Quantum Hall states in rapidly rotating two-component Bose gases

Ultracold atomic gases under rapid rotation offer interesting analogues of quantum Hall systems with variable statistics and spins of constituent particles. Here we study strongly correlated phases of two-component (or pseudo-spin-$1/2$) Bose gases under rapid rotation by means of exact diagonalization. As the ratio of the inter-component contact interaction $g_{\uparrow\downarrow}$ to the intra-component one $g$ increases, the two components are expected to be entangled to form novel ground states. For $g_{\uparrow\downarrow}=g$, we find the formation of gapped spin-singlet states at the filling factors $\nu=k/3+k/3$ (the $k/3$ filling for each component) with integer $k$. In particular, 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 interaction ratio $g_{\uparrow\downarrow}/g$. Reference: Phys. Rev. A 86, 031604(R) (2012).