The Effect Of External Potentials On Solitons Dynamics In The Bose-Einstein Condensate

Bose Einstein condensation(BEC) were successful observed in the alkali metal-atoms gas, which greatly encouraged the scientist to study the nonlinear properties of matter waves. Especially, after the nonlinear phenomena of the bright solitons, dark solitons, and four wave mixing were observed in BEC, the study of nonlinear properties in BEC not only occupies an important position in basic research, but also is a very broad application prospects of the applications of the electronic chip,precision instrument, atomic clock and nano-technology etc..The theory description of the BEC is the Gross-Pitaevskii(GP) equation which builds on the mean field approximation with weak interaction. There are two macro-controlled physical parameters in the GP equation. One parameter is the inter-atomic interaction, the another is the external trapping potential. The external potential could be controlled by external magnetic or laser in experiment. And the inter-atomic interaction could be controlled by nonlinear coefficient, which is realized by the famous Feshbach resonate technology to vary the s-wave scattering length. By far, It have been found that the different external potentials and inter-atomic interactions have a very important effect on the formation and the characteristics of the solitons in BEC. This paper considers the influence of different external potentials on the dynamic behavior of solitons in BEC. Its main structure is the following.Firstly, this paper introduces the research background of Bose-Einstein condensation, the related experimental technique, the researching methods: the multiple-scale method. Subsequently we introduce the significance of studying and the researching contents.Secondly, we analytically study the influence of square well potential on solitons dynamics in the Bose-Einstein condensate by the multiple-scale method. It is found that the amplitude, the velocity, and the width of the solitons in BEC could be controlled by the depth of the square potential. The solitons accelerated when entering the square potential, while decelerating when escaping from the potential. With the increase of potential’s depth, the solitons’ velocity increase, the amplitude increases,and the width reduces.Thirdly, we use the analytically method combined with numerical simulation to study the effect of the double barrier potential on the dynamical properties in the BEC.It is shown that there exhibit stable solitons at the top of the barrier potential and the region of in the absence of the barrier potential. Furthermore, our numericalcalculation showed that the height of the barrier potential had an important effect on the dark solitons dynamical characteristics. With the height of the barrier potential increasing, the amplitude of the two dark solitons becomes smaller, their widths are wider. Especially, in the case of regarding a double barrier potential as the output source of the solitons, the collision both the spots and the pattern(chase, head-on, or localization and through collision) between two dark solitons interaction can be controlled by the height of the barrier potential.Finally, we briefly summarize the work of this paper, at the same time, also prospect for future work.