Phases and phase transitions of quantum gases on optical lattices

该奖项支持凝聚态物质和量子多体理论的理论研究，重点关注在材料中难以实现但可能在光学晶格陷阱中实现冷原子的相和相变。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态现象的原子对应物，或者用来研究尚未探索和发现的物质的新状态。费什巴赫共振允许实时调整原子之间的相互作用，而光学晶格模拟了电子在真实材料中典型移动的晶体晶格。这些工具在过去分别用于创建具有可变相互作用强度的超流体的原子类似物和晶格上可能的凝聚态系统的原子等价物，例如莫特绝缘体。PI将调查结合这两种工具的结果。人们预计，置于相互作用受费什巴赫共振控制的光学晶格中的原子系统将表现出各种相和相变，包括超流体、带和莫特绝缘体、高转变温度下的拓扑超流体、新型拓扑相变以及不寻常的一维相。PI将重点关注以下问题。费米子原子在费希巴赫共振的存在下在三维光学晶格中运动，可以形成成对超流体、带绝缘体和分子莫特绝缘体等状态。包括这些相的精确相图将被绘制出来。在二维光学晶格中，如果研究p波费什巴赫共振，就会产生拓扑超流体。当放置在光学晶格中时，各种拓扑超流体之间的转换是可能的，在相图中，期望丰富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是否在一维晶格中出现新的相。这些包括富尔德-费雷尔-拉金-奥夫钦尼科夫态以及具有解耦准密态的不寻常态。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能带结构的晶格中的超冷原子来制造。PI的目标是找到在材料中没有观察到的非常规绝缘体。这些可以借助该领域发展的各种自旋轨道耦合技术来获得。这些绝缘子的不同设置将从理论上进行研究。PI将通过博尔德凝聚态物质和材料物理暑期学校以及美国和国外的其他暑期学校活动对各机构的学生进行教育。该奖项支持理论研究和教育，旨在研究在许多相互作用的原子或电子系统中出现的物质和物质的新阶段。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来实现，所以并非所有理论研究的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和创造物质新状态的方法。原子的相互作用可以实时控制，可以被困在激光产生的光学晶格中，冷却到非常低的温度，并使其表现得像固体中的电子或理论模型中的假设粒子一样。这些“模拟”的结果可以用来指导寻找材料中物质新状态的研究。本研究将重点研究强相互作用下光学晶格中冷原子的相。原子与激光形成的晶格之间的相互作用以及原子与原子之间的相互作用产生了物质的各种状态。PI将制定一种“路线图”，显示在给定的交互强度下哪些阶段是可能的。晶格中可能存在的一些最令人兴奋的相是拓扑绝缘体，其中一些已经在由元素构成的材料中观察到，例如铋和硒。然而，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以及美国和国外的其他暑期学校活动对各机构的学生进行教育。

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.