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arXiv:cond-mat/0502482 · Physical Review Letters

Dynamics of a Bright Soliton in Bose-Einstein Condensates with Time-Dependent Atomic Scattering Length in an Expulsive Parabolic Potential

Zhaoxin Liang, Zhang Zhi-dong, Weijian Liu

Published Feb 9, 2005• 427 citations
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Abstract

We present a family of exact solutions of the one-dimensional nonlinear Schro dinger equation which describes the dynamics of a bright soliton in Bose-Einstein condensates with the time-dependent interatomic interaction in an expulsive parabolic potential. Our results show that, under a safe range of parameters, the bright soliton can be compressed into very high local matter densities by increasing the absolute value of the atomic scattering length, which can provide an experimental tool for investigating the range of validity of the one-dimensional Gross-Pitaevskii equation. We also find that the number of atoms in the bright soliton keeps dynamic stability: a time-periodic atomic exchange is formed between the bright soliton and the background.

DOI
10.1103/physrevlett.94.050402

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We present a family of exact solutions of the one-dimensional nonlinear Schro dinger equation which describes the dynamics of a bright soliton in Bose-Einstein condensates with the time-dependent interatomic interaction in an expulsive parabolic potential. Our results show that, under a safe range of parameters, the bright soliton can be compressed into very high local matter densities by increasing the absolute value of the atomic scattering length, which can provide an experimental tool for investigating the range of validity of the one-dimensional Gross-Pitaevskii equation. We also find that the number of atoms in the bright soliton keeps dynamic stability: a time-periodic atomic exchange is formed between the bright soliton and the background.
We analyze the dynamics of a bright soliton in Bose–Einstein condensates (BECs) with time-dependent atomic scattering length in an expulsive parabolic potential. Under a safe range of parameters in which the Gross–Pitaevskii (GP) equation is effective in one dimension, our results show that, the dynamics of the bright soliton can be classed into two phases, depending on the value of the scattering length. Meanwhile, there exists a critical value of the absolute value of the atomic scattering length, below which, the dynamics of the bright soliton is very regular. Those phenomena can be useful for developing concrete applications of the nonlinear matter waves. We also obtain the orbital equation of the bright soliton and get some interesting data which may be useful for the experimental observation of the bright soliton and the application of the atom laser with manipulated intensity.
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.
The exact solitonic solutions of the one-dimensional nonlinear Schrödinger equation, which describes the dynamics of bright soliton in Bose–Einstein condensates with the time-dependent interaction in an expulsive parabolic and complex potential, are obtained by Darboux transformation. The results show that one can compress a bright soliton into an assumed peak of matter wave density by adusting the experimental parameter of the ratio of axial oscillation to radial oscillation or feeding parameter. Especially, when parameters satisfy the relation λ = 2γ, the soliton is stable with time evolution without changing its shape and amplitude.
An analytical study on the dynamics of bright solitons of Bose–Einstein condensates (BEC) with a time-varying atomic scattering length in a time-varying expulsive parabolic potential is presented. Exact solutions of the one-dimensional Gross–Pitaevskii equation are obtained. The results show that the bright soliton (including the higher-order bright soliton) can be compressed into a desired width and amplitude in a controllable manner by changing the scattering length and external potential. Furthermore, it is shown numerically that the present method is also efficient for the two-dimensional BEC's compression.