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Journal of Physics Conference Series

Variational analysis of soliton scattering by external potentials

Bakhram Umarov, Azeddine Messikh, N Regaa, Bakhtiyor B. Baizakov

Published Apr 26, 2013• 14 citations
Publisher

Abstract

Dynamics of the width and center-of-mass position of a matter wave soliton subject to interaction with arbitrary external potential is analyzed using the collective coordinates approach. It is shown that approximation of the trial function and external potential only in the interaction region of the spatial domain is sufficient for adequate description of the soliton scattering process. The validity of the developed approach is illustrated for the Gaussian and Pöschl-Teller potentials.

DOI
10.1088/1742-6596/435/1/012024

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Dynamics of the width and center-of-mass position of a matter wave soliton subject to interaction with arbitrary external potential is analyzed using the collective coordinates approach. It is shown that approximation of the trial function and external potential only in the interaction region of the spatial domain is sufficient for adequate description of the soliton scattering process. The validity of the developed approach is illustrated for the Gaussian and Pöschl-Teller potentials.
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Abstract Using the time-dependent variational approach and the numerical solution of the Gross–Pitaevskii (GP) equation, the dynamics of a matter-wave soliton are investigated in a two-dimensional constant external force field. Firstly, the time-dependent variational approach is used to study the movements of the center-of-mass position in a simple harmonic trap and a two-dimensional weakly transmissive reflective barrier. Because the mathematical model for describing soliton dynamics in simple harmonic traps is simple, the analytic dynamical results of a soliton wave packet center-of-mass position is given directly. Since the model describing the weakly transmissive reflective barrier is difficult to solve analytically, we give the Newton’s equation of the center-of-mass position of motion, and then use the numerical solution method to study the movement of the center-of-mass in the case of several parameters. To study the motion of the soliton in the harmonic potential trap in the two-dimensional external force field under rotation , we use the split-step finite difference method to solve the two-dimensional GP equation; the motion of the center-of-mass position is discussed under the conditions of several parameter combinations. The results show that the rotation has a very important influence on the movement of the center-of-mass. When there is no rotation effect, the center-of-mass position acts as a simple harmonic motion under the combined action of the external force field and the potential well. When there is a rotation effect, the center-of-mass position is almost static.
The dynamics of a matter-wave soliton bouncing on the reflecting surface (atomic mirror) under the effect of gravity has been studied by analytical and numerical means. The analytical description is based on the variational approach. Resonant oscillations of the soliton's center of mass and width, induced by appropriate modulation of the atomic scattering length and the slope of the linear potential, are analyzed. In numerical experiments we observe the Fermi-type acceleration of the soliton when the vertical position of the reflecting surface is periodically varied in time. Analytical predictions are compared to the results of numerical simulations of the Gross-Pitaevskii equation and qualitative agreement between them is found.
Static and dynamic properties of matter-wave solitons in dense Bose–Einstein condensates, where three-body interactions play a significant role, have been studied by a variational approximation (VA) and numerical simulations. For experimentally relevant parameters, matter-wave solitons may acquire a flat-top shape, which suggests employing a super-Gaussian trial function for VA. Comparison of the soliton profiles, predicted by VA and those found from numerical solution of the governing Gross–Pitaevskii equation shows good agreement, thereby validating the proposed approach.
We consider, by analytical and numerical means, the dynamics of a matter-wave soliton bouncing on the reflecting surface (atomic mirror) under the influence of gravity, when twobody interactions between atoms are periodically modulated in time. The analytical description is based on the variational approach. The frequencies of small amplitude oscillations of the soliton's center-of-mass and width are obtained. Analytical predictions are compared to the results of numerical simulations of the Gross-Pitaevskii equation and qualitative agreement between them is found.
Static and dynamic properties of matter-wave solitons in dense Bose-Einstein condensates, where three-body interactions play a significant role, have been studied by a variational approximation (VA) and numerical simulations. For experimentally relevant parameters, matter-wave solitons may acquire a flat-top shape, which suggests employing a superGaussian trial function for VA. Comparison of the soliton profiles, predicted by VA and those found from numerical solution of the governing Gross-Pitaevskii equation shows good agreement, thereby validating the proposed approach.