The robustness of composite pulses elucidated by classical mechanics. II. The role of initial state imperfection

TL;DR

This paper extends classical stability analysis of composite pulses in NMR to account for initial state imperfections, revealing how these affect robustness and enabling optimized pulse variants for improved coherence.

Contribution

It introduces a 2D distribution approach for analyzing initial state imperfections in composite pulses, enhancing robustness assessment and optimization methods.

Findings

Levitt's pulse sequence remains robust with initial state spread.

Numerical optimization yields variants with better population inversion.

The framework effectively assesses and improves pulse robustness.

Abstract

In nuclear magnetic resonance (NMR), Composite Pulses (CPs) are widely used to correct for pulse imperfections, e.g., RF field inhomogeneity and resonance offset. Although robust pulse sequences have been developed throughout the years, the imperfection of the initial state has not been widely discussed in the literature as an additional systematic error. In previous work, we developed a classical canonical framework to perform stability analysis and used this as a measure of CP robustness. In that work, a single initial condition was allowed to evolve under various pulse imperfections. The current work extends this approach to $2D$ distributions of initial conditions on the Bloch Sphere; the objective is to minimize the area in order to preserve coherence, while maximizing population inversion of the entire distribution. As a case study, we investigate Levitt's $90(x)180(y)90(x)$ pulse sequence, when there is a spread in initial conditions. The canonical framework enables us to assess the robustness of Levitt's pulse sequence, and we find that it is maintained to a great extent even when considering a spread of initial conditions. Nevertheless, by conducting a numerical optimization, we have identified several variants of Levitt's pulse sequence that produce a larger coherent population inversion when there is a spread in initial conditions.