A route to non-Abelian quantum turbulence in spinor Bose-Einstein condensates

We have studied computationally the collision dynamics of spin-2 Bose--Einstein condensates initially confined in a triple-well trap. Depending on the intra- and inter-component relative phases of the initial state spinor wave function, the collision of the three condensate segments produces one of many possible vortex-antivortex lattices after which the system transitions to quantum turbulence. We find that the emerging vortex lattice structures can be described in terms of multi-wave interference. We show that the three-segment collisions can be used to systematically produce staggered vortex-antivortex honeycomb lattices of fractional-charge vortices, whose collision dynamics are known to be non-Abelian. Such condensate collider experiments could potentially be used as a controllable pathway to generating non-Abelian superfluid turbulence with networks of vortex rungs.