Spin Tensors in Ultracold Atomic Gases

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The quest for quantum materials with novel functionality has led to great advances of modern electronic devices in the past few decades. Spin, a fundamental degree of freedom of particles, and its coupling with orbital degrees of freedom (e.g., momentum) has played a crucial role in the discovery, characterization, and application of novel quantum materials. In conventional materials, electron spins are fully described by spin-1/2 vectors. Recently the study of unconventional quantum materials with large effective spins (e.g., spin-1) has emerged as a forefront of materials research. Since a full description of any large spin (spin-1 and larger) naturally involves spin-tensors, understanding the effects of spin-tensors and their coupling with momentum 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, ultracold atomic gases offer such a controllable platform with an unprecedented level of experimental control and precision. Previous research has realized the coupling between spin vector and momentum for ultracold atoms, which has now become a major research frontier in physics. This project studies the generation of spin-tensors and spin-tensor-momentum coupling for ultracold atoms and explores their applications in engineering new quantum states. The study of such highly controllable spin-tensors in a cold atomic platform will in turn influence future electronic materials design and discovery. The research will not only pave the way for coherent control of cold atomic systems for many important applications (e.g., materials design, spintronics, quantum computation, etc.), but will also influence fundamental research in cold atomic and condensed matter physics. The project provides a diverse platform for both graduate and undergraduate students to explore theoretical cold atomic and condensed matter physics. The scope of this project also includes specific outreach activities for K-12 students including involving students from under-represented groups, such as women and minority students, for broadening participation.The major objective of the project is to address two outstanding questions: i) Can we experimentally realize the coupling between spin tensors of ultracold atoms and their linear momenta? ii) If so, what type new physics may emerge from such spin-tensor-momentum coupling? Specific tasks include: i) Schemes for experimental generation of various types of spin-tensors and spin-tensor-momentum coupling for a large spin (particularly spin-1) atomic gas; ii) Exotic quantum phases induced by spin-tensors, such as spin supersolid stripe phases with long periods and high visibilities, large Chern number topological insulators and superfluids with high-order band touching points, topological triply-degenerate points and nodal lines, etc. Various numerical and analytical methods (e.g., mean field approximation, time-evolving-block-decimation algorithm, perturbation theory, etc.) are applied in the project.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.