Hamiltonian identification through enhanced observability utilizing quantum control

Zaki Leghtas (1) , Gabriel Turinici (2) , Herschel Rabitz (3) , Pierre Rouchon (4)

1 SISYPHE - SIgnals and SYstems in PHysiology & Engineering
2 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision
3 Department of Chemistry
4 CAS - Centre Automatique et Systèmes

This note considers Hamiltonian identification for a controllable quantum system with nondegenerate transitions and a known initial state. We assume to have at our disposal a single scalar control input and the population measure of only one state at an (arbitrarily large) final time T. We prove that the quantum dipole moment matrix is locally observable in the following sense: for any two close but distinct dipole moment matrices, we construct discriminating controls giving two different measurements. This result suggests that what may appear at first to be very restrictive measurements are actually rich for identification, when combined with well designed discriminating controls, to uniquely identify the complete dipole moment of such systems.

Mots clés: Quantum control; Hamiltonian identification

Domaines: Optimisation et contrôle [math.OC]; Physique Quantique [quant-ph]; Systèmes dynamiques [math.DS]

Zaki Leghtas, Gabriel Turinici, Herschel Rabitz, Pierre Rouchon. Hamiltonian identification through enhanced observability utilizing quantum control. IEEE Transactions on Automatic Control, 2012, 57 (10), pp.2679 - 2683. ⟨10.1109/TAC.2012.2190209⟩. ⟨hal-00674698⟩