Theory of degenerate four-wave mixing in resonant Doppler-broadened media. - II. Doppler-free heterodyne spectroscopy via collinear four-wave mixing in two- and three-level systems

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Abstract
In this article, we analyse a new sensitive spectroscopic technique in which a sample cell is irradiated by a two-frequency pump beam (ω + Δ ± δ/2) and a counter-propagating probe beam (ω). The phase-conjugate fields re-emitted at frequencies ω ± δ, via four-wave mixing processes, are detected through their heterodyne beating with the probe field. The properties of the heterodyne beat signal are studied by means of a perturbation calculation of the nonlinear response of the medium, carried out to the third order in the incident fields. In resonant gas media, the emission lineshape exhibits a Doppler-free doublet structure [frequency splitting 3 δ/2 for single-photon resonances, and δ/2 for two-photon transitions]. By using a phase-sensitive detection of the beat signal, one can separately analyse real (dispersion) or imaginary parts (absorption) of the nonlinear susceptibility. For single-photon transitions, the signal phase shift is related to the atomic levels lifetime and allows one to study the relaxation dynamics in gas phase (like quenching collisions, velocity diffusion, etc...). This is particularly interesting for cross-over resonances, in which only the common level contributes. In three-level systems, one also predicts a selective resonant enhancement of the phase-conjugate emission through Raman-type two-photon processes. Most of these predictions have been experimentally verified