Simultaneous time-optimal control of the inversion of two spin 1/2 particles

TL;DR

This paper investigates the optimal control strategies for simultaneously inverting two non-coupled spin-1/2 particles with different chemical shifts, demonstrating that maximum intensity pulse sequences are optimal and validating the approach experimentally.

Contribution

It introduces a method for time-optimal control of two spins with different offsets using a common magnetic field, extending single-spin control techniques.

Findings

Optimal pulse sequences are of maximum intensity.

The control strategy is similar to single-spin inversion with non-resonant fields.

Experimental validation using Nuclear Magnetic Resonance.

Abstract

We analyze the simultaneous time-optimal control of two-spin systems. The two non coupled spins which differ in the value of their chemical offsets are controlled by the same magnetic fields. Using an appropriate rotating frame, we restrict the study to the case of opposite shifts. We then show that the optimal solution of the inversion problem in a rotating frame is composed of a pulse sequence of maximum intensity and is similar to the optimal solution for inverting only one spin by using a non-resonant control field in the laboratory frame. An example is implemented experimentally using techniques of Nuclear Magnetic Resonance.