Communications in Theoretical Physics

Exact Analytical Solutions in Bose–Einstein Condensates with Time-Dependent Atomic Scattering Length

Yong Chen, Li Biao, Yu Jie Zheng

Published Jan 1, 2007• 6 citations

Abstract

In the paper, the generalized Riccati equation rational expansion method is presented. Making use of the method and symbolic computation, we present three families of exact analytical solutions of Bose–Einstein condensates with the time-dependent interatomic interaction in an expulsive parabolic potential. Then the dynamics of two anlytical solutions are demonstrated by computer simulations under some selectable parameters including the Feshbach-managed nonlinear coefficient and the hyperbolic secant function coefficient.

DOI: 10.1088/0253-6102/47/1/028

Related papers

Soliton Solutions in Bose–Einstein Condensates with Time-Dependent Atomic Scattering Length in an Expulsive Parabolic Potential

Zhang Jie-Fang, Yang Qin

We present both the bright and dark solitons of Bose–Einstein condensates with a time-dependent atomic scattering length in an expulsive parabolic potential. As a discussed example, we select the experimental parameter, i.e. the Feshbach-managed nonlinear coefficient reading a ( t ) = g 0 exp(λ t ), and obtain the results which can be recovered in the literature [Phys. Rev. Lett. 94 (2005) 050402].

Chinese Physics LettersJul 29, 200516 citations

Soliton Solutions in Bose-Einstein Condensates with Time-Dependent Atomic Scattering Length in an Expulsive Parabolic Potential

张解放, 杨琴

We present both the bright and dark solitons of Bose-Einstein condensates with a time-dependent atomic scattering length in an expulsive parabolic potential. As a discussed example, we select the experimental parameter, i.e. the Feshbach-managed nonlinear coefficient reading a(t) = go exp(λt), and obtain the results which can be recovered in the literature [Phys. Rev. Lett. 94 (2005) 050402].

Chinese Physics LettersJan 1, 20050 citations

Dynamics of solitons in Bose–Einstein condensate with time-dependent atomic scattering length

Huamei Li

The evolution of solitons in Bose–Einstein condensates (BECs) with time-dependent atomic scattering length in an expulsive parabolic potential is studied. Based on the extended hyperbolic function method, we successfully obtain the bright and dark soliton solutions. In addition, some new soliton solutions in this model are found. The results in this paper include some in the literature ( Phys. Rev. Lett. 94 (2005) 050402 and Chin. Phys. Lett. 22 (2005) 1855).

Chinese PhysicsSep 21, 200616 citations

Solitons in Bose-Einstein condensates with time-dependent atomic scattering length in an expulsive parabolic and complex potential

Biao Li, Xiao-Fei Zhang, Yu-Qi Li +2 more

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.

arXiv:0806.3608Physical Review AAug 5, 200886 citations

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

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.

arXiv:cond-mat/0502482Physical Review LettersFeb 9, 2005427 citations

Exact Analytical Solutions in Bose-Einstein Condensates with Time-Dependent Atomic Scattering Length

Chen, Yong, Li +3 more

在纸，概括 Riccati 方程合理扩大方法被介绍。使用方法和符号的计算，我们在场 Bose 的准确分析答案的三个家庭—有时间依赖者的爱因斯坦冷凝物内部在一个逐出的抛物线的潜力的原子相互作用。然后，二个 anlytical 解决方案的动力学被计算机模拟包括管理 Feshbach 的非线性的系数和夸张正割函数系数在一些可选的参数下面表明。

理论物理通讯：英文版Jan 1, 20071 citation