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Realization of non-Abelian anyons in topological phases is a crucial steptoward topological quantum computation. We propose a scheme to realize anon-Abelian quantum spin liquid (QSL) phase in a three-component Bose gas withcontact interaction on optical Kagome lattices. In the strong coupling regime,the system is described by an effective spin-1 model with two- and three-bodyinteractions between neighboring spins. By mapping out the phase diagram viavariational Monte Carlo method, we find a non-Abelian chiral spin liquid phasein which the Ising-type anyons obey non-Abelian braiding statistics. Thegapless chiral edge states can be detected by measuring the spin-spincorrelation from atomic population. Furthermore, an interesting Z2 QSL phase isobserved exhibiting both topological order and lattice symmetry breaking order.Our scheme can be implemented in cold quantum gases of bosonic atoms.

Abelian and non-Abelian quantum spin liquids in a three-component Bose gas on optical Kagome lattices