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Physical Review Letters

Pressure-Induced Extra Resonances in Four-Wave Mixing

Yehiam Prior, A. R. Bogdan, M. Dagenais, N. Bloembergen

Published Jan 12, 1981• 249 citations
Publisher

Abstract

The first observation of pressure-induced extra resonant enhancements of a coherent four-wave---mixing signal is reported. When the difference between two input frequencies, ${\ensuremath{\omega}}_{1}$ and ${\ensuremath{\omega}}_{2}$, corresponds to the separation of two unpopulated upper levels, a resonant enhancement of the generated intensity at $2{\ensuremath{\omega}}_{1}\ensuremath{-}{\ensuremath{\omega}}_{2}$ is caused by collisions.

DOI
10.1103/physrevlett.46.111

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Collisionless extraresonances (ER) in degenerate four-wave mixing (DFWM) are predicted when the upper state \ensuremath{\Vert}b〉 of the \ensuremath{\Vert}a〉\ensuremath{\rightarrow}\ensuremath{\Vert}b〉 transition, excited by near-resonant incident laser beams, decays to the lower state \ensuremath{\Vert}a〉 both directly (\ensuremath{\Vert}b〉\ensuremath{\rightarrow}\ensuremath{\Vert}a〉) and via one or two intermediate states: \ensuremath{\Vert}b〉\ensuremath{\rightleftarrows}\ensuremath{\Vert}d〉\ensuremath{\rightarrow}\ensuremath{\Vert}a〉 or \ensuremath{\Vert}b〉\ensuremath{\rightarrow}\ensuremath{\Vert}c〉\ensuremath{\rightarrow}\ensuremath{\Vert}d〉\ensuremath{\rightarrow}\ensuremath{\Vert}a〉. The width of the new ER, which depends on the relative decay rates in the cascade process, may be very narrow leading to very strong DFWM signals. Dephasing collisions affect the intensity of the new ER and also produce the usual, pressure-induced ER.

Physical Review A•Mar 1, 1986•14 citations
The first observation of pressure-induced extra resonant enhancements of a coherent four-wave---mixing signal is reported. When the difference between two input frequencies, \ensuremathω1{\ensuremath{\omega}}_{1}\ensuremathω1​ and \ensuremathω2{\ensuremath{\omega}}_{2}\ensuremathω2​, corresponds to the separation of two unpopulated upper levels, a resonant enhancement of the generated intensity at 2\ensuremathω1\ensuremath−\ensuremathω22{\ensuremath{\omega}}_{1}\ensuremath{-}{\ensuremath{\omega}}_{2}2\ensuremathω1​\ensuremath−\ensuremathω2​ is caused by collisions.
Experiments on pressure-induced extra resonances in degenerate four-wave mixing involving Zeeman coherence have been performed on Ba atoms in an argon atmosphere under conditions of large detunings from the Ba resonance line. The dependence on the detuning gives evidence for a breakdown of the impact approximation, when the laser is detuned by more than 5\ifmmode\times\else\texttimes\fi{}1011{10}^{11}1011 rad ${\mathrm{sec}}^{\ensuremath{-}1}$; the behavior can be interpreted semiquantitatively by a model based on optical collisions.
By using the Schenzle-Brewer model, in which the ground state of a two-level system also has a finite lifetime, it is shown that two pressure-induced extraresonant degenerate four-wave mixing signals are obtained. The first extra resonance is similar to that predicted and observed by Bogdan et al. [Opt. Lett. 6, 82, 348 (1981)]. It is characterized by a linewidth equal to the inverse lifetime of the upper state and appears only in the presence of collisional redistribution. The second extra resonance is characterized by a linewidth equal to the inverse lifetime of the ground state and does not depend on collisional redistribution for its appearance.
Collisionless extraresonances (ER) in degenerate four-wave mixing (DFWM) are predicted when the upper state \ensuremath{\Vert}b〉 of the \ensuremath{\Vert}a〉\ensuremath{\rightarrow}\ensuremath{\Vert}b〉 transition, excited by near-resonant incident laser beams, decays to the lower state \ensuremath{\Vert}a〉 both directly (\ensuremath{\Vert}b〉\ensuremath{\rightarrow}\ensuremath{\Vert}a〉) and via one or two intermediate states: \ensuremath{\Vert}b〉\ensuremath{\rightleftarrows}\ensuremath{\Vert}d〉\ensuremath{\rightarrow}\ensuremath{\Vert}a〉 or \ensuremath{\Vert}b〉\ensuremath{\rightarrow}\ensuremath{\Vert}c〉\ensuremath{\rightarrow}\ensuremath{\Vert}d〉\ensuremath{\rightarrow}\ensuremath{\Vert}a〉. The width of the new ER, which depends on the relative decay rates in the cascade process, may be very narrow leading to very strong DFWM signals. Dephasing collisions affect the intensity of the new ER and also produce the usual, pressure-induced ER.