Bose - Einstein Condensate Bright Solitons In The Body And Superfluidity In Optical Lattices - Insulator Transition

The realization of Bose-Einstein condensation (BEC) in dilute atomic gases, it not only proved Einstein's prediction, but also provides a new way to study the dynamics of atom and some physical phenomena in low temperature. We get the exact solitonic solutions of one-dimensional nonlinear Schrodinger equation by Darboux transformation, which describes the dynamics of bright soliton in Bose-Einstein condensates with the time-dependent interaction in an expulsive parabolic potential, and investigate the dynamics of bright soliton influenced by time depen-dent interaction and gain or loss cold atom. Because of atom's quantum effect in low temperature, the atom of condensates can tunnelling in optical lattice, this is in superfluid phase. As the potential depth of the lattice is increased, the atom is confined, a transition is observed from a superfluid to a Mott insulator phase. In the superfluid phase, each atom is spread out over the entire lattice, with long-range phase coherence. But in the insulating phase, exact numbers of atoms are localized at individual lattice sites, with no phase coherence across the lattice. The excitation spectrum is gapless in superfluid phase whereas exhibits a gap in the Mott insulator phase. We get the energy spectrum of cold atom in optical lattice by different method, and the energy spectrum of two component BEC by Green function technique, also analyze the superfluid-Mott insulator phase transition and phase diagram by mean-field approach.This paper contains four chapters. Chapter 1 reviews recent investigation in Bose-Einstein condensation, and analyzes critical point and condition of phase tran-sition when the interaction between atom is zero. Chapter 2 introduces the exper-iment and theoretic studying of Mott insulator and superfluid phase transition in dilute atomic gases, we get the energy spectrum of cold atom in optical lattice by dif-ferent method, and the energy spectrum of two component BEC by Green function technique, analyze the dipole-dipole interaction (it is long range) of two component BEC in optical lattice by Green function technique and mean-field approach. In chapter 3, The exact solitonic solutions of one-dimensional nonlinear Schrodinger equation, which describes the dynamics of bright soliton in Bose-Einstein conden-sates with the time-dependent interaction in an expulsive parabolic, are obtained by Darboux transformation. We investigate the dynamical of bright soliton influ-enced by some experimental parameters and gravity field, and get the condition of stabilized Bright Solitons in BECs. In chapter 4, I summarize this paper.