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Bose-Einstein condensate confined in a one-dimensional ring stirred with a rotating delta link
Physical Review E ( IF 2.4 ) Pub Date : 2020-02-18 , DOI: 10.1103/physreve.101.022212
Axel Pérez-Obiol , Taksu Cheon

We consider a Bose-Einstein condensate with repulsive interactions confined in a one-dimensional ring where a Dirac δ is rotating at constant speed. The spectrum of stationary solutions in the δ comoving frame is analyzed in terms of the nonlinear coupling, δ velocity, and δ strength, which may take positive and negative values. It is organized into a set of energy levels conforming a multiple swallowtail structure in parameter space, consisting of bright solitons, gray and dark solitonic trains, and vortex states. Analytical expressions in terms of Jacobi elliptic functions are provided for the wave functions and chemical potentials. We compute the critical velocities and perform a Bogoliubov analysis for the ground state and first few excited levels, establishing possible adiabatic transitions between the stationary and stable solutions. A set of adiabatic cycles is proposed in which gray and dark solitons, and vortex states of arbitrary quantized angular momenta, are obtained from the ground state by setting and unsetting a rotating δ. These cycles are reproduced by simulations of the time-dependent Gross-Pitaevskii equation with a rotating Gaussian link.

中文翻译:

玻色-爱因斯坦凝聚物被限制在一维环中,并带有旋转的三角链

我们考虑了具有排斥相互作用的玻色-爱因斯坦凝聚物,其凝聚在一个一维环中,其中狄拉克 δ正在以恒定速度旋转。固定溶液的光谱δ 根据非线性耦合分析同移框架 δ 速度和 δ强度,可以取正值和负值。它被组织成一组在参数空间中符合多重燕尾结构的能级,包括明亮的孤子,灰色和黑暗的孤子声列以及涡旋状态。提供了关于雅可比椭圆函数的解析表达式,用于波动函数和化学势。我们计算临界速度,并对基态和前几个激发能级进行Bogoliubov分析,从而建立了稳定解与稳定解之间可能的绝热转变。提出了一组绝热循环,其中通过设置和取消旋转来从基态获得灰度和暗孤子,以及任意量化角动量的涡旋状态。δ。通过对具有旋转高斯链的时间相关的Gross-Pitaevskii方程进行仿真,可以再现这些循环。
更新日期:2020-02-19
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