光晶格中玻色——爱因斯坦凝聚体系的定态解

Stationary state of Bose-Einstein condensates confined in optical lattice

利用变分法研究了一维光晶格势阱中玻色-爱因斯坦凝聚中的定态解。根据高斯型试探波函数和平均场理论求出了波包宽度随时间演化的微分方程和体系的有效势能。根据有效势能是否具有局域最小值判断体系是否具有稳定的定态解,给出了稳定定态解存在时晶格强度与非线性相互作用之间的函数关系,并且利用图示法给出了稳定解存在时的非线性相互作用区间。

We investigate ground state solutions in one-dimensional Bose-Einstein condensate. We derive the second-order differential equation for the evolution of the width and the effective potential for the stability analysis of the system using the Gauss type trial wave function, and give the stable criteria through this effective potential. We also demonstrate the relation between the strength of optical lattice and nonlinearity interaction for stable stationary state.