Dynamical Properties Of Ultra-cold Atomic Ensembles Trapped In Optical Lattice

The physical property of the ultra-cold atomic ensemble in optical lattice is one of the important topics in cold atom physics. Recently the study of ultra-cold atoms in periodic potentials becomes a hot physical topic, because it can mimic many complicated problems encountered in traditional condensed matter and solid state physics. With no impurity and defect and high controllability, the system of ultra-cold atomic ensemble in optical lattice provides us a powerful tool to investigate the quantum phenomenas which do not exist in traditional condensed matter.The recent studies about ultra-cold atoms in optical lattice involve many aspects and we are interesting in two of them. On the one hand, the optical lattice can provide us a powerful tool in the field of spin dynamics and atomic magnetic properties. Among them, the dynamic processes such as spin wave excitations, controlling and detection, will provide useful information in quantum calculation and quantum information when Bose-Einstein condensates (BEC) are used in these areas. However, the study on this field is just emerging. So there exist many open problems for us to solve. For example, due to the existence of long range interaction induced by optical field, the spin dynamics will exhibit many interesting novel physical behaviors.On the other hand, after cooling and trapping ultra-cold atom gases with larger magnetic dipoles have been realized in laboratory, the effect of dipole-dipole interaction on the dynamics of ultra-cold atom gases is emerging as a hot topic of intensive theoretical and experimental investigation. Meanwhile, Bloch oscillations as one of the fundamental solid state phenomena has been investigated in ultra-cold atomic ensembles, in which Bloch oscillations can be measured with a higher precision thanks to the smaller width of the momentum distribution. It has been taken as a tool of ultrahigh precision measurement. The problem that physicists are facing is how to improve the accuracy.This thesis tries to extensively and thoroughly deal with above problems. Some fundamental background knowledge is reviewed in first two chapters. In the first chapter, we simply reviewed laser coolling techniques and realization of BEC. In the second chapter, we first reviewed the realization and properties of optical lattice and BECs confined in it, then we focus on spinor BECs and dipolar gases whose dynamics will be investigated in residual chapters.In the third chapter, by using the mean field approach method, the intrinsic localized spin wave modes in spinor BECs atomic spin chain with strong light-induced dipole-dipole interaction are studied, which show that the long range interaction in this system plays an important role. The long range interaction in optical lattice provides us a powerful tool in the field of studying the effect of nonlinear interaction on spin dynamics in the discrete lattice systems. It also presents a broad prospect for the development of the crossover of quantum information and condensed matter.In the fourth chapter, we have studied the effect of magnetic dipole-dipole interaction on the envelope dynamics of ultra-cold atom gases in an optical lattice. For a quasi-one-dimensional dipolar gas, we have derived the Gross-Pitaeskii equation with a magnetic dipole-dipole interaction. After studying the Fourier spectrum, we find a magical polarization direction along which the repulsive interaction and attractive interaction cancel out each other. We study the dependence of Bloch oscillations on this magical polarization direction, and find it improves the Bloch oscillations to some extended.In the final chapter, we conclude the thesis and propose possible development.