A review of geometric optimal control for quantum systems in nuclear magnetic resonance. (English) Zbl 1238.81181
Summary: We present a geometric framework to analyze optimal control problems of uncoupled spin 1/2 particles occurring in nuclear magnetic resonance. According to the Pontryagin’s maximum principle, the optimal trajectories are solutions of a pseudo-Hamiltonian system. This computation is completed by sufficient optimality conditions based on the concept of conjugate points related to Lagrangian singularities. This approach is applied to analyze two relevant optimal control issues in NMR: the saturation control problem, that is, the problem of steering in minimum time a single spin 1/2 particle from the equilibrium point to the zero magnetization vector, and the contrast imaging problem. The analysis is completed by numerical computations and experimental results.
MSC:
| 81V35 | Nuclear physics |
| 49J15 | Existence theories for optimal control problems involving ordinary differential equations |
| 70E05 | Motion of the gyroscope |
| 49S05 | Variational principles of physics |
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