Twisted toroidal vortex solitons in inhomogeneous media with repulsive nonlinearity.
Twisted toroidal vortex solitons in inhomogeneous media with repulsive nonlinearity.
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DOI：
10.1103/physrevlett.113.264101
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发表时间：
2014-12
影响因子：
8.6
通讯作者：
Y. Kartashov;B. Malomed;Y. Shnir;L. Torner
中科院分区：
文献类型：
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作者：
Y. Kartashov;B. Malomed;Y. Shnir;L. Torner
所谓的 Hopfions 形式的环形模式具有两个独立的绕数，一个隐藏的绕数（扭曲 s），其特征在于嵌入三维孤子中的圆形涡线，以及围绕垂直轴（m）的涡量，出现在许多领域，包括场论、铁磁以及半导体和超导体。这种拓扑状态通常在多组分系统中生成，或者作为环形势中的俘获拟线性模式生成。我们发现，在单分量设置中，可以在没有任何线性势的情况下创建具有这种结构的稳定孤子，并且排斥非线性的强度从中心到外围足够快地增长，以实现陡峭和平滑的调制轮廓。产生 s=1 且涡度 m=0、1、2 的环形模式。当 m≤1 时它们是稳定的，当 s>1 时它们不存在。得到了s=1、m=0的扭环的近似解析解。在外部扭矩的作用下，它像实心环一样旋转。该设置可以通过非均匀磁场控制的费什巴赫共振在玻色-爱因斯坦凝聚体（BEC）中实现。
Toroidal modes in the form of so-called Hopfions, with two independent winding numbers, a hidden one (twist s), which characterizes a circular vortex thread embedded into a three-dimensional soliton, and the vorticity around the vertical axis (m), appear in many fields, including field theory, ferromagnetics, and semi- and superconductors. Such topological states are normally generated in multicomponent systems, or as trapped quasilinear modes in toroidal potentials. We uncover that stable solitons with this structure can be created, without any linear potential, in the single-component setting with the strength of repulsive nonlinearity growing fast enough from the center to the periphery, for both steep and smooth modulation profiles. Toroidal modes with s=1 and vorticity m=0, 1, 2 are produced. They are stable for m≤1, and do not exist for s>1. An approximate analytical solution is obtained for the twisted ring with s=1, m=0. Under the application of an external torque, it rotates like a solid ring. The setting can be implemented in a Bose-Einstein condensate (BEC) by means of the Feshbach resonance controlled by inhomogeneous magnetic fields.