Incommensurate Filling of Ultracold Spin-1 Atoms in Optical Superlattice with a Weak Magnetic Field

The ground states of ultracold spin-1 atoms trapped in an optical superlattice in a weak magnetic field with incommensurate filling of three atoms in one double-well are obtained. It is shown that the ground-state diagrams of the reduced double-well model are remarkably different for the antiferromagnetic and ferromagnetic atoms. These novel spin-states can be controlled easily and exactly by modulating the tunneling parameter and the quadratic Zeeman energy, which may be a tool for the study of spin-entanglement.