Spin Wave Dynamics Of The Ultracold Atom Ensemble Confined In An Optical Lattice

Recently, since the realization of confining the ultracold atoms in the periodic array of optical potentials, this system has received a lot of attention from both theoretical and experimental sides in atomic optics and cold atom physics. As the influences of defects and impurities do not exist in optical lattices, it can be taken as an ideal tool for us to study a number of scientific problems. For example, we can use it to study how the quantum tunneling, quantum noises and quantum dissipation affect quantum transportion and correlation. 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 excitation, control, detection, will provide useful informations in quantum calculation and quantum information when Bose-Einstein condensates(BEC) are used in these areas. On the other hand, as far as we know, the affection of long range interaction on spin dynamics has not been studied yet.The main goal of this thesis is to investigate the affection of long range interaction on the dynamics of atomic spin chain in optical lattice. The main aspects are modulational instability (MI)of nonlinear coherent spin waves and intrinsic localized spin wave mode(ILSM) in this system. In the first chapter, we simply reviewed laser coolling techniques and realization of BEC, as well as realization and properties of optical lattice and BECs confined in it. Because of the comparability between atomic spin chain and solid-state magnetic chain, in second chapter, we reviewed the MI of spin waves and ILSM in solid-state ferromegnatic chain.In the third chapter, we start from BEC atomic spin chain model and establish a physical model to describe the coherent atomic spin chain containing spinor BECs, which are confined in an optical lattice and subject to the long-range dipole-dipole interaction. Using the Holstein-Primarkoff transformation and method of linear stability analysis, we study the MI of extended nonlinear spin waves with the long range site-to-site spin coupling through the dipole-dipole interaction.In the chapter four, using the classical method, the stationary ILSMs 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 provide us a powerful tool in the field of studying the effect of nonlinear interaction on spin dynamics in discret lattice systems.The research in this thesis attributes to the crossover of condensed matter physics, theoretical physics, atom physics, many-body physics, quantum optics and quantum information.