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

We study strongly correlated phases of a pseudo-spin-$\frac{1}{2}$ 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, pseudospin singlets are favored by pseudo-spin-independent interactions. We find a series of incompressible phases at fillings $\nu =2k/3$. 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 nontrivial 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.

Figure 1

Left: Ground-state energies, not showing possible degeneracies, at $N_{\Phi }=6$ for different $N$ and $S$ subspaces with $g_{s_1{s}_2}=1$. Even (odd) values of $S$ correspond to even (odd) $N$. Right: $\Delta$ vs $\nu$ for $N_{\Phi }=6$ and $g_{s_1{s}_2}=1$.

Figure 2

Interaction energy for $N=6$ and $S=0,2$ as a function of $g_{\uparrow \downarrow }$. Left: $N_{\Phi }=6$. Right: $N_{\Phi }=5$.

Figure 3

Energy spectra of singlet states for $N=12$ particles at filling $\nu =4/3$. Black crosses (with the left energy scale) show the results for an SU(2)-symmetric 2BC interaction, while red triangles (with the right energy scale) are the NASS spectrum for any three-body interaction with $g_{s_1{s}_2{s}_3}>0$. We do not show the threefold center-of-mass degeneracy but visualize further degeneracies by slight shifts in $\mathbf{K}$.