Nonlinear acoustic effects in superfluid ³He-B

We consider the nonlinear interaction of zero sound with the collective modes of the order-parameter in superfluid ³He-B. The approximate particle-hole symmetry of the ³He-Fermi liquid determines selection rules for the linear and nonlinear coupling of zero sound to the collective modes. Starting from the quasiclassical theory of superfluid ³He, we have shown that the coupling strenghts have a simple representation in terms of Feynman diagrams. We predict measurable two-photon absorption and nonlinear-Raman scattering by the J = 2⁺ (real squashing) modes at low pressures. Recent observations of two-phonon absorption by a group in Helsinki are compared to the theoretical predictions. Two-phonon absorption can be used to determine the dispersion of the J = 2⁺ modes.