Dissipative dynamics of qubits driven by a bichromatic field in the dispersive regime

We study the coherent dynamics of relaxing qubits driven by a bichromatic radiation in the dispersive regime in the case when the detuning of the frequency ωrf of a longitudinal radio-frequency field from the Rabi frequency ω1 in a transverse microwave field is comparable in magnitude to ωrf and ω1. We analytically describe this regime beyond the rotating wave approximation and find that the dominant feature of the dynamics of qubits is the shift in the Rabi frequency caused by the dynamical Zeeman and Bloch-Siegert-like effects. These fundamental effects can be experimentally separated because, unlike the Bloch-Siegert effect, the dynamical Zeeman effect depends on the detuning sign. Our theoretical results are in good agreement with the experimental data obtained in pulse electron paramagnetic resonance for the E'1 centers in crystalline quartz.