Abstract
Doppler-free population inversion induced by coherent two-photon resonance is calculated analytically for a two-photon analog of the hyperbolic-secant pulse and numerically for a Gaussian, linearly chirped pulse. The numerical calculations are carried out for a two-photon resonance of a chirped ruby laser line with the $6{S}_{\frac{1}{2}}\ensuremath{\rightarrow}9{D}_{\frac{3}{2}}$ transition in Cs. Complete inversion is found when the fractional change in frequency during the pulse lies between 6 \ifmmode\times\else\texttimes\fi{} ${10}^{\ensuremath{-}6}$ and 2 \ifmmode\times\else\texttimes\fi{} ${10}^{\ensuremath{-}5}$. The coherent two-photon resonances are described by optical Bloch equations which are derived from a multiple-time-scale perturbation theory.
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