Rabi frequency

The Rabi frequency is the frequency of oscillation for a given atomic transition in a given light field. It also gives the measure of the fluctuation of population between the levels. It is associated with the strength of the coupling between the light and the atomic transition. Rabi flopping between the levels of a 2-level system illuminated with resonant light, will occur at the Rabi frequency. The Rabi frequency is a semiclassical concept as it is based on a quantum atomic transition and a classical light field.

In the context of a nuclear magnetic resonance experiment, the Rabi frequency is the nutation frequency of a sample's net nuclear magnetization vector about a radiofrequency field. (Note that this is distinct from the Larmor frequency, which characterizes the precession of a transverse nuclear magnetization about a static magnetic field.)

The Rabi frequency is defined as

where ${\displaystyle \scriptstyle {{\vec {d}}_{i,j}}}$ is the transition dipole moment for the ${\displaystyle \scriptstyle {i\rightarrow j}}$ transition and ${\displaystyle \scriptstyle {{\vec {E}}_{0}={\hat {\epsilon }}E_{0}}}$ is the vector electric field amplitude which includes the polarization. The numerator has dimensions of energy, so dividing by ${\displaystyle \scriptstyle {\hbar }}$ gives an angular frequency. Although ${\displaystyle \scriptstyle {{\vec {d}}_{i,j}={\vec {d}}_{j,i}^{*}}}$, one cannot assume that ${\displaystyle \scriptstyle {\chi _{i,j}=\chi _{j,i}^{*}}}$ as ${\displaystyle \scriptstyle {{\hat {\epsilon }}E_{0}}}$ may be complex, as in the case of circularly polarized light.

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