Modulation Algorithms for Manipulating Nuclear Spin States

TL;DR

This paper investigates how exact frequency modulation can significantly reduce the transition time for steering nuclear spin states, proposing new algorithms and hybrid schemes that outperform traditional methods.

Contribution

It introduces 1-stage and 2-stage FAPM algorithms and a hybrid scheme, demonstrating their superiority over existing APM algorithms in reducing transition times.

Findings

Frequency modulation reduces transition time to about 1/4 of traditional methods.

Hybrid FAPM and APM scheme outperforms individual algorithms.

A simplified hybrid algorithm reduces computational complexity.

Abstract

We exploit the impact of exact frequency modulation on transition time of steering nuclear spin states from theoretical point of view. 1-stage and 2-stage Frequency-Amplitude-Phase modulation (FAPM) algorithms are proposed in contrast with 1-stage and 3-stage Amplitude-Phase modulation (APM) algorithms. The sufficient conditions are further present for transiting nuclear spin states within the specified time by these four modulation algorithms. It is demonstrated that transition time performance can be significantly improved if exact frequency modulation is available. It is exemplified that the transition time scale with frequency modulation is about 1/4 of that without frequency modulation. It is also revealed in this research that the hybrid scheme of 1-stage FAPM and APM algorithms is better than all the four modulation algorithms. A simplified hybrid modulation algorithm is also proposed to reduce computational burden.