We discuss order-parameter collective modes in weakly inhomogenous states of superfluid 3He-B, i.e., states in which the scale of the inhomogeneities is considerably longer than the coherence length, ξ0 = ℏ vf / 2π Tc, and the energy associated with the inhomogeneity is small compared to the condensation energy. The theory describes resonance phenomena between order-parameter modes and zero sound. We discuss two specific cases, both of which involve excitation of the J = 2+ modes via a parametric field that lifts the selection rule due to particle-hole symmetry. In the case of a static superflow the modes with J = 2+, M = ± 1 couple to sound for q || H, and should be observable as Zeeman states with a maximum absorption that scales as the square of the superflow velocity. The J = 2+ modes may also be excited parametrically in a three-wave resonance process involving two zero-sound phonons. We summarize the nonlinear response theory for two-photon excitation of these modes.
Invited Paper for the Proceedings of the 19th International Conference on Low Temperature Physics, Brighton, UK.