Time-optimal selective pulses of two uncoupled spin 1/2 particles

We investigate the time-optimal solution of the selective control of two uncoupled spin 1/2 particles. Using the Pontryagin Maximum Principle, we derive the global time-optimal pulses for two spins with different offsets. We show that the Pontryagin Hamiltonian can be written as a one-dimensional ef...

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Bibliographic Details
Published in:arXiv.org 2018-10
Main Authors: L Van Damme, Ansel, Q, Glaser, S J, Sugny, D
Format: Article
Language:English
Subjects:
Bifurcations
Elliptic functions
Maximum principle
Offsets
Optimal control
Particle spin
Time optimal control
Online Access:Get full text
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Summary:We investigate the time-optimal solution of the selective control of two uncoupled spin 1/2 particles. Using the Pontryagin Maximum Principle, we derive the global time-optimal pulses for two spins with different offsets. We show that the Pontryagin Hamiltonian can be written as a one-dimensional effective Hamiltonian. The optimal fields can be expressed analytically in terms of elliptic integrals. The time-optimal control problem is solved for the selective inversion and excitation processes. A bifurcation in the structure of the control fields occurs for a specific offset threshold. In particular, we show that for small offsets, the optimal solution is the concatenation of regular and singular extremals.
ISSN:2331-8422
DOI:10.48550/arxiv.1810.07134