基于偶极玻色爱因斯坦凝聚体的二维各向异性物质波孤子及其相互作用的研究

The recent years have witnessed a rapid development of the experimental abilities to realize Bose-Einstein condensates (BEC) in atoms and molecules with large electrical and magnetic dipolar moments. Dipole-dipole interactions (DDI) in such quantum gases are long-range and anisotropic which can bring rich new phenomena and attracts great attentions. For soliton physics, long-range and anisotropic DDIs provide anisotropic nonlocal nonlinearities, giving rise to the possibility to created stable two-dimensional soliton, which is unable to achieve in traditional cubic nonlinear media. Under the anisotropic nonlocal nonlinearity, soliton also becomes anisotropic not only in the internal structure, but also for the mobility and interactions, which brings new opportunities and challenges to the study of soliton physics. The main goal of this proposal is to theoretically study the stable condition of the 2D anisotropic dipolar matter wave solitons, and clarify the mobility and interactions of them in free space, optical lattice and two-component systems. Especially, the creation of anisotropic vortex soliton in dipolar BEC is the main target of this goal. The results of this proposal can also give suggestions to how to realize such solitons experimentally.

偶极玻色-爱因斯坦凝聚(BEC)是近年来冷原子及相关研究领域中一个热点问题。 这些具有长程各向异性偶极-偶极相互作用(DDI)的量子气体为物质波孤子的研究带来一系列新的物理问题：它可以在二维的自由空间支持孤子的存在，突破了传统的三次非线性介质的局限。而且在各向异性DDI作用下，这些二维孤子也呈现出各向异性的特点，研究这些基于DDI所形成的新孤子，将给孤子研究带来新的机遇和挑战。本项目基于上述研究背景，在自由空间，光晶格和二分量系统下对偶极BEC中二维各向异性物质波孤子的产生及相互作用展开研究，得出这类孤子在上述系统中形成的稳定条件，寿命，以及形态形貌。其中，如何产生和稳定基于偶极BEC的各向异性涡旋态孤子，是一个挑战性问题。在此基础上，本项目将进一步探明这些孤子间由DDI所诱导的各向异性相互作用的机理，并提出相关的实验方案，为实验观产生和探测这类孤子提供有效的理论依据和支持。

本项目在理论上分别对二维自由空间系统，光晶格系统和二分量系统下偶极玻色爱因斯坦凝聚体(BECs)形成的各向异性的物质波孤子在外场控制下的产生、运动及相互作用的问题展开研究并分析了偶极孤子在上述系统中形成的稳定条件，寿命，以及形态形貌。同时，我们借助了BEC中自旋轨道耦合效应在自由空间产生了具有各向异性密度分布的涡旋孤子，并提出了三种对这种各向异性孤子进行调控的方法，成功获得三种获得具有椭圆密度分布的各向异性涡旋孤子。