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 Weiru Chen;Shanquan Lan;Xiyi Liu;Jiexiong Mo;Xiaobao Xu;Guqiang Li

作者机构：Institute of Theoretical PhysicsLingnan Normal UniversityZhanjiang524048GuangdongChina 

出 版 物：《Communications in Theoretical Physics》 (理论物理通讯（英文版）)

年 卷 期：2021年第73卷第8期

页      面：171-181页

核心收录：

学科分类：07[理学] 070205[理学-凝聚态物理] 0702[理学-物理学] 

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 

主　　题：Gross-Pitaevskii equation Padéapproximation quantized-vortex solution 

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.