Perturbative Theory of Higher-Order Collision-Enhanced Wave Mixing

Rick P. Trebino, Larry A. Rahn

Using four-, six-, and eight-wave-mixing geometries, we observe subharmonic resonances in collision-enhanced spectra in a sodium-seeded hydrogen-air flame. Appearing at high intensity, these resonances occur at +/-1/2, +/-1/3, +/-1/4, and +/-1/5 times the frequency of the ground-state hyperfine splitting omega(hfs). We argue that these resonances result from higher-order processes, specifically chi((n)), where n >/= 5. In particular, to describe the resonances at +/-omega(hfs)/5, at least chi((13)) is required. These high-order collision-enhanced effects are true perturbative nonlinearities and not sequential four-wave mixing processes.

Nissim Asida, M. Rosenbluh

Rick P. Trebino, Larry A. Rahn

Collision enhanced resonances represent an interesting class of nonlinear-optical processes. They occur because collisional dephasing can rephase quantum mechanical amplitudes that ordinarily cancel out exactly, thereby allowing otherwise unobservable wave-mixing resonances to be seen. This is an especially interesting phenomenon because these resonances are coherent effects that are induced by an incoherent process (collisional dephasing). First predicted1 in the late 1970s and eventually observed2 in 1981, these novel effects have now been seen in a wide variety of four-wave-mixing experiments, ranging from self-focusing to coherent anti-Stokes Raman spectroscopy.

E. U. Condon

Aditi Ray, Ravinder Rupchand Puri

Resonances of the six-wave mixing susceptibility χ(5)(ω1, ω1, ω1,-ω2,-ω2) at frequency 3ω1-2ω2 of a system of two-level atoms dissipating through the spontaneous emission and collisions and driven by a weak bichromatic external field of frequencies ω1 and ω2 in a finite Q cavity are analyzed. It is shown that the atomic collisions not only induce the usual Bloembergen resonances but that they also play a major role in enhancing the transitions among the higher-order dressed states, thereby bringing out some of the quantum resonances that are suppressed in the absence of collisions. The important contribution of collisions in this higher-order nonlinear process is the generation of the subharmonic resonances at ±1/2 times the hyperfine splitting of the first and the second excited manifolds.

Jian Cheng Huang