Rotating Spin-1 Bose Clusters

We propose a simple scheme for generating rotating atomic clusters in an optical lattice which produces states with quantum Hall and spin liquid properties. As the rotation frequencies increase, the ground state of a rotating cluster of spin-1 Bose atoms undergoes a sequence of (spin and orbit) transitions, which terminates at an angular momentum $L^{*}$ substantially lower than that of the boson Laughlin state. The spin-orbit correlations reflect “fermionization” of bosons facilitated by their spin degrees of freedom. We also show that the density of an expanding group of clusters has a scaling form which reveals the quantum Hall and spin structure of a single cluster.

Figure 1

${\mathcal{V}}_L$ for an $N=4$ cluster with $c_2>0$. (b) The column densities of a $N=5$ cluster with with $L=0,3,6,9,12$. The central density of these clusters decreases with increasing $L$. The $L=12$ data is in bold. (c) The spin densities of the $L=3$ cluster in (b); ($S=1$). Densities, $\rho$, are scaled by ${\rho }_0=1/\pi a^2$.