中国物理B ›› 2008, Vol. 17 ›› Issue (6): 2160-2169.doi: 10.1088/1674-1056/17/6/037

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Slowly moving matter--wave gap soliton propagation in weak random nonlinear potential

张永亮1, 蒋寻涯1, 资剑2, 张铭锐3   

  1. (1)Institute of Microsystem and Information Technology, Chinese Academy of Sciences, Shanghai 200050, China; (2)Surface Physics Laboratory (National Key Lab), Fudan University, Shanghai 200433, China; (3)Surface Physics Laboratory (National Key Lab), Fudan University, Shanghai 200433, China;Institute of Microsystem and Information Technology, Chinese Academy of Sciences, Shanghai 200050, China
  • 收稿日期:2007-05-15 修回日期:2007-12-25 出版日期:2008-06-20 发布日期:2008-06-20
  • 基金资助:
    Project supported by the National Basic Research Program of China (Grant No 2006CB921701-6), Pujiang Talent Project (Grant No PJ2005(00593)), and the Hundred Tarent Project of the Chinese Academy of Sciences, China.

Slowly moving matter--wave gap soliton propagation in weak random nonlinear potential

Zhang Ming-Rui(张铭锐)a)b)†, Zhang Yong-Liang(张永亮)b), Jiang Xun-Ya(蒋寻涯)b), and Zi Jian(资剑)a)   

  1. a Surface Physics Laboratory (National Key Lab), Fudan University, Shanghai 200433, China; bInstitute of Microsystem and Information Technology, Chinese Academy of Sciences, Shanghai 200050, China
  • Received:2007-05-15 Revised:2007-12-25 Online:2008-06-20 Published:2008-06-20
  • Supported by:
    Project supported by the National Basic Research Program of China (Grant No 2006CB921701-6), Pujiang Talent Project (Grant No PJ2005(00593)), and the Hundred Tarent Project of the Chinese Academy of Sciences, China.

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摘要： We systematically investigate the motion of slowly moving matter--wave gap solitons in a nonlinear potential, produced by the weak random spatial variation of the atomic scattering length. With the weak randomness, we construct an effective-particle theory to study the motion of gap solitons. Based on the effective-particle theory, the effect of the randomness on gap solitons is obtained, and the motion of gap solitons is finally solved. Moreover, the analytic results for the general behaviours of gap soliton motion, such as the ensemble-average speed and the reflection probability depending on the weak randomness are obtained. We find that with the increase of the random strength the ensemble-average speed of gap solitons decreases slowly where the reduction is proportional to the variance of the weak randomness, and the reflection probability becomes larger. The theoretical results are in good agreement with the numerical simulations based on the Gross--Pitaevskii equation.

关键词: gap soliton, weak random nonlinear potentials, effective particle picture

Abstract: We systematically investigate the motion of slowly moving matter--wave gap solitons in a nonlinear potential, produced by the weak random spatial variation of the atomic scattering length. With the weak randomness, we construct an effective-particle theory to study the motion of gap solitons. Based on the effective-particle theory, the effect of the randomness on gap solitons is obtained, and the motion of gap solitons is finally solved. Moreover, the analytic results for the general behaviours of gap soliton motion, such as the ensemble-average speed and the reflection probability depending on the weak randomness are obtained. We find that with the increase of the random strength the ensemble-average speed of gap solitons decreases slowly where the reduction is proportional to the variance of the weak randomness, and the reflection probability becomes larger. The theoretical results are in good agreement with the numerical simulations based on the Gross--Pitaevskii equation.

Key words: gap soliton, weak random nonlinear potentials, effective particle picture

中图分类号:  (Tunneling, Josephson effect, Bose-Einstein condensates in periodic potentials, solitons, vortices, and topological excitations)

  • 03.75.Lm
42.65.Tg (Optical solitons; nonlinear guided waves)