  We study Rabi oscillations of the second-order Raman transition realized on
dressed states of a qubit excited by an amplitude-modulated microwave field.
The co-rotating component of the ultrastrong low-frequency modulation field
excites virtual multiple photon processes between the dressed states and forms
the Rabi frequency in the so-called rotating wave approximation (RWA). The
counter-rotating modulation component also gives a significant contribution to
the Rabi frequency owing to the Bloch--Siegert effect. It is shown that for
properly chosen parameters of the modulation field and qubit, the Rabi
oscillations in the RWA vanish due to destructive interference of multiple
photon processes. In this case the Rabi oscillation results exclusively from
the Bloch--Siegert effect and is directly observed in the time-resolved
coherent dynamics as the Bloch--Siegert oscillation. Correspondingly, in
Fourier spectra of the coherent response, triplets are transformed into
doublets with the splitting between the lines equal to twice the Bloch--Siegert
shift. We demonstrate these features by calculations of the qubit's evolution
in the conditions of experiments with a NV center in diamond, where Raman
transitions were observed. The direct observation of the Bloch--Siegert
oscillation offers new possibilities for studying driven quantum systems in the
ultastrong regime.
