EUROPHYSICS LETTERS Europhys. Lett., 9 (5)) pp. 459-464 (1989) 1 July 1989 Acoustic Order Parameter Three-Wave Resonance in Superfluid 3He-B. R. H. MCKENZIE and J. A. SAULS Department of Physics and Astronomy, Northwestern University Evanston, IL 60208, U.S.A. (received 15 March 1989; accepted 26 April 1989) PACS. 67.50F - Superfluid phase. PACS. 43.25 - General linear acoustics. PACS. 42.65C - Stimulated Raman scattering and spectra; CARS; stimulated Brillouin and stimulated Rayleigh scattering and spectra. Abstract. - We consider the nonlinear interaction of zero sound with the collective modes of the order parameter in superfluid 3He-B. Starting from the quasi-classicaltheory of superfluid 3He, we derive equations describing a three-wave resonance between the J = 2+ (real squashing) modes and two zero-sound phonons at different frequencies. We point out similarities between the nonlinear excitation of collective modes of the 3He-B order parameter and related effects in nonlinear optical systems. In particular, it should be possible to observe stimulated Raman scattering of zero sound and two-phonon absorption by the 2' mode. Zero sound has been used extensively to study the collective modes of the order parameter of superfluid 3He-B [l]. Although the condensate of Cooper pairs in 3He-Bis not a simple coll'ection of molecules, many of the observed properties of the absorption and group velocity spectra of zero sound, such as the Zeeman splitting'of the collective mode absorption peaks, have analogues in the optical spectroscopy of atoms and molecules. Most experiments have been carried out in the linear response regime in which sound couples only to modes of the same frequency and wavevector. However, it is natural to investigate whether in superfluid 3He there exist acoustic analogues of the nonlinear effects which have been studied in optical systems. Some nonlinear optical effects occur because the intense electromagnetic wave causes a macroscopic population of one or more of the excited states of the medium. Consequently, the population of the ground state of the system must be included as a dynamical variable in the equations describing these phenomena. Examples of this class of effects are population inversion, saturation effects and self-induced transparency [2]. Another class of nonlinear effects are parametric processes such as harmonic generation, stimulated Raman scattering and two-photon absorption[2,3]. Here the population of the ground state is usually not treated as a dynamical variable, but is assumed to have its equilibrium value. Except for a paper by Serene [4] on third-harmonic generation, previous investigations [5-71 of nonlinear