Quantum spin nematic states in Bose-Einstein condensates

We review some recent results on discrete symmetries and topological order in spinor Bose-Einstein condensates (BECs) of Na-23. For spin one bosons with two-body scatterings dominated by a total spin equal to two channel, the BECs are in quantum spin nematic states at a low density limit. We study spin correlations in condensates at different limits and analyze hidden symmetries using a non-perturbative approach developed recently. Furthermore we investigate the influence of hidden Z(2) symmetries and U(1) quantum orders in symmetry partially restored states, particularly the effects on topological excitations.