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Chinese Physics B

Controlling the amplitude of soliton in a growing Bose–Einstein condensate by means of Feshbach resonance

He Zhang-Ming, Denglong Wang, Weixi Zhang, Fengjiao Wang, Jianwen Ding

Published Oct 1, 2008• 11 citations
Publisher

Abstract

By using Darboux transformation, this paper studies analytically the nonlinear dynamics of a one-dimensional growing Bose–Einstein condensate (BEC). It is shown that the growing model has an important effect on the amplitude of the soliton in the condensates. In the absence of the growing model, there exhibits the stable alternate bright solitons in the condensates. In the presence of the growing model, the obtained results show that the amplitude of the bright soliton decreases (increases) for the BEC growing coefficient Ω < 0 (Ω > 0). Furthermore, we propose experimental protocols to manipulate the amplitude of the bright soliton by varying the scattering length via the Feshbach resonance in the future experiment.

DOI
10.1088/1674-1056/17/10/018

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By using Darboux transformation, this paper studies analytically the nonlinear dynamics of a one-dimensional growing Bose–Einstein condensate (BEC). It is shown that the growing model has an important effect on the amplitude of the soliton in the condensates. In the absence of the growing model, there exhibits the stable alternate bright solitons in the condensates. In the presence of the growing model, the obtained results show that the amplitude of the bright soliton decreases (increases) for the BEC growing coefficient Ω < 0 (Ω > 0). Furthermore, we propose experimental protocols to manipulate the amplitude of the bright soliton by varying the scattering length via the Feshbach resonance in the future experiment.
We analytically study the interaction characteristics of two bright solitons in a one-dimensional growing Bose–Einstein condensate with time-dependent periodic atomic scattering length. It is shown that the interaction between two bright solitons can generate fission and fusion in the presence of both time-dependent periodic atomic scattering length and the growing case. Furthermore, we propose experimental protocols to realize these interaction phenomena by varying the scattering length via the Feshbach resonance in the future experiment.
We present an analytical study on the dynamics of bright and dark solitons in Bose–Einstein condensates with time-varying atomic scattering length in a time-varying external parabolic potential. A set of exact soliton solutions of the one-dimensional Gross–Pitaevskii equation are obtained, including fundamental bright solitons, higher-order bright solitons, and dark solitons. The results show that the soliton's parameters (amplitude, width, and period) can be changed in a controllable manner by changing the scattering length and external potential. This may be helpful to design experiments.
Considering the periodically driving linear potential, we study the interactions between two solitons in Bose-Einstein condensate (BEC). By using Darboux transformation, the double bright soliton solution of Gross-Pitaevskii equation is obtained. Then we numerically calculate the properties of interaction between the two bright solitons in BEC, and obtain a critical value of the S-wave scattering length (SL). It is shown that, when the SL is more than the critical value, the attractive interaction and the atom transfer between two bright solitons can be observed. While the SL is less than the critical value, two bright solitons can keep stable and localized. Furthermore, the stable periodic oscillations of two solitons can be observed by slowly changing the potential. These results will be conducive to the BEC soliton experiments.
We present how to control interactions between solitons, either bright or dark, in Bose-Einstein condensates by synchronizing Feshbach resonance and harmonic trap. Our results show that as long as the scattering length is to be modulated in time via a changing magnetic field near the Feshbach resonance, and the harmonic trapping frequencies are also modulated in time, exact solutions of the one-dimensional nonlinear Schr\"odinger equation can be found in a general closed form, and interactions between two solitons are modulated in detail in currently experimental conditions. We also propose experimental protocols to observe the phenomena such as fusion, fission, warp, oscillation, elastic collision in future experiments.
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.