Quantum Hall states in rapidly rotating two-component Bose gases

We investigate strongly correlated phases of two-component (or pseudospin-$1/2$) Bose gases under rapid rotation through exact diagonalization on a torus geometry. In the case of pseudospin-independent contact interactions, we find the formation of gapped spin-singlet states at the filling factors ν=k/3+k/3 ($k/3$ filling for each component) with integer k. We present numerical evidences that the gapped state with $k=2$ is well described as a non-Abelian spin-singlet (NASS) state, in which excitations feature non-Abelian statistics. Furthermore, we find the phase transition from the product of composite fermion states to the NASS state by changing the ratio of the intercomponent-to-intracomponent interactions.