Bloch–Siegert oscillations in the Rabi model with an amplitude-modulated driving field

Abstract

We study the coherent dynamics of a qubit excited by an amplitude-modulated electromagnetic field under the Rabi resonance when the frequency of the low-frequency modulation field matches the Rabi frequency in the high-frequency field. Due to destructive interference of multiple photon processes at the ultrastrong coupling between the qubit and the low-frequency driving field, Rabi oscillations result exclusively from the Bloch-Siegert effect. It is directly observed in the timeresolved coherent dynamics as the Bloch-Siegert oscillation. In this case, triplets in Fourier spectra of the coherent response are transformed into doublets with the splitting between the lines equal to twice the Bloch-Siegert shift. These unusual properties are demonstrated in conditions of experiments with a nitrogen vacancy center in diamond.

Quantum optimal control using phase-modulated driving fields

“…It can be seen that the phases φ j are time independent, thus, depending on the number N, the control function g s (t) can be represented by only several discrete frequencies in Fourier space, which can be rather coarse. In contrast to the SFB, inspired by the recently developed Floquet coherent controlling techniques, see, e.g., [63][64][65][66], we introduce a temporal modulation in the phases of the driving field according to…”