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

Multiphoton Raman transitions and Rabi oscillations in driven spin systems