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Physical Review A

Time-optimal control of spin-1/2 particles with dissipative and generalized radiation-damping effects

M. Lapert, Elie Assémat, Y. Zhang, Steffen J. Glaser, Dominique Sugny

Published Apr 17, 2013• 16 citations
Publisher

Abstract

We analyze the time-optimal control of spin-1/2 particles with bounded field amplitudes in the presence of dissipative and radiation damping effects. Using tools of geometric optimal control theory, we determine different optimal syntheses for specific values of the system parameters. We show the nontrivial role of the effective radiation damping effect on the optimal control law.

DOI
10.1103/physreva.87.043417

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We analyze the time-optimal control of spin-1/2 particles with bounded field amplitudes in the presence of dissipative and radiation damping effects. Using tools of geometric optimal control theory, we determine different optimal syntheses for specific values of the system parameters. We show the nontrivial role of the effective radiation damping effect on the optimal control law.
We consider the time-optimal control of an ensemble of uncoupled spin 1/2 particles in the presence of relaxation and radiation damping effects, whose dynamics is governed by nonlinear equations generalizing the standard linear Bloch equations. For a single spin, the optimal control strategy can be fully characterized analytically. However, in order to take into account the inhomogeneity of the static magnetic field, an ensemble of isochromats at different frequencies must be considered. For this case, numerically optimized pulse sequences are computed and the dynamics under the corresponding optimal field is experimentally demonstrated using nuclear magnetic resonance techniques.
We consider the time-optimal control of a spin-1/2 particle whose dynamics is governed by the Bloch equations with both longitudinal and transverse relaxation terms. We solve this control problem by using geometric optimal control techniques. We show the crucial role of singular extremals in the time-optimal synthesis. This role can mainly be attributed to the presence of dissipation. We also analyse the robustness of the optimal control sequence when both the maximum amplitude of the control field and the dissipative parameters are varied. Finally, we present an experimental implementation of the different solutions using techniques of nuclear magnetic resonance.
We consider the time-optimal control by magnetic fields of a spin 1/2 particle in a dissipative environment. This system is used as an illustrative example to show the role of singular extremals in the control of quantum systems. We analyze a simple case where the control law is explicitly determined. We experimentally implement the optimal control using techniques of nuclear magnetic resonance. To our knowledge, this is the first experimental demonstration of singular extremals in quantum systems with bounded control amplitudes.
We propose an analysis of the time-optimal control of a dissipative two-level quantum system whose dynamics is governed by the Lindblad equation. This simple system allows one to use tools of geometric control theory and to construct its optimal synthesis, i.e., to determine the set of all the optimal trajectories starting from a given initial point. We study different processes such as conversion of a pure state into a mixed state and purification of a mixed state. In particular cases, we show that dissipation is not undesirable and can help accelerating the control.