Fundamental modes in a waveguide pipe twisted by inverted nonlinear double-well potential
Fundamental modes in a waveguide pipe twisted by inverted nonlinear double-well potential
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DOI：
10.1088/1054-660x/24/4/045403
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发表时间：
2014-04
期刊：
影响因子：
1.2
通讯作者：
Haoxu Guo;Zhaopin Chen;Jing-Feng Liu;Yongyao Li
中科院分区：
文献类型：
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作者：
Haoxu Guo;Zhaopin Chen;Jing-Feng Liu;Yongyao Li
我们研究了在旋转环中被局部强度调制为V （θ−ωz）和- V （θ−ωz）的线性和非线性电位所捕获的基模，其中θ为方位角，调制模式为V (θ) ~ cos2θ，这是−π≤θ < π域中的双阱分布。该模型基于周期性边界条件下的非线性Schrödinger方程，适用于光在扭曲波导管中的传播，以及在旋转光场和Feshbach共振诱导的旋转π相外线性势和非线性伪势作用下加载到环形阱中的玻色-爱因斯坦凝聚体。在自聚焦的情况下，确定了三种类型的基本捕获模式，一种对称模式和两种非对称模式。这与最近考虑的纯线性或非线性旋转势的设置不同。在这种情况下，只能找到两种基本模态。在第一旋转布里渊区研究了这些模式的形状和稳定性，以及它们之间的跃迁。调制深度和V （θ, ω）的转速对对称破缺的影响很大，将对称模转变为非对称模。在这三种类型中确定了基态模式，而不稳定的非对称模式的演化主要被困在一个潜在的井中，其特征是两个井之间的约瑟夫森振荡。
We study the fundamental modes trapped in a rotating ring with the local strength of the linear and nonlinear potentials modulated as V (θ − ωz) and − V (θ − ωz), respectively, where θ is the azimuthal angle and the modulation pattern is V (θ) ∼cos2θ, which is a double-well profile in the domain of − π ≤ θ < π. The model, based on the nonlinear Schrödinger equation with periodic boundary conditions, applies to light propagation in a twisted waveguiding pipe, and to a Bose–Einstein condensate loaded into a toroidal trap under the action of a rotating π-out-of-phase linear potential and nonlinear pseudopotential, induced by means of a rotating optical field and the Feshbach resonance, respectively. In the case of self-focusing, three types of fundamental trapped modes are identified, one symmetric and two asymmetric. This is different from the recently considered setting with purely linear or nonlinear rotating potential. In that setting, only two fundamental modes can be found. The shapes and stability of these modes, together with the transitions between them, are investigated in the first rotational Brillouin zone. The symmetry breaking, which transforms the symmetric mode into the asymmetric ones, is strongly affected by the modulation depth and the rotation speed of V (θ, ω). The ground-state mode is identified among these three types, and the evolution of an unstable asymmetric mode, which is chiefly trapped in one potential well, features Josephson oscillations between the two wells.