Quantum Phases Of Atoms With An Attractive Two-body Interaction In Optical Lattices

It is of great interest that the quantum phase transition between the superfluid and Mott phases can be observed when cold bosonic atoms with a repulsive two-body interaction are loaded into an optical lattice. In this dissertation, the quantum phases that may arise when bosonic atoms with an attractive two-body interaction are loaded into an optical lattice arc studied. To our best knowledge, this is the first piece of work on this subject in the physics community.This dissertation is organized as follows. In Chapter I, the Bose-Einstein condensation and ground state properties of bosonic atoms in traps and the effects of the three-body repulsion on the Bose-Einstein condensation with an attractive two-body interaction are reviewed. In Chapter II, the creation of an optical lattice as well as its properties and potential applications are discussed. In Chapter III, the superfluid and Mott insulator quantum phases of bosonic atoms in an optical lattice are first introduced. Their properties as well as the quantum phase transition between them are then presented.Chapter IV, the most important part of this dissertation, contains the new results obtained in the research work performed for this dissertation. The phases of ~7Li atoms loaded into an optical lattice are carefully studied in this chapter. The phase diagram for ~7Li atoms within a mean-field approximation is found to be composed of the superfluid and Mott-insulator phases as for bosonic atoms with a repulsive two-body interaction. However, the repulsive three-body interaction is indispensable for stable quantum phases of ~7Li atoms in contrast to the repulsive case. The ground state energy and the average atom number per lattice site in the quantum phases have been calculated and found to be consistent with the nature of these quantum phases. The excitation spectra of quasiparticles and quasiholes in the Mott-insulator phase have also been calculated. In our general investigation of the effects of the three-body interaction that is allowed to vary, it is found that the energies of quasiparticles are substantially increased as the strength of the repulsive three-body interaction is raised, whereas the energies of quasiholes are slightly decreased at low filling factors of atoms and substantially decreased at large filling factors.