Phases and phase transitions of quantum gases on optical lattices

技术总结该奖项支持凝聚态和量子多体理论的理论研究，专注于在材料中难以实现但可能通过光学晶格中的冷原子实现的相和相变。冷原子系统可以模拟真实材料中电子和原子的行为。它们可以用来创造已知凝聚物质现象的原子对应物，或者研究尚未探索和尚未发现的新物质状态。Feshbach共振允许实时调整原子之间的相互作用，而光学晶格模拟晶格，电子通常在真实材料中通过晶格移动。过去，这些工具分别用于创建相互作用强度可变的超流体的原子类似物，以及晶格上可能存在的凝聚态系统相的原子等价物，例如Mott绝缘体。PI将调查结合这两个工具的结果。被Feshbach共振控制相互作用的光学晶格中的原子系统将会呈现出各种各样的相变和相变，包括超流体、带和Mott绝缘体、高温下的拓扑超流体、新型的拓扑相变以及异常的一维相变。国际和平倡议将重点解决以下问题。费米子原子在Feshbach共振作用下在三维光学晶格中运动，可以形成成对超流体、带绝缘体和分子Mott绝缘体等态。将制定包含这些阶段的精确相图。在二维光学晶格中，如果人们用p波Feshbach共振工作，就可能产生拓扑超流体。当放置在光学晶格中时，各种拓扑超流体之间的转变是可能的，在相图中预计会有丰富的相图并导致更稳定的拓扑超流体。PI将调查这种情况是否以及如何发生。PI将使用各种方法来探索一维晶格中是否出现新的相。其中包括Fulde-Ferrell-Larkin-Ovchinnikov态，以及具有去耦合准凝聚态的不寻常态。PI还将研究拓扑绝缘体，这种绝缘体可以用放置在具有拓扑带结构的晶格中的超冷原子创建。PI的目标是找到材料中没有观察到的非传统绝缘体。这些可以通过在该领域开发的各种自旋-轨道耦合技术来获得。这些绝缘体的不同设置将进行理论研究。PI将通过博尔德凝聚态物质和材料物理暑期学校和美国国内外的其他暑期学校活动来教育各机构的学生。该奖项支持理论研究和教育，旨在研究许多相互作用的原子或电子系统中出现的物质和新的物质相。由于控制电子环境的困难，或者因为它们需要特殊类型的相互作用，而这些相互作用很难或不可能通过材料中的电子实现，所以并不是理论上研究的所有相都已经或可以在实际材料中找到。被困在激光晶格中的冷原子提供了一种模拟现有材料并创造新的物质状态的方法。原子的相互作用可以实时控制，它可以被捕获在激光创造的光学晶格中，冷却到非常低的温度，并使其表现得像电子在固体中的行为，或作为理论模型中的假设粒子。这些“模拟”的结果可以用来指导研究在材料中寻找新的物质状态。本研究将重点研究强相互作用条件下光学晶格中冷原子的相结构。原子与激光形成的晶格的相互作用，以及原子与彼此的相互作用，产生了物质的各种状态。PI将制定一种“路线图”，显示对于给定的相互作用强度，哪些阶段是可能的。晶格中最激动人心的一些相是拓扑绝缘体，其中一些已经在由元素铋和硒组成的材料中观察到。然而，人们预测了更多类型的拓扑绝缘体，但尚未在材料中观察到。这项研究将探索用冷原子制造它们的方法。PI将通过博尔德凝聚态物质和材料物理暑期学校和其他美国国内外的暑期学校活动来教育不同机构的学生。

TECHNICAL SUMMARYThis award supports theoretical research in condensed matter and quantum many body theory, concentrating on phases and phase transitions which are difficult to realize in materials but may be possible to realize with cold atoms in optical lattice traps.Cold atomic systems can emulate the behavior of electrons and atoms in real materials. They can be used to create atomic counterparts of known condensed matter phenomena, or to study yet unexplored and undiscovered new states of matter. Feshbach resonances allow real-time tuning of interactions among the atoms, while optical lattices emulate crystalline lattices through which electrons typically move in real materials. These tools were used separately in the past to create atomic analogs of superfluids with variable interaction strength and atomic equivalents of phases of condensed matter systems possible on a lattice, such as Mott insulators. The PI will investigate the outcome of combining the two tools. It is expected that atomic systems placed in optical lattices whose interactions are controlled by Feshbach resonances will exhibit a variety of phases and phase transitions among them, including superfluids, band and Mott insulators, topological superfluids at high transition temperature, and new types of topological phase transitions, as well as unusual one dimensional phases. The PI will focus on the following issues. Fermionic atoms moving in three-dimensional optical lattices in the presence of Feshbach resonances can form states such as a paired superfluid, a band insulator and molecular Mott insulators. Precise phase diagrams encompassing these phases will be worked out. In two-dimensional optical lattices, topological superfluids can arise if one works with p-wave Feshbach resonances. When placed in optical lattices, transitions among various topological superfluids are possible, in a phase diagram which is expected to be rich and lead to more stable topological superfluids. The PI will investigate whether and how this happens. The PI will use a variety of methods to explore whether new phases occur in one dimensional lattices. These include the Fulde-Ferrell-Larkin-Ovchinnikov state as well as unusual states with decoupled quasicondensates. The PI will also study topological insulators which can be created with the ultracold atoms placed in lattices with topological band structure. The PI aims to find unconventional insulators which were not observed in materials. These can be obtained with the help of a variety of spin-orbit coupling techniques developed in the field. Different setups for these insulators will be investigated theoretically.The PI will educate students across institutions through the Boulder Summer School on Condensed Matter and Materials Physics and other summer school activities within the United states and abroad.NONTECHNICAL SUMMARY This award supports theoretical research and education with the aim to study matter and new phases of matter that arise in systems of many interacting atoms or electrons. Not all phases investigated theoretically have been or can be found in real materials because of difficulties in controlling the environment of the electrons or because they require special types of interactions that are difficult or impossible to realize through electrons in materials. Cold atoms trapped in lattices of laser light offer a way to simulate existing materials and create new states of matter. Atoms, whose interactions can be controlled in real time, can be trapped in an optical lattice created by lasers, cooled to very low temperatures, and made to behave like electrons do in solids or as hypothetical particles in theoretical models. The results of these 'simulations' can then be used to guide investigations seeking new states of matter in materials. This research will focus on studying the phases of cold atoms in optical lattices in the presence of strong interactions. The interplay of the interaction of atoms with the lattices formed by lasers and the interaction of atoms with each other, gives rise to a variety of states of matter. The PI will develop a kind of 'roadmap' showing which phases are possible for given interaction strengths. Some of the most exciting phases possible in lattices are topological insulators, some of which have been observed in materials made of, for example the elements bismuth and selenium. However many more types of topological insulator are predicted but have not yet been observed in materials. This research will explore ways to make them with cold atoms. The PI will educate students across institutions through the Boulder Summer School on Condensed Matter and Materials Physics and other summer school activities within the United states and abroad.