Optimal control of the inversion of two spins in Nuclear Magnetic Resonance

被引：4

作者：

Assemat, E. ^{[1
]}

Attar, L. ^{[1
]}

Penouilh, M. -J. ^{[2
]}

Picquet, M. ^{[2
]}

Tabard, A. ^{[2
]}

Zhang, Y. ^{[3
]}

Glaser, S. J. ^{[3
]}

Sugny, D. ^{[1
]}

机构：

[1] Univ Bourgogne, Lab Interdisciplinaire Carnot Bourgogne ICB, UMR CNRS 6303, F-21078 Dijon, France

[2] Univ Bourgogne, ICMUB, UMR CNRS 6302, F-21078 Dijon, France

[3] Tech Univ Munich, Dept Chem, D-85747 Garching, Germany

来源：

CHEMICAL PHYSICS | 2012年 / 405卷

关键词：

Optimal control theory; Nuclear Magnetic Resonance; Spin inversion; OPTIMAL-CONTROL DESIGN; EXCITATION PULSES; 2-LEVEL;

D O I：

10.1016/j.chemphys.2012.06.013

中图分类号：

O64 [物理化学（理论化学）、化学物理学];

学科分类号：

070304 ; 081704 ;

摘要：

We investigate the optimal control of the inversion of two spin 1/2 particles in Nuclear Magnetic Resonance. The two spins, which differ by their resonance offset, are controlled by the same radio frequency magnetic field. Using the Pontryagin Maximum Principle, we compute the optimal control sequence which allows to reach the target state in a given time, while minimizing the energy of the magnetic field. A comparison with the time-optimal solution for bounded control amplitude realizing the same control in the same time is made. An experimental illustration is done using techniques of Nuclear Magnetic Resonance. (C) 2012 Elsevier B.V. All rights reserved.

引用

页码：71 / 75

页数：5

共 38 条

[1] Simultaneous time-optimal control of the inversion of two spin-1/2 particles [J].

Assemat, E. ;

Lapert, M. ;

Zhang, Y. ;

Braun, M. ;

Glaser, S. J. ;

Sugny, D. .

PHYSICAL REVIEW A, 2010, 82 (01)

[2] The energy minimization problem for two-level dissipative quantum systems [J].

Bonnard, B. ;

Cots, O. ;

Shcherbakova, N. ;

Sugny, D. .

JOURNAL OF MATHEMATICAL PHYSICS, 2010, 51 (09)

[3]

Bonnard B., 2003, MATH APPLIC, V40

[4] Time-Minimal Control of Dissipative Two-Level Quantum Systems: The Generic Case [J].

Bonnard, Bernard ;

Chyba, Monique ;

Sugny, Dominique .

IEEE TRANSACTIONS ON AUTOMATIC CONTROL, 2009, 54 (11) :2598-2610

[5] TIME-MINIMAL CONTROL OF DISSIPATIVE TWO-LEVEL QUANTUM SYSTEMS: THE INTEGRABLE CASE [J].

Bonnard, Bernard ;

Sugny, Dominique .

SIAM JOURNAL ON CONTROL AND OPTIMIZATION, 2009, 48 (03) :1289-1308

[6] Optimal control in laser-induced population transfer for two- and three-level quantum systems [J].

Boscain, U ;

Charlot, G ;

Gauthier, JP ;

Guérin, S ;

Jauslin, HR .

JOURNAL OF MATHEMATICAL PHYSICS, 2002, 43 (05) :2107-2132

[7]

Boscain U., 2004, MATH APPLIC, V1, P1

[8] Time minimal trajectories for a spin 1/2 particle in a magnetic field [J].

Boscain, Ugo ;

Mason, Paolo .

JOURNAL OF MATHEMATICAL PHYSICS, 2006, 47 (06)

[9]

Bryson A.E., 2018, Applied optimal control: optimization, estimation and control

[10] MRI: Use of the inversion recovery pulse sequence [J].

Bydder, GM ;

Hajnal, JV ;

Young, IR .

CLINICAL RADIOLOGY, 1998, 53 (03) :159-176

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