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Quantum Electronics

Coherent population trapping and vast enhancement of the efficiency of resonant three-wave mixing in isotropic media

Vasily G. Arkhipkin, S. A. Myslivets

Published Sep 30, 1995• 3 citations
Publisher

Abstract

A study is made of exactly on-resonant sumfrequency generation in isotropic media under coherent population trapping conditions. A huge increase in the conversion efficiency (by a factor of 10 6 or more) is predicted and the conditions for this enhancement are identified.
DOI
10.1070/qe1995v025n09abeh000498

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An investigation is reported of resonant four-wave frequency mixing of the type ω 4 =ω 1 —ω 2 +ω 3 under coherent population trapping conditions. Such mixing may appear when radiations of frequencies ω 1,2 are strong and when ω 1 —ω 2 =ω 20 (ω 20 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.
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We study resonant four-wave mixing process (omega) 4 equals (omega) 1 minus (omega) 2 plus (omega) 3 under conditions of coherent population trapping (CPT) when radiations with frequencies (omega) 1,2 are strong, and (omega) 1 minus (omega) 2 equals (omega) 20 ((omega) 20 is a frequency of electrodipole-forbidden transition). It is shown that under the CPT sufficiently large nonlinear polarization (the same as linear polarization or higher) may be created. We show that in atomic Ba vapor for cw lasers quantum conversion efficiency can be as high as several tens percent.
We develop a nonperturbative approach to study the generation of nonlinear signals in a coherently prepared medium. Specifically, we study the process ${\ensuremath{\omega}}_{1}\ensuremath{-}{\ensuremath{\omega}}_{2}+({\ensuremath{\omega}}_{2}+\ensuremath{\Omega})$, in a system prepared in a coherent-population-trapping state. We calculate enhancement factors of the order of $\ensuremath{\sim}{10}^{2}$ in the generated signal, under a variety of conditions thus supplementing the work of Jain et al. [Phys. Rev. Lett. 77, 4326 (1996)]. Our approach also enables us to study other related issues. We demonstrate the existence of pulse matching at higher probe powers.