Selective and Robust Time-Optimal Rotations of Spin Systems
| Autor: | Steffen J. Glaser, Dominique Sugny, Quentin Ansel |
|---|---|
| Přispěvatelé: | Univers, Transport, Interfaces, Nanostructures, Atmosphère et environnement, Molécules (UMR 6213) (UTINAM), Institut national des sciences de l'Univers (INSU - CNRS)-Centre National de la Recherche Scientifique (CNRS)-Université de Franche-Comté (UFC), Université Bourgogne Franche-Comté [COMUE] (UBFC)-Université Bourgogne Franche-Comté [COMUE] (UBFC), Munich Center for Quantum Science and Technology (MCQST), Technische Universität Munchen - Université Technique de Munich [Munich, Allemagne] (TUM), Laboratoire Interdisciplinaire Carnot de Bourgogne [Dijon] (LICB), Université de Bourgogne (UB)-Université de Technologie de Belfort-Montbeliard (UTBM)-Centre National de la Recherche Scientifique (CNRS) |
| Jazyk: | angličtina |
| Rok vydání: | 2020 |
| Předmět: |
Statistics and Probability
0209 industrial biotechnology Offset (computer science) Geometric analysis Computation Bloch equation General Physics and Astronomy FOS: Physical sciences 02 engineering and technology 01 natural sciences Pontryagin's minimum principle 020901 industrial engineering & automation Simple (abstract algebra) selective and robust processes Pontryagin maximum principle 0103 physical sciences Applied mathematics 010306 general physics Mathematical Physics Mathematics Spin-½ [PHYS]Physics [physics] Quantum Physics Spins Statistical and Nonlinear Physics Bloch equations Modeling and Simulation spin-1/2 particles time-optimal control Quantum Physics (quant-ph) ensemble control on SO(3) |
| Zdroj: | Journal of Physics A: Mathematical and Theoretical Journal of Physics A: Mathematical and Theoretical, IOP Publishing, 2021, 54 (8), pp.085204. ⟨10.1088/1751-8121/abdba1⟩ |
| ISSN: | 1751-8113 1751-8121 |
| Popis: | We study the selective and robust time-optimal rotation control of several spin-1/2 particles with different offset terms. For that purpose, the Pontryagin maximum principle is applied to a model of two spins, which is simple enough for analytic computations and sufficiently complex to describe inhomogeneity effects. We find that selective and robust controls are respectively described by singular and regular trajectories. Using a geometric analysis combined with numerical simulations, we determine the optimal solutions of different control problems. Selective and robust controls can be derived analytically without numerical optimization. We show the optimality of several standard control mechanisms in Nuclear Magnetic Resonance, but new robust controls are also designed. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|