Three-body spin mixing in spin-1 Bose-Einstein condensates

We study zero-energy collisions between three identical bosons with spin f=1 interacting via pairwise potentials. We quantify the corresponding three-body scattering hypervolumes, which parametrize the effective three-body interaction strengths in a many-body description of spin-1 Bose-Einstein condensates. Our results demonstrate universal behavior of the scattering hypervolumes for strong s- and p-wave two-body interactions. At weak interactions, we find that the real parts of the scattering hypervolumes are predominantly determined by hard-hyperspherelike collisions, which we characterize by a simple formula. With this universal result, we estimate that spin mixing via three-body collisions starts to dominate over two-body spin mixing at a typical particle density of 1017cm-3 for Na23 and K41 spinor condensates. This density can be reduced by tuning the two-body interactions to an s- or p-wave dimer resonance or to a point where two-body spin mixing effectively vanishes. Another possibility to observe the effects of three-body spin mixing involves the application of weak magnetic fields to cancel out the effective two-body interaction strength in the characteristic timescale describing the spin dynamics.