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Communications in Theoretical Physics

Solitons in Bose–Einstein Condensates with Time-Dependent Atomic Scattering Length in a Harmonic Trap

Zhang Xiao-Fei, Zhang Pei, Yang Qin

Published Dec 1, 2008• 1 citation
Publisher

Abstract

We obtain the integrable relation for the one-dimensional nonlinear Schrödinger equations which describes the dynamics of a Bose–Einstein Condensates with time-dependent scattering length in a harmonic potential. The exact one- and two-soliton solutions are constructed analytically by using the Hirota method. Then we further discuss the dynamics of the one soliton and the interactions between two solitons in currently experimental conditions.

DOI
10.1088/0253-6102/50/6/15

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We obtain the integrable relation for the one-dimensional nonlinear Schrödinger equations which describes the dynamics of a Bose–Einstein Condensates with time-dependent scattering length in a harmonic potential. The exact one- and two-soliton solutions are constructed analytically by using the Hirota method. Then we further discuss the dynamics of the one soliton and the interactions between two solitons in currently experimental conditions.
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We present two families of analytical solutions of the one-dimensional nonlinear Schr\"odinger equation, which describe the dynamics of bright and dark solitons in Bose-Einstein condensates (BECs) with the time-dependent interatomic interaction in an expulsive parabolic and complex potential. We also demonstrate that the lifetime of both a bright soliton and a dark soliton in BECs can be extended by reducing both the ratio of the axial oscillation frequency to radial oscillation frequency and the loss of atoms. It is interesting that a train of bright solitons may be excited with a strong enough background. An experimental protocol is further designed for observing this phenomenon.
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We present three families of one-soliton solutions for (2+l)-dimensional Gross-Pitaevskii equation withboth time-dependent scattering length and gain or loss in a harmonic trap.Then we investigate the dynamics of thesesolitons in Bose-Einstein condensates (BECs) by some selected control functions.Our results show that the intensitiesof these solitons first increase rapidly to the condensation peak,then decay very slowly to the background;thus thelifetime of a bright soliton,a train of bright solitons and a dark soliton in BECs can be all greatly extended.Our resultsoffer a useful method for observing matter-wave solitons in BECs in future experiments.
We present two families of one-soliton solutions and three families of two-soliton solutions for a generalized nonlinear Schrödinger equation, which is characterized by the time-dependent scattering length and varying potentials. Then, we investigate the propagation of one-soliton and interactions of two-soliton by some selected control functions. The results show that the intensities of one- and two-soliton first increase rapidly to a peak value, and then decay very slowly to the background value; thus, the lifetimes of both one-soliton and two-soliton in Bose–Einstein condensates can be extended largely at least to the order of the lifetime of a Bose–Einstein condensate in real experiments. Our results open up new ways of considerable experimental interest for the management of matter-wave solitons in Bose–Einstein condensates.
We derive exact solitonic solutions of a class of Gross–Pitaevskii equations with a time-dependent harmonic trapping potential and interatomic interaction. We find families of exact single-solitonic, multi-solitonic and solitary wave solutions. We show that, with the special case of an oscillating trapping potential and interatomic interaction, a soliton can be localized indefinitely at an arbitrary position. The localization is shown to be experimentally possible for sufficiently long time even with only an oscillating trapping potential and a constant interatomic interaction.