CAREER: Quantum Gas Microscopy of Frustrated Hubbard Systems

一般观众摘要：许多电子的量子系统在计算上是难以处理的，但对于理解超导性和量子磁性等材料性质具有深远的重要性。直接成像材料中的电子，包括它们的局部相关性和纠缠几乎是不可能的，但量子模拟可以揭示这些复杂量子系统的微观特性。这个CAREER奖支持这些系统的量子模拟，使用被困在人造光晶体中的费米原子冷却到几十亿分之一度。这种方法提供了一个通用的平台，具有广泛的可调性，基于良好的特征组件。一个具有高分辨率成像能力的量子气体显微镜将被构造并用于研究几何阻挫晶格中具有单位和单原子分辨率的多费米子系统。在这些受抑系统中，几个能量约束不能同时最小化，它们的竞争导致了奇异的低温特性。这项研究工作将调查晶格几何形状对多费米子系统性质的影响，并将为指导寻找新型高温超导体提供见解。研究活动嵌入在K-12，本科，研究生和博士后水平的科学教育计划中。教育和推广计划的两个主要支柱是（a）K-12学生的实践研讨会计划和（B）面向公众的主动学习实验的移动的展览。技术观众摘要：量子多体系统中的几何挫折导致有趣的现象，如奇异的新兴低能物理，大规模基态纠缠和拓扑秩序。它自然地实现在非二分晶格上的反铁磁相互作用的系统中，其中所有相邻自旋之间的反平行取向被抑制。本研究计划将在三角晶格上实现费米-哈伯德模型，作为具有反铁磁相互作用的非二分晶格系统的表现。超冷费米子锂原子将被加载到三角形光学晶格中，并使用最先进的量子气体显微镜技术进行检测，以解析晶格中的所有单个原子，从而前所未有地获得单原子可观测量和真实空间相关性。所有的哈密顿参数都可以在很宽的范围内进行调整和独立校准，从而可以对相图进行广泛的研究。没有一个独特的基态导致丰富的相图，并可能允许实现一个稳定的量子自旋液体在费米-哈伯德模型预测的数值计算。主要的研究方向是：（a）几何阻挫费米晶格气体的相图。(b)检测短程相关性。(c)测量三角形哈伯德模型中的手征相关性。(d)搜索量子自旋液体的特征。该奖项反映了NSF的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

General audience abstract:Quantum systems of many electrons are computationally intractable but are of profound importance for the understanding of material properties like superconductivity and quantum magnetism. Direct imaging of electrons in materials including their local correlations and entanglement is almost impossible, but quantum simulation can shed light on the microscopic properties of these complex quantum systems. This CAREER award supports quantum simulation of these systems using fermionic atoms cooled to a few billionth of a degree trapped in an artificial crystal of light. This approach provides a versatile platform with wide tunability based on well-characterized components. A quantum gas microscope with high-resolution imaging capabilities will be constructed and used to study many-fermion systems with single-site and single-atom resolution in geometrically frustrated lattices. In these frustrated systems, several energetic constraints cannot be minimized at the same time, and their competition leads to exotic low-temperature properties. This research effort will investigate the impact of the lattice geometry on the properties of many-fermion systems and will provide insights guiding the search for novel high-temperature superconductors. The research activities are embedded in a science education program operating at the K-12, undergraduate, graduate, and postdoctoral level. The two main pillars of the educational and outreach program are (a) a hands-on workshop program for K-12 students and (b) a mobile exhibition of active-learning experiments for the general public.Technical audience abstract:Geometric frustration in quantum many-body systems leads to intriguing phenomena like exotic emergent low-energy physics, massive ground-state entanglement, and topological order. It is naturally realized in systems with antiferromagnetic interactions on non-bipartite lattices where antiparallel orientation between all neighboring spins is inhibited. This research program will realize the Fermi-Hubbard model on a triangular lattice as a manifestation of a non-bipartite lattice system with antiferromagnetic interactions. Ultracold fermionic lithium atoms will be loaded in a triangular optical lattice and detected using the state-of-the-art techniques of quantum gas microscopy to resolve all individual atoms in the lattice, allowing unprecedented access to single-atom observables and real-space correlations. All Hamiltonian parameters can be adjusted over a wide range and calibrated independently, enabling an extensive study of the phase diagram. The absence of a unique ground state leads to a rich phase diagram and may allow for the realization of a stable quantum spin liquid in a Fermi-Hubbard model as predicted by numerical calculations. The main research thrusts are: (a) Probing the phase diagram of geometrically frustrated Fermi lattice gases. (b) Detecting short-range correlations. (c) Measuring chiral correlations in the triangular Hubbard model. (d) Searching signatures of a quantum spin liquid.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.