  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.
