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，它代表了一种新的物质态，包含了一种新的有序-拓扑有序。理解导致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，并有望用于未来的应用，如拓扑量子计算机。然而，在量子霍尔凝聚态材料中，微观物理和量子特性（如纠缠）无法直接探测。因此，本计画将利用超冷原子在光学晶格中建立一个模型系统。原子的行为完全是量子力学的，可以作为量子模拟器。量子气体显微镜可以实现完全的微观控制，并将使该团队能够揭示分数量子霍尔物理学的微观起源，并直接探测量子纠缠，这对于未来在量子信息中使用拓扑材料至关重要。 该项目还将培养学生在原子物理学和凝聚态物理学方面的能力，并帮助他们为参与高科技工作做好准备。自从量子霍尔效应作为分数朗道能级填充的量子化霍尔电导被发现以来，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没有得到很好的理解，例如多体基态的性质，激发性质（特别是对缺陷的依赖性）或晶格结构的作用。理论研究表明，分数量子霍尔（Fractional quantum Hall，简称FWHH）效应应该存在于玻色子和费米子粒子统计中，并且已经表明，复杂性来自粒子之间的强相互作用和拓扑特征的相互作用。本计画将在二维光晶格上的少玻色子系统中，创造出一个强的合成规范场，以实现一个呈现出Wavelet H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，该团队还将通过Hong-Ou-Mandel型干涉实验，测量系统的纠缠熵，从而表征与拓扑序相关的全局纠缠。该奖项反映了NSF的法定使命，通过使用基金会的智力价值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.