Spin - Orbital Angular Momentum Coupled Ultra-cold Atomic Gases

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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.