Novel properties of multi-component ultra-cold atom systems

非技术总结该奖项支持理论研究和教育的新的物质状态与超冷原子和分子冷却到超冷温度在百万分之一度以上绝对零度。原子和分子经常被困在激光束产生的人工晶体结构中。尽管能量尺度非常不同，原子和分子发展量子相干性，并且行为与固体中的电子非常相似。与固态系统相比，超冷原子和分子系统的一个主要优点是可以将相互作用控制在前所未有的水平。这为通过研究光晶体中的超冷原子来研究材料中的相关电子运动开辟了一个全新的机会。超冷原子和分子的物理学开辟了物质的新方向和新状态，而这些都是不存在的，或者至少是很难在材料中使用电子来实现的。电子之间的库仑相互作用仅取决于它们的分离。相反，两个偶极分子之间的相互作用取决于连接两个分子的位移矢量的方向。这些新的特征导致了新的和复杂的多体物理学，这是不容易在材料中获得的。PI的目的是在超冷原子和分子的研究中发展新的方向，并为寻找新的物质状态的实验努力提供理论指导。该研究处于冷原子物理和凝聚态物理的交界处，将为物质的量子态（包括磁性、超导性和拓扑态）带来新的理解。学生将参与研究，并通过课程学习、研讨会和与实验学家的交流，获得扎实的训练，培养学生在凝聚态物理前沿领域的广泛兴趣和技能。将强调对称性和拓扑学原理的应用和欣赏。冷原子物理学的进展将与传统上不提供的多体物理学的最新观点结合到课程研究中。技术总结该奖项支持理论研究和教育，以研究具有多个内部自由度的超冷原子和偶极分子的重要方向。PI将使用分析和数值方法来解释实验结果，并预测未来实验测试的新特性。这些研究成果将极大地丰富超流物理、量子磁学和拓扑态物理的内容。本研究的主要内容包括：1）量子磁学的非微扰研究。证明了一类二维和三维p轨道带中充满冷费米子的系统存在巡游铁磁基态。系统的量子蒙特-卡罗模拟免费的符号问题，计划照亮巡回铁磁性的基态和热力学性质的公开问题。碱土费米子的奇异量子反铁磁性具有SU（2N）对称性。PI将使用量子蒙特卡罗模拟来研究强电荷和磁涨落的挑战性问题。2）PI计划研究金刚石晶格中p轨道带中的超冷原子，包括三维平坦带中的强关联效应，和一个新的统计4-着色模型描述的受抑超流态。PI将探索四元数在超冷原子三维拓扑态研究中的应用。特别是，我们将重点研究具有四元数解析性质的三维朗道能级。4）研究Majorana平带与偶极费米子非常规配对态的相互作用效应。该项目旨在探索多组分冷原子和分子系统中的新物质状态。该研究处于凝聚态物理和冷原子物理的交界处，对这两个领域都有很大的益处。学生将参与研究，并将通过课程学习、研讨会和与实验人员的交流，得到扎实的训练，培养学生在凝聚态物理前沿领域的广泛兴趣和技能。将强调对称性和拓扑学原理的应用和欣赏。冷原子物理学的进展将被纳入课程研究，并从传统上不提供的多体物理学的最新视角。

NONTECHNICAL SUMMARYThis award supports the theoretical research and education on novel states of matter with ultra-cold atoms and molecules cooled down to ultra-cold temperatures at one millionth of a degree above absolute zero. Atoms and molecules are often trapped in the artificial crystalline structures generated by laser beams. In spite of very different energy scales, atoms and molecules develop quantum coherence and behave very similarly to electrons in solids. Compared to solid state systems, a major advantage of the ultra-cold atom and molecular systems is that interaction effects can be controlled at an unprecedented level. This opens up a whole new opportunity for the study correlated electron motion in materials through the study of ultra-cold atoms in crystals of light.The physics of ultra-cold atoms and molecules opens new directions and new states of matter than cannot exist or at least would be very difficult to make using electrons in materials. The Coulomb interaction between electrons depends only on their separation. In contrast, the interaction between two dipolar molecules depends on the orientation of the displacement vector joining the two molecules. These new features lead to novel and complex many-body physics which are not easily accessible in materials.The PI aims to develop new directions in the study of ultra-cold atoms and molecules and to provide theoretical guidance for the experimental effort to find new states of matter. This research lies at the interface between cold atom and condensed matter physics, and will bring new understanding on quantum states of matter including magnetism, superconductivity, and topological states.Students will be involved in the research and will receive solid training to develop broad interests and skills in the frontiers of condensed matter physics through course study, seminars, and communications with experimentalists. The application and appreciation of the principles of symmetry and topology will be emphasized. Advances in cold atom physics will be incorporated into course studies with an up-to-date perspective from many-body physics that is not traditionally provided.TECHNICAL SUMMARYThis award supports the theoretical research and education to study important direction in ultra-cold atoms and dipolar molecules with multiple internal degrees of freedom. The PI will use both analytical and numerical methods to explain experimental results and predict novel properties for future experimental tests. Knowledge gained from this research will greatly enrich the physics of superfluidity, quantum magnetism, and topological states.The research has the following foci:1) The non-perturbative study of quantum magnetism. An itinerant ferromagnetic ground state has been proved to exist for a class of systems with two and three dimensional p-orbital bands filled with cold fermions. Systematic quantum Monte-Carlo simulations free of the sign problem are planned to illuminate open issues of ground-state and thermodynamic properties of itinerant ferromagnetism. The exotic quantum antiferromagnetism of alkaline-earth fermions exhibit SU(2N) symmetries. The PI will study the challenging problem of the strong charge and magnetic fluctuations using quantum Mote-Carlo simulations.2) The PI plans to study ultra-cold atoms in the p-orbital bands in the diamond lattice, including strong-correlation effects in the three dimensional flat bands, and the frustrated superfluid state described by a novel statistical 4-coloring model.3) The PI will explore the application of quaternions in the study of 3D topological states for ultra-cold atoms with synthetic spin-orbit coupling. In particular, the study will focus on the three dimensional Landau levels with quaternionic analytic properties.4) The study of interaction effects in Majorana flat bands in unconventional pairing states with dipolar fermions. This projects aims at exploring new states of matter in multi-component cold atom and molecular systems. This research lies at the interface between condensed matter and cold atom physics and will greatly benefit both fields.Students will be involved in the research and will receive solid training to develop broad interests and skills in the frontiers of condensed matter physics through course study, seminars, and communications with experimentalists. The application and appreciation of the principles of symmetry and topology will be emphasized. Advances in cold atom physics will be incorporated into course studies with an up-to-date perspective from many-body physics that is not traditionally provided.