光晶格中玻色-爱因斯坦凝聚体量子化涡旋的稳定性
Stability of Quantized Vortices in a Bose-Einstein Condensate Confined in an Optical Lattice
摘要：
研究了二维空间中周期势和抛物势下非线性Schroedinger方程单电荷和多电荷量子化涡旋态的存在性，特别是线性稳定性.本研究的动机是在磁和光的共同作用下对饼状玻色-爱因斯坦凝聚体的研究。对于位于晶格局部最小值或局部最大值的单量子化和双量子化涡旋态，扫描凝聚体化学势与周期势强度的双参数空间。三重带电涡旋也简要讨论。单电荷涡被发现是稳定的余弦电位和正弦的不稳定的临界强度以上。更高的电荷涡旋对于两种类型的势都更不稳定，并且它们的动力学演化导致分裂成单电荷涡旋。
英文摘要：
We investigate the existence and especially the linear stability of single and multiple-charge quantized vortex states of nonlinear Schroedinger equations in the presence of a periodic and a parabolic potential in two spatial dimensions. The study is motivated by the examination of pancake-shaped Bose-Einstein condensates in the presence of magnetic and optical confiement. A two-parameter space of the condensate's chemical potential versus the periodic potential's strength is scanned for both single- and double-quantized vortex states located at a local minimum or a local maximum of the lattice. Triply charged vortices are also briefly discussed. Single-charged vortices are found to be stable for cosinusoidal potentials and unstable for sinusoidal ones above a critical strength. Higher charge vortices are more unstable for both types of potentials and their dynamical evolution leads to breakup into single-charged vortices.
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