Spin Tensors in Ultracold Atomic Gases

在过去的几十年里，对具有新功能的量子材料的追求导致了现代电子设备的巨大进步。自旋是粒子的一个基本自由度，它与轨道自由度(如动量)的耦合在新型量子材料的发现、表征和应用中起着至关重要的作用。在传统材料中，电子自旋完全由自旋1/2矢量来描述。近年来，具有大有效自旋的非传统量子材料(如自旋-1)的研究已成为材料研究的前沿。由于对任何大自旋(自旋为1或更大)的完整描述自然涉及自旋张量，了解自旋张量的效应及其与可控平台中动量的耦合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的指导方针。在此背景下，超冷原子气体提供了这样一个可控平台，具有前所未有的实验控制和精度水平。以前的研究已经实现了超冷原子的自旋矢量和动量的耦合，这现在已经成为物理学的一个主要研究前沿。这个项目研究了超冷原子的自旋张量和自旋张量动量耦合的产生，并探索了它们在工程新量子态中的应用。在冷原子平台上研究这种高度可控的自旋张量将反过来影响未来电子材料的设计和发现。这项研究不仅将为冷原子系统的相干控制在许多重要应用(如材料设计、自旋电子学、量子计算等)铺平道路，而且还将影响冷原子和凝聚态物理的基础研究。该项目为研究生和本科生提供了一个探索理论冷原子和凝聚态物理的多样化平台。这个项目的范围还包括针对K-12学生的具体外展活动，包括吸收来自代表性不足群体的学生，如女性和少数族裔学生，以扩大参与范围。该项目的主要目标是解决两个悬而未决的问题：i)我们能否通过实验实现超冷原子的自旋张量与其线动量之间的耦合？Ii)如果是这样的话，这种自旋-张量-动量耦合可能会出现什么类型的新物理？具体任务包括：i)实验产生各种类型的自旋张量和大自旋(特别是自旋-1)原子气体的自旋张量动量耦合；ii)由自旋张量引起的奇异量子相，如长周期和高能见度的自旋超固态条状相，大陈数拓扑绝缘体和具有高阶带接触点的超流体，拓扑三简并点和节线等。各种数值和分析方法(如平均场近似，时间演化块抽取算法，微扰理论等)。这一奖项反映了NSF的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。

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.