  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.

Quantum Gases;Quantum Physics