Rabi Oscillations in Strongly-Driven Magnetic Resonance Systems

The sensitivity of the Rabi oscillations of a resonantly driven spin- $\frac{1}{2}$ 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 ${B}_{1}\ensuremath{\ll}{B}_{0}$) upon proper choice of the domains of modulation frequency ${\ensuremath{\omega}}_{m}$ and amplitude ${B}_{2}$ . 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 ${B}_{2}$ 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.The sensitivity of the Rabi oscillations of a resonantly driven spin-$\frac{1}{2}$ 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 ${B}_{1}\ensuremath{\ll}{B}_{0}$) upon proper choice of the domains of modulation frequency ${\ensuremath{\omega}}_{m}$ and amplitude ${B}_{2}$. 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 ${B}_{2}$ 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.

arXiv:1212.5957Physical Review BApr 15, 201319 citations

Resonant effect of the strongly-driven Rabi model

Qifeng Liang, Lixian Yu, Gang Chen +1 more

The European Physical Journal DJan 1, 20132 citations

Rabi-vibronic resonance with large number of vibrational quanta

Rachel Glenn, M. É. Raǐkh

We study theoretically the Rabi oscillations of a resonantly driven two-level system linearly coupled to a harmonic oscillator (vibrational mode) with frequency ${\ensuremath{\omega}}_{0}$. We show that for weak coupling, ${\ensuremath{\omega}}_{p}\ensuremath{\ll}{\ensuremath{\omega}}_{0}$, where ${\ensuremath{\omega}}_{p}$ is the polaronic shift, Rabi oscillations are strongly modified in the vicinity of the Rabi-vibronic resonance ${\ensuremath{\Omega}}_{R}={\ensuremath{\omega}}_{0}$, where ${\ensuremath{\Omega}}_{R}$ is the Rabi frequency. The width of the resonance is $({\ensuremath{\Omega}}_{R}\ensuremath{-}{\ensuremath{\omega}}_{0})\ensuremath{\sim}{\ensuremath{\omega}}_{p}^{2/3}{\ensuremath{\omega}}_{0}^{1/3}\ensuremath{\gg}{\ensuremath{\omega}}_{p}$. Within this domain of ${\ensuremath{\Omega}}_{R}$ the actual frequency of the Rabi oscillations exhibits a bistable behavior as a function of ${\ensuremath{\Omega}}_{R}$. Importantly, within the resonant domain, the oscillator is highly excited, which allows us to treat it classically.We study theoretically the Rabi oscillations of a resonantly driven two-level system linearly coupled to a harmonic oscillator (vibrational mode) with frequency ${\ensuremath{\omega}}_{0}$. We show that for weak coupling, ${\ensuremath{\omega}}_{p}\ensuremath{\ll}{\ensuremath{\omega}}_{0}$, where ${\ensuremath{\omega}}_{p}$ is the polaronic shift, Rabi oscillations are strongly modified in the vicinity of the Rabi-vibronic resonance ${\ensuremath{\Omega}}_{R}={\ensuremath{\omega}}_{0}$, where ${\ensuremath{\Omega}}_{R}$ is the Rabi frequency. The width of the resonance is $({\ensuremath{\Omega}}_{R}\ensuremath{-}{\ensuremath{\omega}}_{0})\ensuremath{\sim}{\ensuremath{\omega}}_{p}^{2/3}{\ensuremath{\omega}}_{0}^{1/3}\ensuremath{\gg}{\ensuremath{\omega}}_{p}$. Within this domain of ${\ensuremath{\Omega}}_{R}$ the actual frequency of the Rabi oscillations exhibits a bistable behavior as a function of ${\ensuremath{\Omega}}_{R}$. Importantly, within the resonant domain, the oscillator is highly excited, which allows us to treat it classically.

arXiv:1106.0278Physical Review BNov 23, 20114 citations

Resonant retuning of Rabi oscillations in a two-level system

А. В. Леонов, И. Д. Феранчук

Journal of Applied SpectroscopyJul 1, 20090 citations

The sensitivity of the Rabi oscillations of a resonantly driven spin-

\frac{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 ${B}_{1}\ensuremath{\ll}{B}_{0}$) upon proper choice of the domains of modulation frequency ${\ensuremath{\omega}}_{m}$ and amplitude

{B}_{2}

. 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

{B}_{2}

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.