Singular constant control trajectories and transition degeneracies in a closed 4-level quantum system

Andreea Grigoriu (1) , Mohamed Belhadj (2) , Gabriel Turinici (1)

1 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision
2 Institut Supérieur des Mathématiques Appliquées et d'Informatique de Kairouan

We analyze in this paper controllability aspects for a 4-dimensional quantum system. The "strong regularity" (cf. [1]) has been proven to be sufficient condition for global controllability. A conjecture in the literature asks whether this condition (up to the introduction of an additive constant in the control field) is also necessary. We prove here a negative result. The result also applies to the study of singularity of trajectories associated to constant control field.

Domaines: Analyse numérique [math.NA]

Andreea Grigoriu, Mohamed Belhadj, Gabriel Turinici. Singular constant control trajectories and transition degeneracies in a closed 4-level quantum system. 49TH IEEE CONFERENCE ON DECISION AND CONTROL (CDC), Atlanta 2010, Dec 2010, Atlanta (GA), United States. pp.5444-5449, ⟨10.1109/CDC.2010.5717900⟩. ⟨hal-00522130⟩