Rabi frequency

Rabi frequency

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. 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.)

Definition

: chi_{i,j} = {vec{d}_{i,j}cdotvec{E}_0 over hbar}

where scriptstyle{vec{d}_{i,j is the transition dipole moment for the scriptstyle{i ightarrow j} transition and scriptstyle{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 scriptstyle{hbar} gives an angular frequency. Although scriptstyle{vec{d}_{i,j} = vec{d}_{j,i}^*}, one cannot assume that scriptstyle{chi_{i,j} = chi_{j,i}^*} as scriptstyle{hat{epsilon}E_0} may be complex, as in the case of circularly polarized light.cite book| title = Lasers | edition = | last = Milonni | first = Peter W. | coauthors = Eberly, Joseph H. | year = 1998| publisher = John Wiley & Sons| id = ISBN 0-471-62731-3| pages = p. 191]

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 cos heta, where heta 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.

Generalized Rabi frequency

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

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

where Delta = omega_{light} - omega_{transition} is the "detuning", a measure of how far the light is off resonance with the transition.

ee also

*Rabi cycle
*Vacuum Rabi oscillation

References


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