变分法研究二维光晶格中玻色-爱因斯坦凝聚的调制不稳定性

Modulational instability of a two-dimensional Bose-Einstein condensate in an optical lattice through a variational approach

利用含时变分法研究了二维光晶格中准二维玻色-爱因斯坦凝聚中的调制不稳定性.在平均场近似下,由准二维Gross-Pitaevskii方程出发,利用变分法给出了调制波振幅和相位所满足的时间演化方程,通过求解时间演化方程和能量分析法给出了发生调制不稳定性的条件,决定于平面波振幅,晶格强度,调制波的波矢量和原子之间的两体相互作用.

We investigate the modulational instability of a two-dimensional Bose-Einstein condensate in a two-dimensional optical lattice using a time-dependent variational approach. Within this framework, we derive the ordinary differential equations for time evolution of the amplitude and phase of modulational perturbations. Analyzing these equations and the Hamiltonian of the system, we obtain the modulational instability criterion.