  In the framework of the non-secular perturbation theory based on the
Bogoliubov averaging method, the coherent dynamics of multiphoton Raman
transitions in a two-level spin system driven by an amplitude-modulated
microwave field is studied. Closed-form expressions for the Rabi frequencies of
these transitions have been obtained beyond the rotating wave approximation for
the low-frequency driving component. It is shown that spin states dressed by
the high-frequency component of the driving field are shifted due to the
Bloch-Siegert-like effect caused by antiresonant interactions with the strong
low-frequency driving. We predict that with increasing the order of the Raman
transition the Rabi frequency decreases and the contribution of the
Bloch-Siegert shift to this frequency becomes dominant. It is found that the
amplitude and phase of the Rabi oscillations strongly depend on the initial
phase of the low-frequency field as well as on detuning from multiphoton
resonance. The recent experimental data for the second- and third-order Raman
transitions observed for nitrogen-vacancy center in diamond [Z. Shu, et al.,
arXiv:1804. 10492] are well described in the frame of our approach. Our results
provide new possibilities for coherent control of quantum systems.
