric fields. The well-posedness of the problem is proved, mainly focusing on the uniqueness of the solution. A numerical approach is also introduced with an illustration of its efficiency on a test problem.

Mots clés: Inverse problem; quantum systems; Hamiltonian identification; optimal identification

Domaines: Analyse numérique [math.NA]; Physique Quantique [quant-ph]

Claude Le Bris, Mazyar Mirrahimi, Herschel Rabitz, Gabriel Turinici. Hamiltonian identification for quantum systems : well posedness and numerical approaches. ESAIM: Control, Optimisation and Calculus of Variations, 2007, 13 (2), pp.378-395. ⟨10.1051/cocv:2007013⟩. ⟨hal-00798211⟩