Saturation of a spin 1/2 particle by generalized Local control

TL;DR

This paper introduces a generalized local control method for saturating a spin 1/2 particle in NMR, utilizing second derivatives of a Lyapunov function to determine control fields and comparing its efficiency with time-optimal solutions.

Contribution

It presents a novel generalized local control approach that does not depend explicitly on the control field, enhancing saturation control of spin 1/2 particles.

Findings

The method effectively saturates the spin system.

It compares favorably with time-optimal solutions.

The approach is applicable in NMR control scenarios.

Abstract

We show how to apply a generalization of Local control design to the problem of saturation of a spin 1/2 particle by magnetic fields in Nuclear Magnetic Resonance. The generalization of local or Lyapunov control arises from the fact that the derivative of the Lyapunov function does not depend explicitly on the control field. The second derivative is used to determine the local control field. We compare the efficiency of this approach with respect to the time-optimal solution which has been recently derived using geometric methods.