二维线性与非线性光晶格中物质波孤立子的稳定性

摘要

利用变分法和数值计算方法研究了二维线性和非线性光晶格中二维玻色-爱因斯坦凝聚体系中物质波孤立子的存在及其稳定性。利用定态变分原理及Vakhitov-Kolokolov判据总结了线性和非线性结合光晶格中几种参数组合下定态定域解的稳定性。结果表明，当存在二维非线性光晶格时，在吸引和排斥相互作用的原子体系中均可以存在稳定的物质波孤立子。另外，利用含时变分法研究了线性和非线性光晶格中物质波孤立子随时间的传播特性，使波包参数对时间的一阶导数等于零，可以给出稳定状态对应的参数，结论和定态变分法给出的结果一致。最后用数值计算方法研究变分结果的正确性，把变分结果作为初始条件代入Gross-Pitaevskii方程研究其随时间传播特征，得到了稳定的传播过程，所得到的结果和变分分析结果一致。%By means of variational solution and direct numerical simulation of the Gross-Pitaevskii equation (GPE), we have studied the stability of matter-wave solitons in two-dimensional (2D) Bose-Einstein condensations (BECs), with 2D linear and nonlinear optical lattices (OLs). Using the static variational approach and Vakhitov-Kolokolov criterion necessary for stability, we obtain the stability condition for solitons in different combinations of OL’s parameters. We show that the 2D linear and nonlinear optical lattices allow us to stabilize 2D solitons for both attractive and repulsive interactions. We also study the time-evolution problems of 2D BECs, using the time-dependent variational approach and numerical solution of GPE for 2D linear and nonlinear OLs. Very good agreement between the results corresponding to both treatments is observed.