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We study Rabi oscillations of the second-order Raman transition realized ondressed states of a qubit excited by an amplitude-modulated microwave field.The co-rotating component of the ultrastrong low-frequency modulation fieldexcites virtual multiple photon processes between the dressed states and formsthe Rabi frequency in the so-called rotating wave approximation (RWA). Thecounter-rotating modulation component also gives a significant contribution tothe Rabi frequency owing to the Bloch--Siegert effect. It is shown that forproperly chosen parameters of the modulation field and qubit, the Rabioscillations in the RWA vanish due to destructive interference of multiplephoton processes. In this case the Rabi oscillation results exclusively fromthe Bloch--Siegert effect and is directly observed in the time-resolvedcoherent dynamics as the Bloch--Siegert oscillation. Correspondingly, inFourier spectra of the coherent response, triplets are transformed intodoublets with the splitting between the lines equal to twice the Bloch--Siegertshift. We demonstrate these features by calculations of the qubit's evolutionin the conditions of experiments with a NV center in diamond, where Ramantransitions were observed. The direct observation of the Bloch--Siegertoscillation offers new possibilities for studying driven quantum systems in theultastrong regime.

The possibility of direct observation of the Bloch-Siegert shift in coherent dynamics of multiphoton Raman transitions