Control through operators for quantum chemistry

Philippe Laurent (1) , Herschel Rabitz (2) , Julien Salomon (3) , Gabriel Turinici (3)

1 IRCCyN - Institut de Recherche en Communications et en Cybernétique de Nantes
2 Department of Chemistry
3 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision

We consider the problem of operator identification in quantum control. The free Hamiltonian and the dipole moment are searched such that a given target state is reached at a given time. A local existence result is obtained. As a by-product, our works reveals necessary conditions on the laser field to make the identification feasible. In the last part of this work, some Newton algorithms are proposed together with a continuation method to compute effectively these operators.

Mots clés: Approximation methods; Controllability; Equations; Laser theory; Mathematical model; Newton method; Symmetric matrices; discrete systems; quantum chemistry; Hamiltonian moment; Newton algorithms; continuation method; dipole moment; laser field; operator identification; quantum control

Domaines: Optimisation et contrôle [math.OC]

Philippe Laurent, Herschel Rabitz, Julien Salomon, Gabriel Turinici. Control through operators for quantum chemistry. 2012 IEEE 51st Annual Conference on Decision and Control (CDC), Dec 2012, Maui, Hawaii, United States. ⟨hal-00678040v2⟩