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I read that the Rabi frequency $\Omega$ for a constant intensity laser with intensity $I$ is given by $$\Omega=9.95 \times10^7 \sqrt I$$ from Equation 3 in this paper.

For a pulsed laser, how does one calculate the Rabi frequency?

For example, with a pulsed laser of Gaussian intensity envelope with full width at half maximum (FWHM) of $F$ seconds and pulse energy of $E$ joules, what is the equation to use to find its Rabi frequency?

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I think your equation applies to a specific laser, since the Rabi frequency generally depends in the matrix element between the active levels, not only on the intensity of the emitted radiation. E.g., in the Wikipedia article cited it is: $$\Omega_{i,j}=\frac{\mathbf{d}_{i,j}\cdot\mathbf{E}_0}{\hbar}.$$ For a pulsed laser the Rabi frequency is given by the same equation. However, there is no guarantee that a full oscillation is realized during the duration of a pulse.

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