Effective mass approach for a Bose-Einstein condensate in an optical lattice  

作　　者：DUAN ZhengLu STEEL M J XU AiTing ZHANG WeiPing 

机构地区：[1]State Key Laboratory of Precision Spectroscopy, Department of Physics, East Normal University of China, Shanghai 200062, China [2]School of Mathematics, Physics, Computing and Electronics, Macquarie University, North Ryde, New South Wales 2109, Australia

出　　处：《Chinese Science Bulletin》2009年第22期4182-4196,共15页

基　　金：Supported by the National Natural Science Foundation of China (Grant Nos. 10588402, 10474055, 10874045);National Basic Research Program of China (Grant No. 2006CB921104);Science and Technology Commission of Shanghai Municipal-ity (Grant No. 05PJ14038, 08PJ1402000);Program of Shanghai Subject Chief Scien-tist (Grant No. 08XD14017);Program for Changjiang Scholars and Innovative Research Team in University, Shanghai Leading Academic Discipline Project (Grant No. B480)

摘　　要：We study the stationary and propagating solutions for a Bose-Einstein condensate (BEC) in a periodic optical potential with an additional confining optical or magnetic potential. Using an effective mass approximation we express the condensate wave function in terms of slowly-varying envelopes modulating the Bloch modes of the optical lattice. In the limit of a weak nonlinearity, we derive a nonlinear Schrdinger equation for propagation of the envelope function which does not contain the rapid oscillation of the lattice. We then consider the ground state solutions in detail in the regime of weak, moderate and strong nonlinear interactions. We describe the form of solution which is appropriate in each regime, and place careful limits on the validity of each type of solution. Finally we extend the study to the propagating dynamics of a spinor atomic BEC in an optical lattice and some interesting phenomena are revealed.We study the stationary and propagating solutions for a Bose-Einstein condensate （BEC） in a periodic optical potential with an additional confining optical or magnetic potential. Using an effective mass approximation we express the condensate wave function in terms of slowly-varying envelopes modulating the Bloch modes of the optical lattice. In the limit of a weak nonlinearity, we derive a nonlinear Schrodinger equation for propagation of the envelope function which does not contain the rapid oscillation of the lattice. We then consider the ground state solutions in detail in the regime of weak, moderate and strong nonlinear interactions. We describe the form of solution which is appropriate in each regime, and place careful limits on the validity of each type of solution. Finally we extend the study to the propagating dynamics of a spinor atomic BEC in an optical lattice and some interesting phenomena are revealed.

关 键 词：爱因斯坦 有效质量 冷凝水 光晶格 玻色 非线性薛定谔方程 非线性相互作用 弱非线性 

分 类 号：O412.1[理学—理论物理] O471.1[理学—物理]