Rabi frequency

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The Rabi frequency for a given atomic transition in a given light field gives the strength of the coupling between the light and the transition. Rabi flopping between the levels of a 2-level system illuminated with resonant light, will occur at the Rabi frequency.

[edit] Definition

\chi_{i,j} = {\vec{d}_{i,j}.\vec{E}_0 \over \hbar}

where

\vec{d}_{i,j} is the transition dipole moment for the i \rightarrow j transition.
\vec{E}_0 = \hat{\epsilon}E_0 is the vector electric field amplitude which includes the polarization.

The numerator has dimensions of energy, dividing by \hbar gives an angular frequency.

By analogy with a classical dipole, it is clear that an atom with a large dipole moment will be more susceptible to perturbation by electric and magnetic fields. The dot product includes a factor of cosθ, where θ is the angle between the polarization of the light and the transition dipole moment. When they are parallel or antiparallel the interaction is strongest, when they are perpendicular there is no interaction at all. The vector electric field amplitude defines both the intensity and the polarization of the light.

[edit] Generalized Rabi frequency

For light that is off resonance with a transition, it is common to define the generalized Rabi frequency Ωi,j. Rabi flopping actually occurs at the generalized Rabi frequency.

\Omega_{i,j} = \sqrt{|\chi_{i,j}|^2 + \Delta^2}

where Δ = ωlight − ωtransition is the detuning, a measure of how far the light is off resonance with the transition.

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