On modulation methods of manipulating nuclear spin states

In this paper, we explore Frequency-Amplitude-Phase modulation (FAPM) and Amplitude-Phase modulation (APM) methods of steering nuclear spin states from one arbitrary initial state to another arbitrary target state. The sufficient conditions are also given for transiting nuclear spin states within the specified time by FAPM and APM methods, respectively. It is exemplified that nuclei ¹H can be controlled by the aforementioned modulation methods. It is revealed that transition time performance can be improved if frequency modulation is available. However, neither FAPM nor APM is globally optimal modulation algorithm in terms of time performance. This research suggests that hybrid scheme of FAPM and APM should be better than both of them in terms of time performance.