Spin - Orbital Angular Momentum Coupled Ultra-cold Atomic Gases

现代电子设备的进步往往是由新量子材料的发现所推动的。在许多材料中，电子自旋与其运动自由度（线性动量和轨道角动量）之间的耦合，即自旋-轨道耦合，在潜在的材料性质中起着至关重要的作用。了解自旋轨道耦合在可控平台中的影响可以为未来设计和发现具有理想性质和功能的新量子材料提供重要指导。在这种情况下，超冷原子气体为材料设计和发现提供了一个可控的平台，在实验中具有前所未有的控制和精度。以往的研究已经实现了超冷原子的一种自旋-轨道耦合（自旋与线性动量之间的耦合），成为物理学的一个重要研究前沿。然而，对于超冷原子气体，另一种重要而基本的自旋-轨道耦合，即自旋与轨道角动量之间的耦合（SOAM耦合）尚未得到探索。本项目将研究超冷原子SOAM耦合的产生及其在工程新量子态中的应用。这种高度可控的SOAM耦合冷原子平台的研究将反过来影响未来电子材料的设计和发现。这项工作不仅将为冷原子系统的相干控制铺平道路，用于许多重要应用（例如，材料设计，量子计算，精密测量等），而且还将影响冷原子和凝聚态物理的基础研究。本项目的主要目的是利用高阶拉盖尔-高斯（LG）激光模式研究超冷原子气体中SOAM耦合的产生和应用。另一个目标是利用高阶厄米特-高斯（HG）激光模式研究具有空间变化自旋-线性-动量耦合的冷原子物理。具体任务包括：1)研究利用LG或HG拉曼激光模式产生SOAM耦合或空间变化的SLM耦合；2)研究SOAM耦合和HG-SLM耦合下冷原子的基态和集体动力学；c)探索由SOAM或HG-SLM耦合诱导的玻色子和费米子的新量子相。各种数值和解析方法（例如，平均场近似，时变块抽取算法，摄动理论等）将被应用。这项工作将为研究生和本科生探索理论冷原子和凝聚态物理提供一个多样化的平台。此外，这项工作还将包括针对K-12学生的外展活动，以及女性和少数族裔学生等代表性不足群体的学生的参与。

The advances of modern electrical devices are often driven by the discovery of new quantum materials. In many materials, the coupling between electron spins and their motional degrees of freedom (linear momentum and orbital angular momentum), i.e., spin-orbit coupling, plays a crucial role in the underlying material properties. Understanding the effects of spin-orbit coupling in a controllable platform could provide important guidelines for future design and discovery of new quantum materials with desirable properties and functionalities. In this context, ultra-cold atomic gases offer such a controllable platform for material design and discovery with unprecedented level of control and precision in experiments. Previous research has realized one type of spin-orbit coupling (the coupling between spin and linear momentum) for ultra-cold atoms, which now becomes one major research frontier in physics. However, another important and fundamental type of spin-orbit coupling, the coupling between spin and orbital angular momentum (SOAM coupling), has not been explored for ultra-cold atomic gases. In this project, the generation of SOAM coupling for ultra-cold atoms and their applications in engineering new quantum states will be studied. The study of such highly controllable SOAM coupled cold atomic platform will in turn influence the future electronic material design and discovery. This work will not only pave the way for coherent control of cold atomic systems for many important applications (e.g., material design, quantum computation, precision measurement, etc.), but will also influence fundamental research in cold atomic and condensed matter physics. The major objective of this project is to investigate the generation and applications of SOAM coupling in ultra-cold atomic gases using higher order Laguerre-Gaussian (LG) laser modes. Another goal is to study the cold atomic physics with spatially varying spin-linear-momentum (SLM) coupling using higher order Hermit-Gaussian (HG)) laser modes. Specific tasks include: 1) Study the generation of SOAM coupling or spatially varying SLM coupling using LG or HG Raman laser modes; 2) Investigate ground states and collective dynamics of cold atoms in the presence of SOAM coupling and HG-SLM coupling; c) Explore novel quantum phases induced by SOAM or HG-SLM couplings for both bosons and fermions. Various numerical and analytical methods (e.g., mean field approximation, time-evolving-block-decimation algorithm, perturbation theory, etc.) will be applied. The work will provide a diverse platform for both graduate and undergraduate students to explore theoretical cold atomic and condensed matter physics. In addition, this effort will include outreach activities for K-12 students and involvement of students from under-represented groups, such as women and minority students.