Magnetic resonance in slowly modulated longitudinal field: Modified shape of the Rabi oscillations

The sensitivity of the Rabi oscillations of a resonantly driven spin1 2 system to a weak and slow modulation of the static longitudinal magnetic fieldB0 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 B1 B0) upon proper choice of the domains of modulation frequency ωm and amplitudeB2. Fast modulationωm R , where R is the Rabi frequency, emulates the regime of driving frequency much bigger than the resonant frequency. Strong modulation B2 B1 emulates the regime B1 B0. Resonant modulation ωm ≈ 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 ωm 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.