Raman frequency mixing under coherent population trapping conditions

An investigation is reported of resonant four-wave frequency mixing of the type ω₄ = ω₁ – ω₂ + ω₃ under coherent population trapping conditions. Such mixing may appear when radiations of frequencies ω_1,2 are strong and when ω₁ – ω₂ = ω₂₀ (ω₂₀ is the frequency of a dipole-forbidden transition). The density matrix method is used to calculate (taking quantum interference into account) the absorption coefficients, the refractive indices, and the nonlinear susceptibilities exactly for the strong fields and in the first order of perturbation theory for the weak fields. A study is made of the dependence of the power of nonlinear optical generation on various characteristics of the transitions and of the radiation, subject to the propagation effects. The cases of homogeneous and Doppler broadening of the resonant transitions are considered. The characteristics of transitions in the barium atom are used in numerical illustrations. It is shown that the efficiency of resonant nonlinear-optical conversion of radiation can be enhanced by utilising interference processes in quantum transitions, which represent coherent population trapping.