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Efiects of localized impurity on a dark soliton in a.pdf

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Efiects of localized impurity on a dark soliton in a

Vol 18 No 7, July 2009 c? 2009 Chin. Phys. Soc. 1674-1056/2009/18(07)/2659-08 Chinese Physics B and IOP Publishing Ltd Effects of localized impurity on a dark soliton in a Bose–Einstein condensate with an external magnetic trap? Li Hong(李宏)a)b)?, and Wang Dong-Ning(王东宁)c) a)School of Physics and Electronic Science, Hubei Normal University, Huangshi 435002, China b)School of Mechanical and Electronic Engineering, Huangshi Institute of Technology, Huangshi 435003, China c)Department of Electrical Engineering, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong, China (Received 11 January 2009; revised manuscript received 31 January 2009) The dynamics of a dark soliton has been investigated in a Bose–Einstein condensate with an external magnetic trap, and the effects of localized impurity on the dynamics are discussed by the variational approach based on the renormalized integrals of motion. The reciprocal movement of the dark soliton is discussed by performing a standard linear analysis, and it is found that the effects of the localized impurity depend strictly on the positive or negative value of the impurity strength corresponding to the repulsive or attractive impurity. The numerical results confirm the theoretical analysis, and show that the effects also depend on the effective nonlinear coefficient and the harmonic frequency. Keywords: Bose–Einstein condensate, dark soliton, the variational approach, impurity PACC: 0530J, 0290, 1110L 1. Introduction The current experimental and theoretical stud- ies of Bose–Einstein condensates (BECs) have at- tracted a great deal of interest, and the behaviour of the BECs crucially depends on the sign of the atomic interactions. The mean-field description for the macroscopic BEC wavefunction is constructed us- ing the Hartree–Fock approximation, and results in the Gross–Pitaevskii equation (GPE), and it is well known that the GPE supports solitonic solutions.[1?5] Dark solitons (with positive scattering length) o