The sensitivity of the Rabi oscillations of a resonantly driven spin-
21 system to a weak and slow modulation of the static longitudinal magnetic field
B0 is studied theoretically. We establish the mapping of a weakly driven two-level system with modulation onto a strongly driven system without modulation. The mapping suggests that different regimes of spin dynamics, known for a strongly driven system, can be realized under common experimental conditions of weak driving (driving field ${B}_{1}\ensuremath{\ll}{B}_{0}$) upon proper choice of the domains of modulation frequency ${\ensuremath{\omega}}_{m}$ and amplitude
B2. Fast modulation ${\ensuremath{\omega}}_{m}\ensuremath{\gg}{\ensuremath{\Omega}}_{R}$, where ${\ensuremath{\Omega}}_{R}$ is the Rabi frequency, emulates the regime of driving frequency much bigger than the resonant frequency. Strong modulation ${B}_{2}\ensuremath{\gg}{B}_{1}$ emulates the regime ${B}_{1}\ensuremath{\gg}{B}_{0}$. Resonant modulation ${\ensuremath{\omega}}_{m}\ensuremath{\approx}{\ensuremath{\Omega}}_{R}$ gives rise to an envelope of the Rabi oscillations. The shape of this envelope is highly sensitive to the detuning of the driving frequency from the resonance. Theoretical predictions for different domains of
B2 and ${\ensuremath{\omega}}_{m}$ were tested experimentally using NMR of protons in water, where, without modulation, the pattern of Rabi oscillations could be observed over many periods. We present experimental results which reproduce the three predicted modulation regimes, and agree with theory quantitatively.
We propose and experimentally demonstrate a scheme to simulate the interaction between a two-level system and a classical light field. Under the transversal driving of two microwave tones, the effective Hamiltonian in an appropriate rotating frame is identical to that of the general semi-classical Rabi model. We experimentally realize this Hamiltonian with a superconducting transmon qubit. By tuning the strength, phase, and frequency of the two microwave driving fields, we simulate the quantum dynamics from the weak to extremely strong driving regime. Under these conditions, we observe that, as a function of increased Rabi drive strength, the qubit evolution gradually deviates from the normal sinusoidal Rabi oscillation, in accordance with the predictions of the general semi-classical Rabi model far beyond the weak driving limit. Our scheme provides an effective approach to investigate the extremely strong interaction between a two-level system and a classical light field. Such strong interactions are usually inaccessible in experiments.