自旋轨道耦合玻色-爱因斯坦凝聚体中无序效应的研究

In 2011, a spin-orbit coupled Bose-Einstein condensate was realized in an ultracold atom experiment. Due to the Nonabelian characteristics of spin-orbit coupling and the macroscopic degeneracy of ground states of a free boson system, the Bose-Einstein condensates exhibit many novel behaviors in off-diagonal long-range orders, topological excitations, dynamical behaviors, etc. In this program, we will study the mechanism of the interplay between disorders and spin-orbit coupled Bose-Einstein condensates, and also the resulting effects on the properties of the condensates. We will first consider a classical impurity moving in a spin-orbit coupled Bose-Einstein condensate, and calculate the screening effects experienced by the impurity due to the condensate. Then, we will further consider quantum impurities, that is, Rydberg electron and quantum dot. We will calculate the scattering cross section of interactions between the Rydberg electron and the condensate, the screening effects experienced by the Rydberg electron, the energy levels of the Rydberg electron, and also the hopping dynamics between the energy levels due to scattering with the condensate. We will also study the hopping processes for the electron in the quantum dot when it moves in the condensate. The other part in this program is to study the mechanism of interplay between quenched disorder and particle-particle interactions in a disordered spin-orbit coupled Bose-Einstein condensate, and also the effects on the localization properties of wave functions of the bosons. We will calculate the renormalization of the particle-particle interactions and also the mass of the bosons due to the existence of the quenched disorder. We will also study the screening effects on the impurity potentials and the corresponding mechanisms. After that, we will obtain the localization behaviors of the wave functions of the bosons. These studies will help to understand the special role of the spin-orbit coupling in Bose-Einstein condensates and also the mechanism of interplay between disorders and the spin-orbit coupled Bose-Einstein condensates. Besides, these studies will also be useful for the applications of spin-orbit coupled Bose-Einstein condensates.

2011年超冷原子实验实现了自旋轨道耦合玻色-爱因斯坦凝聚体。由于自旋轨道耦合的非阿贝尔性质及其系统基态具有无穷简并度，凝聚体在许多方面呈现新颖的行为，如非对角长程序、拓扑激发态、动力学等。本项目将研究自旋轨道耦合凝聚体中的无序效应及物理机制。首先研究单个动力学杂质与凝聚体作用，分别考虑经典杂质、里德堡电子、量子点。研究经典杂质受到的屏蔽效应，里德堡电子与凝聚体作用的散射截面及受到的屏蔽效应，其能级、波函数和能级跃迁动力学，量子点内部能级跃迁动力学等。然后研究淬火型无序与玻色子两体相互作用之间的相互影响及对波函数局域化的影响，得到无序对两体相互作用和有效质量的重整化及两体相互作用对杂质势的屏蔽效应，以及波函数的局域化行为。这些研究将有助于揭示自旋轨道耦合在玻色系统中的作用以及无序与自旋轨道耦合凝聚体相互作用机理，同时也对自旋轨道耦合凝聚体的应用起理论指导作用。

超冷原子系统中通过光与原子相互作用产生作用于原子的有效的规范场，实验中通过这种方式产生了具有自旋轨道耦合作用的玻色-爱因斯坦凝聚的原子气体。这种物质态首次在实验室中制备。本项目主要通过研究杂质在其中的动力学行为来研究自旋轨道耦合起的特定的作用以及该玻色-爱因斯坦凝聚体的特有的性质。在项目执行期间 在该课题上发表取得两个成果。一是研究了两杂质在该凝聚体中的Casimir势，发现了具有振荡的行为。二是研究了杂质在Weyl以及Rashba自旋轨道耦合凝聚体中的超流临界速度，揭示了自旋轨道耦合对系统对称性的影响以及对超流临界速度的影响。此外，在相关的问题上也取得一些成果，包括在自旋轨道耦合光晶格系统中的绝缘体的行为，在具有Rashba作用的巨磁阻效应中的热产生问题。由本项目资助的论文中，项目负责人以第一作者已发表Physical Review A一篇，培养的硕士研究生为第一作者项目负责人为通讯作者已发表SCI论文一篇，项目负责人参与的SCI论文已发表3篇，项目组成员已发表Physical Review A一篇。通过本项目的研究对深入研究具有自旋轨道耦合的玻色-爱因斯坦凝聚体的性质以及自旋轨道耦合在凝聚态中起的作用具有一定的意义。研究成果对实验以及潜在的应用具有一定的借鉴意义。

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