Line-space description of resonant four-wave mixing: theory for isotropic molecular states.
Based on the quantum Liouville formalism, a theory of the two-color, triply resonant four-wave mixing is developed for molecules with isotropically oriented angular momenta. The approach allows to strictly incorporate the relaxation matrices Γ((r)) (r = 0, 1, 2) into the third-order susceptibility χ((3)) whose expression acquires therewith the form of a scalar product in the line space. Thanks to this representation, isolation of all resonance terms from χ((3)) becomes a routine task. Some of these terms correspond to the case when a molecule initially interacts with two pump photons of the same frequency. Such interactions give rise to the grating line-space vectors which have the same (zero) eigenfrequency. Due to this degeneracy, the latter are easily mixed by rotationally inelastic collisions which shows up in a state-resolved coherence transfer. The satellite signals induced thereby provide a great scope to study the state-to-state inelastic rates in situ by purely optical means. If the diagonal form of Γ is assumed, the satellites become forbidden and our results reduce to conventional expressions for the main resonances. Polarization configurations are designed for direct measurements of the population (r = 0), orientation (r = 1), and alignment (r = 2) contributions to χ((3)). Finally, depending on the photon-molecule interaction sequence, the resonance terms of χ((3)) are shown to be differently affected by velocity averaging, the effect which conspicuously manifests itself when Doppler broadening becomes paramount.
Department of Physics, Saint-Petersburg State University, Ulyanovskaya str. 3, Peterhof, Saint-Petersburg 198504, Russia.
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Kouzov
Paul Scherrer Institute, CH-5232 Villigen, Switzerland.
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Radi