Singular constant control trajectories and transition degeneracies in a closed 4-level quantum system
- Resource Type
- Conference
- Authors
- Belhadj, Mohamed; Grigoriu, Andreea; Turinici, Gabriel
- Source
- 49th IEEE Conference on Decision and Control (CDC) Decision and Control (CDC), 2010 49th IEEE Conference on. :5444-5449 Dec, 2010
- Subject
- Robotics and Control Systems
Signal Processing and Analysis
Controllability
Symmetric matrices
Algebra
Eigenvalues and eigenfunctions
Trajectory
Nuclear magnetic resonance
- Language
- ISSN
- 0191-2216
0743-1546
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 fields. The theoretical result is supported by numerical simulations.