Exploring Interacting Topological Fluids in a Synthetic Lattice

这项研究将使用冷的和稀的原子气体来研究由拓扑和无序形成的物质的新相。在过去的一个世纪里，利用金属、绝缘体和半导体等不同材料中电子的不同行为的能力导致了显著的技术发展和经济增长。新量子材料的发现和工程有望在未来几十年塑造未来的技术。特别是，具有高度鲁棒性的非平凡拓扑的材料，有望在自旋电子学和容错量子计算等不同领域发挥重要作用。虽然这些系统的重要方面很难在真实材料中探测，但量子模拟的方法，其中高度可调的量子系统可以用来模拟更笨拙的量子系统，允许探索新的拓扑材料类别。这个项目将使用非常好的控制和很好理解的中性原子系统，冷却到绝对零度以上不到百万分之一度，并且具有比空气低一百万倍的超低密度，来设计合成量子材料。这项研究的一个重点将是开发基于简单原子系统中可用的高度光谱控制的新技术，以设计合成材料。这些实验有望为迄今为止尚未探索的现象提供基于实验室的研究，并为高基态简并系统中鲜为人知的突现行为提供新的线索。开发的技术还将扩展用于基于原子干涉测量的惯性传感的工具集。此外，该计划将为学生提供高科技相关领域的科学和专业培训。该研究项目将开发晶格和带结构工程的新技术，以解决与拓扑和无序材料相关的突出问题。采用非传统的方法，合成晶格不是在真实空间中设计，而是在由一组离散量子态跨越的空间中设计，该项目将实现与哈密顿工程相关的全新能力，并将通过量子模拟开辟新的材料系统类别。这些研究的重点是基于激光的超冷玻色子量子气体操作，其中干涉激光对可以驱动不同原子动量态之间的转换，从而产生动量空间晶格。这个项目将有三个主要目标。第一个将是发展在一维和二维中设计任意晶格结构的能力，并设计预测的新型拓扑晶格结构，探索由无序和拓扑相互作用驱动的相变，并探索当拓扑有序被无序破坏时发生的复杂量子临界现象。其次，我们将探索在晶格结构中出现的新现象，这些现象是由几何挫折引起的，它们可以在小扰动和相互作用的驱动下产生涌现现象。第三，将探索构建合成晶格的替代方法，不是基于原子动量态，而是基于原子的内部自旋自由度，这可能为研究强相关拓扑系统带来更大的前景。

This research will use cold and dilute gases of atoms to investigate new phases of matter shaped by topology and disorder. The ability to harness the diverse behaviors of electrons in different materials, such as metals, insulators, and semiconductors, has led to remarkable technological development and economic growth over the past century. The discovery and engineering of new quantum materials promises to shape future technologies for many decades to come. In particular, materials with nontrivial topology, relating to highly robust properties, promise to play an important role in diverse areas such as spintronics and fault-tolerant quantum computing. While important aspects of these systems are difficult to probe in real materials, the approach of quantum simulation, where a highly tunable quantum system can be used to mimic a more unwieldy quantum system, allows for the exploration of new classes of topological materials. This project will use extremely well-controlled and well-understood systems of neutral atoms, cooled to less than one-millionth of a degree above absolute zero temperature and having ultralow densities a million times less than that of air, to engineer synthetic quantum materials. A key focus of this research will be on the development of new techniques, based on the high degree of spectroscopic control available in simple atomic systems, to engineer designer synthetic materials. These experiments promise to provide laboratory-based studies of hitherto unexplored phenomena, and to shed new light on poorly understood emergent behavior in systems with high ground state degeneracy. The developed techniques will also expand the set of tools used for inertial sensing based on atom interferometry. Additionally, this program will provide scientific and professional training to students in areas of high technological relevance. This research project will develop new techniques for lattice and band structure engineering, to address outstanding problems related to topological and disordered materials. Taking an unconventional approach, where a synthetic lattice is engineered not in real space, but rather in the space spanned by a discrete set of quantum states, this project will enable completely new capabilities related to Hamiltonian engineering, and will open up new classes of material systems to investigation through quantum simulation. The studies focus on a laser-based manipulation of ultracold bosonic quantum gases, where pairs of interfering lasers can drive transitions between distinct atomic momentum states, creating a momentum-space lattice. This project will have three primary goals. The first will be to develop the ability to engineer arbitrary lattice structures in one and two dimensions, and to engineer predicted new classes of topological lattice structures, explore phase transitions driven by the interplay of disorder and topology, and probe the complex quantum critical phenomena occurring as topological order is destroyed by disorder. Second, novel phenomena will be explored that occur in lattice structures with engineered flat energy bands, stemming from geometrical frustration, that can play host to emergent phenomena driven by small perturbations and interactions. Third, alternative methods will be explored for constructing synthetic lattices, not based on atomic momentum states but rather on the atoms' internal spin degree of freedom, which may hold added prospects for studying strongly correlated topological systems.