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Non-Abelian spin singlet states of two-component Bose gases in artificial gauge fields

We study strongly correlated phases of a pseudo-spin-1/2 Bose gas in an artificial gauge field using the exact diagonalization method. The atoms are confined in two dimensions and interact via a two-body contact potential. In Abelian gauge fields, pseudo-spin singlets are favored by pseudo-spin independent interactions. We find a series of incompressible phases at fillings ν=2k/3. By comparison with the non-Abelian spin singlet (NASS) states, constructed as zero-energy eigenstates of a (k+1)-body contact interaction, we classify the non-trivial topology of the states. An additional spin-orbit coupling is shown to switch between NASS-like states and spin-polarized phases from the Read-Rezayi series.