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

TL;DR

This paper investigates how slow modulation of a static magnetic field affects Rabi oscillations in a spin-1/2 system, revealing regimes that can be emulated under weak driving conditions and confirming predictions through NMR experiments.

Contribution

The study introduces a theoretical mapping of weakly driven, modulated two-level systems onto strongly driven systems, and experimentally verifies the predicted modulation regimes in NMR.

Findings

Different modulation regimes can emulate strong driving conditions.

The shape of Rabi oscillation envelopes is highly sensitive to detuning.

Experimental results agree quantitatively with theoretical predictions.

Abstract

The sensitivity of the Rabi oscillations of a resonantly driven spin-1/2 system to a weak and slow modulation of the static longitudinal magnetic field, B_0, 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 << B_ 0) upon proper choice of the domains of modulation frequency, \omega_m, and amplitude, B_2. Fast modulation \omega_m >> \Omega_R, where \Omega_R is the Rabi frequency, emulates the regime of driving frequency much bigger than the resonant frequency. Strong modulation, B_2 >> B_1, emulates the regime B_1 >> B_0. Resonant modulation, \omega_m \approx \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 B_2 and \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.