Microscopy of Bosonic Fractional Quantum Hall States in Optical Lattices

分数量子霍尔态是由Tsui，Stormer和Gossard在二维电子系统中发现的，它代表了包含一种新的有序-拓扑有序的物质的新状态。理解产生这种行为的物理起源将深刻地增强我们对拓扑材料的看法，并有望在未来的应用，如拓扑量子计算机。然而，量子霍尔凝聚态材料中的纠缠等微观物理和量子性质是不能直接探讨的。因此，本项目将利用光学晶格中的超冷原子建立一个模型系统。原子的行为完全是量子力学的，可以作为量子模拟器。量子气体显微镜能够进行完全的微观控制，并将使该团队能够阐明分数量子霍尔物理的微观起源，并直接探测量子纠缠，这对于未来拓扑材料在量子信息中的使用至关重要。这个项目还将培训学生原子物理和凝聚态物理，并帮助他们为参与高科技工作做准备。自从它被发现为分数朗道能级填充的量子化霍尔电导以来，量子霍尔效应一直受到密集的理论和实验研究。然而，引起许多相关现象的微观机制还不是很清楚，例如多体基态的性质、激发性质(特别是对缺陷的依赖)或晶格结构的作用。理论研究表明，对于玻色子粒子统计和费米子粒子统计，分数量子霍尔(FQH)效应都应该存在，并且已经表明这种复杂性是由于粒子之间的强相互作用和拓扑特征的相互作用而产生的。这个项目将通过在二维光学晶格上的少数玻色子系统中创建一个强大的合成规范场来实现一个显示FQH效应的系统。借助单点分辨率量子气体显微镜的操作和检测技术，该团队将能够通过分析单原子水平上的密度分布来确定系统的多体状态。此外，该团队将致力于通过使用Hong-Ou-Mandel类型的干涉实验测量系统的纠缠熵来表征与拓扑秩序相关的全球纠缠。这一奖项反映了NSF的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。

Fractional quantum Hall states, discovered by Tsui, Stormer and Gossard in two-dimensional electron systems, represent new states of matter that contain a novel kind of order - topological order. Understanding the physical origin that gives rise to such a behavior will profoundly enhance our perspective on topological materials and is promising for future applications such as topological quantum computers. However, the microscopic physics and quantum properties such as entanglement cannot be probed directly in quantum Hall condensed matter materials. Therefore, this project will build a model system using ultracold atoms in optical lattices. The atoms behave fully quantum mechanically and can serve as a quantum simulator. A quantum gas microscope enables full microscopic control, and will enable this team to shed light on the microscopic origin of fractional quantum Hall physics, and to directly probe quantum entanglement, which is essential for the future use of topological materials in quantum information. This project will also train students in atomic physics and condensed matter physics, and will help prepare them to participate in the high-tech work force.Since its discovery as quantized Hall conductance at fractional Landau level filling, the quantum Hall effect has been subject to intense theoretical and experimental study. Yet the microscopic mechanisms giving rise to many associated phenomena are not well understood, for example the nature of the many-body ground state, excitation properties (in particular the depedence on defects) or the role of a lattice structure. Theoretical studies suggest the fractional quantum Hall (FQH) effect should exist both for bosonic and fermionic particle statistics and have shown that the complexity arises from the interplay of strong interactions among the particles and topological features. This project will realize a system exhibiting the FQH effect by creating a strong synthetic gauge field in a few-boson system on a two-dimensional optical lattice. With the manipulation and detection techniques of a quantum gas microscope with single site resolution, this team will be able to determine the many-body state of the system by analyzing the density distribution on the level of single atoms. Furthermore, this team will work towards characterizing the global entanglement associated with the topological order by measuring the entanglement entropy of the system with a Hong-Ou-Mandel-type interference experiment.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.