线性与非线性光晶格中偶极孤立子的稳定性

摘要

利用变分法研究了线性和非线性交叉光晶格中偶极玻色-爱因斯坦凝聚(BEC)体系中物质波孤立子的稳定性。选用柱对称高斯型试探波函数，得出参数的Euler-Lagrange方程和体系的有效作用势能，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孤立子解。结果表明，由于存在接触相互作用的空间调制，在排斥和吸引偶极相互作用下，均能形成稳定的孤立子解。给出了参数空间中存在稳定解的区域和物质波波包宽度随时间的变化曲线。%Stability of a dipolar Bose-Einstein condensate (BEC) soliton in crossed linear and nonlinear optical lattices is investigated using variational approximation. The Euler-Lagrange equations for variational parameters and the effective potential are derived by means of a cylindrically symmetric Gaussian ansatz, while the equilibrium widths are determined by minimization of the effective potential. In the presence of a periodic spatial variation of short-range contact interaction, the localized bound states can exist for both attractive and repulsive dipolar interactions. And the domain of stable dipolar BEC solitons is illustrated in a phase plot of the nonlinearities. Finally, we give the evolution of the variational width for different values of the nonlinearities.