复合脉冲的鲁棒性通过经典力学阐明。II. 初始状态不完美性的作用
The robustness of composite pulses elucidated by classical mechanics. II. The role of initial state imperfection
AI总结：
本文通过经典力学框架研究复合脉冲的鲁棒性，发现初始状态不完美性对脉冲序列性能有显著影响，并提出优化方法以提升相干群体倒转效率。
摘要：
在核磁共振（NMR）中，复合脉冲（CPs）被广泛用于校正脉冲不完美性，例如射频场不均匀性和共振偏移。尽管多年来已经开发出鲁棒脉冲序列，但文献中并未广泛讨论初始状态的不完美性作为额外的系统误差。在以前的工作中，我们开发了一个经典的 canonical 框架来进行稳定性分析，并将其用作 CP 鲁棒性的度量。在该工作中，允许单一初始条件在各种脉冲不完美性下演化。当前的工作将这种方法扩展到 Bloch 球上的 2D 初始条件分布；目标是通过最小化面积来保持相干性，同时最大化整个分布的群体倒转。作为案例研究，我们研究了 Levitt 的 90(x)180(y)90(x) 脉冲序列，在初始条件存在分散时的情况。经典的框架使我们能够评估 Levitt 脉冲序列的鲁棒性，并发现即使考虑初始条件的分散，其鲁棒性也得以保持。然而，通过进行数值优化，我们识别出几种 Levitt 脉冲序列的变体，在初始条件存在分散时能产生更大的相干群体倒转。
英文摘要：
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.
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