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Journal of Physics B Atomic Molecular and Optical Physics

Dynamics of bright matter wave solitons in Bose–Einstein condensates in an expulsive parabolic and complex potential

Emmanuel Kengne, Pierre Kisito Talla

Published Aug 29, 2006• 49 citations
Publisher

Abstract

We present a new family of analytic solutions of the nonlinear Schrödinger equation with an imaginary potential that describes the dynamics of a bright soliton in a Bose–Einstein condensate with an expulsive parabolic and complex potential. We found that under a safe range of parameters, the bright soliton can be compressed into very high local matter densities by increasing the value of the feeding parameter.

DOI
10.1088/0953-4075/39/17/023

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We present a new family of analytic solutions of the nonlinear Schrödinger equation with an imaginary potential that describes the dynamics of a bright soliton in a Bose–Einstein condensate with an expulsive parabolic and complex potential. We found that under a safe range of parameters, the bright soliton can be compressed into very high local matter densities by increasing the value of the feeding parameter.
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.
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 present analytical solutions of the one-dimensional nonlinear Schrodinger equations of Bose–Einstein condensates in an expulsive parabolic background with a complex potential and gravitational field, by performing the Darboux transformation from a trivial seed solution. It is shown that under a safe range of parameter, the shape of bright soliton can be controlled well by adjusting the experimental parameter of the ratio of axial oscillation to radial oscillation and feeding condensates from a thermal cloud. The gravitational field can change the contrail of the bright soliton trains without changing their peak and width.
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.
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.
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.