Sustaining Rabi oscillations by using a phase-tunable image drive
Recent electron spin resonance experiments on CaWO$_4$:Gd$^{3+}$ and on other magnetic impurities have demonstrated that sustained Rabi oscillations can be created by driving a magnetic moment with a microwave field frequency slightly larger than the Larmor frequency and tuned to the Floquet resonance together with another microwave field (image drive). These observations are confirmed by the new experimental results reported in this paper. We investigate several mechanisms of decoherence and dissipation by using a combination of numerical and analytical techniques. The first microscopic model describes a magnetic moment in external magnetic fields, interacting with a bath of two-level systems acting as a source of decoherence and dissipation. The second model describes a collection of the identical, interacting magnetics moments, all subject to the same magnetic fields. In this case, the many-body interactions causes a decay of the Rabi oscillations. In addition, we also study the effect of the inhomogeneity of the microwave radiation on the decay of the Rabi oscillations. Our simulation results show that the dynamics of a magnetic moment subject to the two microwave fields with different frequencies and in contact with an environment is highly nontrivial. We show that under appropriate conditions, and in particular at the Floquet resonance, the magnetization exhibits sustained Rabi oscillations, in some cases with additional beatings. Although these two microscopic models separately describe the experimental data well, a simulation study that simultaneously accounts for both types of interactions is currently prohibitively costly. To gain further insight into the microscopic dynamics of these two different models, we study the time dependence of the bath and system energy and of the correlations of the spins, data that is not readily accessible experimentally.