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arXiv:quant-ph/0005089 · Physical Review A

Enhanced four-wave mixing via elimination of inhomogeneous broadening by coherent driving of quantum transitions with control fields

A. K. Popov, Alexander S. Baev

Published Jul 19, 2000• 16 citations
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Abstract

We show that atoms from a wide velocity interval can be concurrently involved in Doppler-free two-photon resonant four-wave mixing that is far from being frequency dependent, with the aid of an auxiliary electromagnetic field. This gives rise to substantial enhancement of the output radiation generated in an optically thick medium. Numerical illustrations of typical experimental conditions are given.

DOI
10.1103/physreva.62.025801

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arXiv:quant-ph/0501001•Physical Review A•Apr 12, 2005•24 citations
We show that atoms from a wide velocity interval can be concurrently involved in Doppler-free two-photon resonant four-wave mixing that is far from being frequency dependent, with the aid of an auxiliary electromagnetic field. This gives rise to substantial enhancement of the output radiation generated in an optically thick medium. Numerical illustrations of typical experimental conditions are given.
The influence of nonlinear interference processes and of changes in populations in strong electromagnetic fields, and also of the Doppler broadening on resonant four-wave frequency mixing is investigated for a system of Raman-type transitions. The case in which a quantum system interacts with one weak field and two strong fields is considered. Each of the energy levels is assumed to be perturbed by just one strong field. It is shown that the Doppler broadening alters drastically the contributions of the populations of the various levels to the investigated process and that this can alter by several orders of magnitude and nonlinear susceptibilities averaged over the velocities and influence significantly the selection of optimal configurations of the transitions and of the experimental conditions for effective resonant four-wave conversion of the radiation frequencies. A numerical analysis of the derived expressions is used to account for the experimentally observed considerable differences between the spectral dependences of the output power and the conclusions drawn from perturbation theory.
An explicit solution is obtained for the four-wave frequency mixing ${\ensuremath{\omega}}_{d}={\ensuremath{\omega}}_{a}\ensuremath{-}{\ensuremath{\omega}}_{b}+{\ensuremath{\omega}}_{c}$ of two strong fields a and c and two weak fields b and d in a four-level system with large Doppler broadening in collinear geometry, where the frequencies of weak fields are nearly equal, ${\ensuremath{\omega}}_{b}\ensuremath{\simeq}{\ensuremath{\omega}}_{d},$ and the medium is optically thin. Without weak fields there are two independent two-level systems. A pair of weak fields probes two other allowed transitions. A peak of the mixing coefficient as a function of intensity is found around an equal Rabi splitting of both two-level systems. The effect is based on a resonance between two closed cycles of four-wave mixing via different dressed states. Three, four, or six peaks are predicted in the dependence of the mixing coefficient on the frequency of the weak field; two of them are a consequence of averaging over velocities. The model allows an interpretation of the dependence of the output wave power on the intensity and detuning in recent experiments on frequency mixing in sodium vapor.
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.
The effect of electromagnetically induced transparency in resonant four-wave-mixing schemes is investigated in an analysis that goes beyond perturbation theory in the coherent driving field. In addition we examine the case where the two-photon pump field is sufficiently strong to necessitate a nonperturbative treatment. This allows us to examine the cases where either one or both of the driving fields are strong. Phase matching is included in a plane-wave propagation treatment that matches the situation most likely to be encountered in actual experiments. The calculations are in part intended to model real experimental situations and thus incorporate driving and pump-field linewidths via the phase-diffusion model and Doppler broadening. With a strong pump-field laser, large enhancements in the efficiency of light generation occur at frequencies corresponding to the Autler-Townes satellites induced by the strong driving field. In this situation gain and high four-wave-mixing efficiency are simultaneously present, resulting in the production of a large intensity of coherent radiation. \textcopyright{} 1996 The American Physical Society.
Specific features of nonlinear interference processes at quantum transitions in near- and fully resonant Doppler-broadened optically dense media are studied. The possibility of all-optical switching of the medium to opaque or, alternatively, to absolutely transparent, or even to strongly amplifying states is explored, which is controlled by a small variation of two driving or probe radiations and does not require any change of the level populations. Optimum conditions for inversionless amplification of short-wavelength radiation above the oscillation threshold at the expense of the longer-wavelength control fields are investigated. The feasibility of overcoming the fundamental limitation on a velocity-interval of resonantly coupled molecules imposed by the Doppler effect is shown, based on quantum coherence.