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

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Abstract

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.

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Authors and Affiliations

  1. School of Mathematics and Physics, Jiangsu University of Science and Technology, Jiangsu, 212003, China

    Xinwei Fan, Yu Zhou, Yalun Li & Ying Wang

  2. Department of Physics, Ben-Gurion University of the Negev, Beer Sheva, 84105, Israel

    Shuyu Zhou

  3. Key Laboratory for Quantum Optics, Shanghai Institute of Optics and Fine Mechanics, The Chinese Academy of Sciences, Shanghai, 201800, China

    Shuyu Zhou

Authors
  1. Xinwei Fan
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  2. Yu Zhou
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  3. Yalun Li
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  4. Ying Wang
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  5. Shuyu Zhou
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Correspondence to Ying Wang.

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Fan, X., Zhou, Y., Li, Y. et al. Dark soliton solution of the three-dimensional Gross-Pitaevskii equation with an isotropic harmonic potential and nonlinearity in polytropic approximation. Journal of the Korean Physical Society 68, 383–386 (2016). https://doi.org/10.3938/jkps.68.383

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  • DOI: https://doi.org/10.3938/jkps.68.383

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