Superfluid-Mott Insulator Phase Transition Of Bose-Einstein Condensates In Optical Lattice

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. 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 two component BEC by Green function technique and analyze 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 transition. Chapter 2 introduces the experiment of Mott insulator and superfluid phase transition in dilute atomic gases, theoretic mode and some studying. In chapter 3, we study the influence of dipole-dipole interaction (it is long range) of two component BEC in optical lattice, by Green function technique and mean-field approach. The results show that long range interaction and dipole-dipole interaction can be strongly influence the phase transition of two component. In chapter 4 , we summarize this paper.