Hamiltonian identification for quantum systems : well posedness and numerical approaches

Turinici, Gabriel; Rabitz, Herschel; Mirrahimi, Mazyar; Le Bris, Claude

Turinici, Gabriel; Rabitz, Herschel; Mirrahimi, Mazyar; Le Bris, Claude (2007), Hamiltonian identification for quantum systems : well posedness and numerical approaches, ESAIM. COCV, 13, 2, p. 378-395. http://dx.doi.org/10.1051/cocv:2007013

Type

Article accepté pour publication ou publié

External document link

http://hal.archives-ouvertes.fr/hal-00798211

Date

2007

Journal name

ESAIM. COCV

Volume

Number

Publisher

EDP Sciences

Pages

378-395

Abstract (EN)

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.

Subjects / Keywords

optimal identification; Hamiltonian identification; quantum systems; Inverse problem