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We investigate strongly correlated phases of two-component (orpseudo-spin-1/2) Bose gases under rapid rotation through exact diagonalizationon a torus geometry. In the case of pseudo-spin-independent contactinteractions, we find the formation of gapped spin-singlet states at thefilling factors \nu=k/3+k/3 (k/3 filling for each component) with integer k. Wepresent numerical evidences that the gapped state with k=2 is well described asa non-Abelian spin-singlet (NASS) state, in which excitations featurenon-Abelian statistics. Furthermore, we find the phase transition from theproduct of composite fermion states to the NASS state by changing the ratio ofthe intercomponent to intracomponent interactions.

Quantum Hall States in Rapidly Rotating Two-Component Bose Gases