Acoustic order parameter three-wave resonance in superfluid ³He-B

We consider the nonlinear interaction of zero sound with the collective modes of the order parameter in superfluid ³He-B. Starting from the quasi-classical theory 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.