Dark soliton solution of the three-dimensional Gross-Pitaevskii equation with an isotropic harmonic potential and nonlinearity in polytropic approximation

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• 作者：Xinwei Fan ; Yu Zhou ; Yalun Li ; Ying Wang…
• 关键词：Gross ; Pitaevskii equation ; Self ; similar transformation ; Soliton
• 刊名：Journal of the Korean Physical Society
• 出版年：2016
• 出版时间：February 2016
• 年：2016
• 卷：68
• 期：3
• 页码：383-386
• 全文大小：240 KB
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• 作者单位：Xinwei Fan (1)
  Yu Zhou (1)
  Yalun Li (1)
  Ying Wang (1)
  Shuyu Zhou (2) (3)
  
  1. School of Mathematics and Physics, Jiangsu University of Science and Technology, Jiangsu, 212003, China
  2. Department of Physics, Ben-Gurion University of the Negev, Beer Sheva, 84105, Israel
  3. Key Laboratory for Quantum Optics, Shanghai Institute of Optics and Fine Mechanics, The Chinese Academy of Sciences, Shanghai, 201800, China
  
• 刊物主题：Physics, general; Theoretical, Mathematical and Computational Physics; Particle and Nuclear Physics;
• 出版者：Springer Netherlands
• ISSN：1976-8524

文摘

We study the three-dimensional Fermi gas in an isotropic harmonic trap during the Bardeen- Cooper-Schrieffer superfluid to Bose-Einstein condensate (BCS-BEC) crossover, which is modeled by using the generalized Gross-Pitaevskii equation (GGPE) in the polytropic approximation. We analytically solved the 3D GGPE with a coupled modulus-phase transformation without introducing any additional integrability constraint, reaching the dark soliton-like solution. We find that the dark soliton identified undergoes an oscillation with a constant period over the whole BCS-BEC crossover region, although the amplitude of the dark soliton varies with polytropic index, demonstrating the peculiar nonlinear properties for the system modeled by using the 3D GGPE.