The possibility of direct observation of the Bloch-Siegert shift in coherent dynamics of multiphoton Raman transitions. (arXiv:1906.04528v1 [quant-ph])

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.

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