Novel Quantum Phases in Orbital and Large Spin Systems with Cold Atoms

该奖项支持关于冷原子轨道和大自旋系统中新量子相位的理论研究和教育。这项研究探索了新的量子相位和冷原子的涌现对称性，这些在通常的固态系统中是无法获得的，并为新的实验提供了指导。对称性原理的应用对这个项目至关重要，它不仅加深了我们的理解，而且为新的发现提供了指导。 本研究采用了凝聚态物理和场论中的各种方法，包括玻色化、重整化群、大N方法、自洽平均场理论和能带结构计算。第一个研究课题是研究光学晶格中高轨道带中的新量子相。p-轨道玻色子表现出复值多体波函数，其特征在于形成了原位轨道角动量矩。该研究包括各种晶格中的轨道超流性，这些晶格表现出共线有序（例如，交错和条纹状）、非共线排序和轨道角动量矩的“受抑"分布。对于费米子轨道系统，研究将集中在蜂窝晶格，这是一个p_xy轨道对应的石墨烯。第二个研究课题是用冷费米子研究大自旋物理。 特别注意的是自旋3/2系统，具有一般的SO（5）对称性，无需微调。 这种对称性产生了重要的结果，如集体激发中的受保护简并性、量子蒙特-卡罗符号问题的新性质、五重配对超流性和四费米子四重超流性。计划中的研究包括自旋3/2系统和其他大自旋系统（如赝自旋1系统和自旋5/2系统）中的量子磁性。 这项研究将为奇异轨道超流、轨道交换物理和量子磁态的涌现提供新的思路。它还为未来的实验提出了新的方向。本研究的成果加深了我们对冷原子和凝聚态系统中强关联物理的理解，是凝聚态物理和冷原子物理的一个交叉点，对两个领域都有重要意义。学生将接受对称性原理应用方面的培训，研究将激发学生在强相关系统的前沿领域发展广泛的兴趣和技能。该研究的各个方面，特别是基础理论技术，构成了PI在他的大学开发的高级物理课程的主题的一部分。非技术性总结：该奖项支持理论研究和教育，旨在预测由人造光晶体中的超冷原子组成的物质的新状态。研究人员发现，原子可以被困在调制的激光束中，就像电子被困在结晶固体中原子核的力场中一样。电子有两种内部构型，这与它们的磁性有关。原子可以有更多的内部结构，导致可能的新物质状态，这些状态在传统材料中没有对应物，但具有有趣的性质，并可能显示有趣的现象。这项研究发展了理论来解释这些冷原子在光晶体中的新量子力学性质。这些理论为新的实验提供了指导，加深了我们对量子物理和物质状态的理解，并导致了新的发现。 这是基础研究，位于原子和凝聚态物理学的界面。然而，冷原子系统是有趣的，可能为未来的技术提供可能性。其中最引人注目的是基于量子力学原理实现强大的新计算方法的潜力。这项研究位于凝聚态和冷原子物理学之间的界面，将使这两个领域受益。学生将接受对称性原理应用方面的培训，研究将激发学生在强相关系统的前沿领域发展广泛的兴趣和技能。研究的各个方面，特别是基本的理论技术，形成了PI在他的大学开发的高级物理课程的主题的一部分。

TECHNICAL SUMMARY:This award supports theoretical research and education on novel quantum phases in orbital and large spin systems with cold atoms. The research explores novel quantum phases and emergent symmetries with cold atoms which are not accessible in usual solid state systems and provides guidance for new experiments. The application of symmetry principles is essential for this project which not only deepens our understanding but also provides the guidance to new discoveries. A variety of methods in condensed matter physics and field theory are employed, including bosonization, the renormalization group, the large-N method, the self-consistent mean-field theory, and band structure calculations.The first research topic is the study of novel quantum phases in high orbital bands in optical lattices. The p-orbital bosons exhibit complex-valued many-body wave functions characterized by the formation of on-site orbital angular momentum moments. The research encompasses orbital superfluidity in various lattices which exhibit collinear ordering (e.g., staggered and stripe-like), non-collinear ordering, and ''frustrated'' distributions of orbital angular momentum moments. For fermionic orbital systems, the research will focus on the honeycomb lattice, which is a p_xy-orbital counterpart of graphene. The second research topic is the study of large spin physics with cold fermions. Particular attention is paid to spin-3/2 systems which possess a generic SO(5) symmetry without fine tuning. The symmetry gives rise to important consequences such as the protected degeneracy in collective excitations, new properties of the quantum Monte-Carlo sign problem, the quintet pairing superfluidity, and the four-fermion quartetting superfluidity. Planned investigations include quantum magnetism in the spin-3/2 systems and other large spin systems as well, such as the pseudospin-1 systems and the spin-5/2 systems. The research will provide new ideas on exotic orbital superfluidity, orbital exchange physics, and emergent quantum magnetic states. It also suggests new directions for future experiments. Knowledge gained from this research deepens our understanding on strong correlation physics in both cold atom and condensed matter systems.This research lies at the interface between condensed matter and cold atom physics and will benefit both fields. Students will receive training in the application of the symmetry principles and the research will stimulate students to develop broad interests and skills in the frontiers of strongly correlated systems. Aspects of the research, particularly the underlying theoretical techniques, form part of the subject matter of the advanced physics courses being developed by the PI at his university.NONTECHNICAL SUMMARY:This award supports theoretical research and education that seeks to predict new states of matter composed of ultracold atoms in artificial crystals of light. Researchers have found that atoms can be trapped in modulated laser beams much like electrons are trapped in the force fields of atomic nuclei in a crystalline solid. Electrons have two internal configurations; these are related to their magnetic properties. Atoms can have many more internal configurations, leading to possible new states of matter that have no counterparts in conventional materials, but have intriguing properties and may display interesting phenomena. The research develops theories to explain the novel quantum mechanical properties of these cold atoms in crystals of light. The theories provide guidance for new experiments, deepening our understanding of quantum physics and states of matter and leading to new discoveries. This is fundamental research that lies at the interface of atomic and condensed matter physics. However, systems of cold atoms are intriguing and may hold possibilities for future technologies. Conspicuous among these is the potential to realize powerful new methods of computation based on the principles of quantum mechanics. This research lies at the interface between condensed matter and cold atom physics and will benefit both fields. Students will receive training in the application of the symmetry principles and the research will stimulate students to develop broad interests and skills in the frontiers of strongly correlated systems. Aspects of the research, particularly the underlying theoretical techniques, form part of the subject matter of the advanced physics courses being developed by the PI at his university.