Padé approximations of quantized-vortex solutions of the Gross–Pitaevskii equation  

作　　者：Weiru Chen Shanquan Lan Xiyi Liu Jiexiong Mo Xiaobao Xu Guqiang Li 

机构地区：[1]Institute of Theoretical Physics,Lingnan Normal University,Zhanjiang,524048,Guangdong,China

出　　处：《Communications in Theoretical Physics》2021年第8期171-181,共11页理论物理通讯（英文版）

基　　金：Undergraduate Innovation and Entrepreneurship Program Grant No.S201910579797;National Natural Science Foundation of China with Grant No.12005088,11847001,11747017;Guangdong Basic and Applied Basic Research Foundation with Grant No.2021A1515010246;supported by the Lingnan Normal University Project with Grant No.YL20200203,ZL1930。

摘　　要：Quantized vortices are important topological excitations in Bose–Einstein condensates. The Gross–Pitaevskii equation is a widely accepted theoretical tool. High accuracy quantized-vortex solutions are desirable in many numerical and analytical studies. We successfully derive the Padéapproximate solutions for quantized vortices with winding numbers ω = 1, 2, 3, 4, 5, 6 in the context of the Gross–Pitaevskii equation for a uniform condensate. Compared with the numerical solutions, we find that(1) they approximate the entire solutions quite well from the core to infinity;(2) higher-order Padé approximate solutions have higher accuracy;(3) Padé approximate solutions for larger winding numbers have lower accuracy. The healing lengths of the quantized vortices are calculated and found to increase almost linearly with the winding number. Based on experiments performed with 87Rb cold atoms, the healing lengths of quantized vortices and the number of particles within the healing lengths are calculated, and they may be checked by experiment. Our results show that the Gross–Pitaevskii equation is capable of describing the structure of quantized vortices and physics at length scales smaller than the healing length.

关 键 词：Gross-Pitaevskii equation Padéapproximation quantized-vortex solution 

分 类 号：O469[理学—凝聚态物理]