Ground States Of Ultracold Spin-1Atoms In An Optical Superlattice With Incommensurate Filling

Recently, ultracold atoms trapped in an optical lattice of double-well potential, the so-calledoptical superlattice have become a hot topic in the field of cold atoms and received much attention inboth theoretical and experimental studies. In the array of the double-well optical superlattice, manyidentical instances of experiment in parallel may be carried out. It can be used to obtain the quantummechanical expectation values of the observables in a single run. Many novel phenomena wereobserved in the new test ground. In this paper, the ground state diagrams of ultracold spin-1atomstrapped in a deep one-dimension double-well optical superlattice with incommensurate filling in thepresence of a weak magnetic field are obtained by exact diagonalization the reduced matrices of thetotal Hamiltonian.First, the Bose-Hubbard model of the ultracold spin-1atoms trapped in an optical lattice and thequantum phase transition are introduced. Next, a protocol to realize the double-well opticalsuperlattice is given. Finally, the ground states and the phase diagram of ultracold spin-1atomstrapped in a symmetrical double-well optical superlattice with incommensurate filling in a weakmagnetic field are obtained by the exact diagonalization. It is shown that the ground-state diagramsare remarkably different for the antiferromagnetic and ferromagnetic condensates. These novelspin-states can be controlled easily and exactly by modulating the tunneling parameter and thequadratic Zeeman energy, which may be a tool for the study of spin-entanglement.