Study of ultra-cold orbital, large spin, and dipolar systems in optical lattices

该奖项支持具有冷原子和偶极分子的物质新状态的理论研究，这在典型材料中是不容易获得的。为当前的实验工作提供了理论指导。PI将使用解析和数值方法，包括自洽平均场理论，经典和量子场理论方法，以及量子蒙特卡罗模拟。本研究有三个重点：1)；光学晶格高轨道带中超冷玻色子和费米子奇异态的研究。对于轨道玻色子，基于他之前对超越“无节点”定理的非常规玻色-爱因斯坦凝聚的研究，PI将进一步研究它们的集体激发和量子相变。对费米子的研究将集中在具有有趣能带拓扑的量子反常霍尔绝缘子和轨道交换受挫的奇异莫特绝缘子上。2)。对超冷大自旋碱原子和碱土原子的竞争相进行了研究，重点研究了具有强量子涨落特征的奇异量子磁性。3)。由超冷电和磁偶极相互作用产生的非常规库珀对的研究导致了p波三重态库珀对的新机制。该项目旨在预测尚未在材料中发现的物质的新状态，但目前是冷原子实验的主题。这项研究处于凝聚态物质和冷原子物理的界面，将使这两个领域受益。学生将接受强相关系统的分析和数值方法的培训，并将发展广泛的研究兴趣。研究成果将纳入高级研究生课程。该奖项支持理论研究和教育，旨在研究一种“光晶体”中出现的物质的新状态，这种晶体是由非常接近绝对零度的原子组成的，这些原子被困在形成规则原子阵列的激光束中。这些超冷原子的行为方式类似于材料中的电子运动，为发现和研究由于电子之间的强相互作用而产生的物质的电子状态提供了另一种方法。这些新的电子状态可能存在于一类被称为强相关材料的材料中。研究超冷原子类似物的一个优点是，被激光捕获的原子之间的相互作用比材料中的电子更容易调谐。被激光捕获的超冷原子在它们的权利上是有趣的，因为它们可以形成新的量子力学状态，这些状态在材料的电子中不可能发生或不易观察到。原子之间的相互作用可能比电子之间的相互作用更复杂，从而导致物质的有趣的新状态。PI的目标是发展理论来解释光晶体中这些冷原子的新量子力学特性。这些理论为新的实验提供了指导，加深了我们对量子物理学和超冷原子和电子等物质状态的理解，并带来了新的发现。这是原子和凝聚态物理的交叉领域的基础研究。冷原子系统很有趣，可能为未来的技术提供可能性。其中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。学生将接受高级理论凝聚态物理方面的培训，这将激发学生在科学前沿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，构成了PI将开发的高级物理课程的主题的一部分。

TECHNICAL SUMMARYThis award supports the theoretical study of novel states of matter with cold atoms and dipolar molecules, which are not easily accessible in typical materials. It also provides theoretical guidance for current experimental efforts. The PI will use both analytical and numerical methods including self-consistent mean-field theory, classical and quantum field theoretical methods, and quantum Monte-Carlo simulations. The research has three foci: 1.) The study of exotic states of ultra-cold bosons and fermions in the high orbital bands of optical lattices. For orbital bosons, based on his previous study on unconventional Bose-Einstein condensations beyond the 'no-node' theorem, the PI will further investigate their collective excitations and quantum phase transitions. The research on fermions will focus on the quantum anomalous Hall insulators with interesting band topology and exotic Mott insulators with frustrated orbital exchanges. 2.) The study of the competing phases of ultra-cold large-spin alkali and alkaline earth atoms with a particular focus on the exotic quantum magnetism characterized by strong quantum fluctuations. 3.) The study of unconventional Cooper pairing that arises from ultra-cold electric and magnetic dipolar interactions leading to new mechanisms for p-wave triplet Cooper pairing. This project seeks to predict new states of matter that have not yet been found in materials but are currently the subject of cold atom experiments. This research lies at the interface between condensed matter and cold atom physics and will benefit both fields. Students will receive train-ing in analytical and numerical methods for strongly correlated systems, and will develop broad research interests. Research results will be incorporated into advanced graduate courses. NONTECHNICAL SUMMARYThis award supports theoretical research and education that seek to study new states of matter that arise in a kind of 'crystal of light,' which is made from atoms that are very close to the absolute zero of temperature and are trapped in laser beams forming a regular array of atoms. These ultra-cold atoms can behave in ways that are analogous to electrons moving in materials and provide another way to discover and study electronic states of matter that arise as a consequence of strong interactions among electrons. These novel electronic states may live in a class of mate-rials known as strongly correlated materials. An advantage of studying ultra-cold atom analogs is that the interactions between atoms trapped in laser light can be more easily tuned than the elec-trons in a material.Ultra-cold atoms trapped by lasers are interesting in their right as they can form novel quantum mechanical states that cannot occur or are not easily observed in the electrons of a material. The interactions among atoms can be more complex than those among electrons leading to interesting novel states of matter. The PI aims to develop 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 of ultra-cold atoms and electrons alike, and leading to new discoveries.This is fundamental research that lies at the interface of atomic and condensed matter physics. 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. Students will receive training in advanced theoretical condensed matter physics which will stimulate students to develop broad interests and skills in the scientific frontiers. Aspects of the research, particularly the underlying theoretical techniques, form part of the subject matter of the advanced physics courses that the PI will develop.