Controllability Analysis of Quantum Systems Immersed within an Engineered Environment

Andreea Grigoriu (1) , Herschel Rabitz (2) , Gabriel Turinici (3)

1 LJLL - Laboratoire Jacques-Louis Lions
2 Department of Chemistry
3 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision

The problem of controllability of quantum systems interacting with an engineered environment, whose dynamics are described by a non-Markowian master equation is addressed. The manipulations of the dy- namics is realized with both a laser eld and a tailored non-equilibrium, and generally time-dependent, state of the surrounding environment. Lie algebra theory is used to characterize the structures of the reachable state sets and to prove controllability. The theoretical results are supported by examples.

Mots clés: quantum control; controllability of non-Markovian equations; Lie group controllability; controlla- bility in a non-compact Lie group

Domaines: Analyse numérique [math.NA]; Chimie théorique et/ou physique; Physique Quantique [quant-ph]

Andreea Grigoriu, Herschel Rabitz, Gabriel Turinici. Controllability Analysis of Quantum Systems Immersed within an Engineered Environment. Journal of Mathematical Chemistry, 2013, 51 (6), pp.1548-1560. ⟨10.1007/s10910-013-0163-6⟩. ⟨hal-00696546v3⟩