Fractional Quantum Hall Physics with Ultracold Atoms

这个项目的目的是发现和探索物质的新状态，特别是量子力学理论的反直觉和令人惊讶的效应在其中起到至关重要的作用。在导体、超导体和磁体等凝聚态材料中，原子排列在规则的晶体中，材料的电磁特性由晶体中电子的运动产生。这一运动的物理学非常复杂，许多相关的基本问题都没有得到解答。为了更好地理解这一物理学，参与该项目的科学家正在建立一个扩大的此类物质的模型系统：他们使用原子而不是电子，这些原子在由光形成的晶体中运动。原子必须处于极低的温度，仅比绝对零度高出十亿分之一度。这样，它们的量子力学行为就像凝聚态系统中的电子一样。超冷系统的一个奇怪特征是每个原子同时出现在许多地方。这个合成的凝聚态系统可以得到很好的表征，并可以直接与理论进行比较，使用“量子气体显微镜”(在NSF资助这个研究小组的上一个周期中发明)，以完美的保真度成像每个原子。这项工作特别关注的是创造“玻色分数量子霍尔态”--一种由“纠缠”决定其行为的物质状态，“纠缠”是量子力学最非经典的表现形式，阿尔伯特·爱因斯坦曾将其描述为“远距离的幽灵作用”。通过解决与这些材料有关的悬而未决的问题，由这笔赠款支持的研究人员正在努力推动科学朝着从零开始定制具有未知性质的新量子材料的最终目标前进。这种材料可以在量子信息设备和量子计量学中找到应用。该项目对学生和博士后进行广泛的物理学和许多现代技术方面的培训，如激光光学。分数量子霍尔态代表了包含拓扑有序的物质的新状态。虽然以前在2D电子材料中观察到了电子的费米子分数量子霍尔态，但由这项授权工作支持的工作旨在通过实验实现和探索具有强烈相互作用的玻色子原子的小集合的分数量子霍尔态，这些原子在二维简谐陷阱中快速旋转。这样的系综会经历一个规范场，并有望绝热跃迁到玻色分数量子霍尔态。虽然这种集合中的粒子数量很少，大约为4-10个粒子，但量子气体显微镜将使研究人员能够以接近单位保真度的方式探测到每一个粒子。因此，他们可以对介观多体系统进行完全的量子限制测量。特别是，他们寻求直接测量动量空间中的粒子关联函数，这将给出高度纠缠的多体状态的非常直接的证据。

This project is aimed at finding and exploring new states of matter, particularly "quantum matter" in which the counterintuitive and surprising effects of the theory of quantum mechanics plays a crucial role. In condensed matter materials such as conductors, superconductors, and magnets, atoms are arranged in regular crystals, and the electric and magnetic properties of the material emerge from the motion of electrons within that crystal. The physics of this motion is very complex, and many associated fundamental questions are unanswered. In order to better understand this physics, the scientists working on this project are building an enlarged model system of such matter: they are using atoms instead of electrons, and these atoms move in crystals formed by light. The atoms have to be at extremely cold temperatures, only a billionth of a degree above absolute zero. This way they behave quantum mechanically like the electrons in condensed matter systems. One strange feature of the ultracold system is that each atom is at many places at the same time. This synthetic condensed matter system can be very well characterized and directly compared to theory using a "Quantum Gas Microscope" (invented during the previous cycle of NSF funding to this research group) to image every single atom with perfect fidelity. The particular focus of this work is to create "Bosonic fractional quantum hall states"--states of matter whose behavior is dictated by "Entanglement," the most non-classical manifestation of quantum mechanics, famously described by Albert Einstein as "Spooky action in a distance." By addressing open questions linked to these materials, the researchers supported by this grant are working to advance science towards the ultimate goal of tailoring new quantum materials from scratch with yet unknown properties. Such materials could find applications in quantum information devices, and in quantum metrology. This project trains students and postdocs in a broad range of physics and in many modern technologies such as laser optics. Fractional quantum Hall states represent new states of matter that contain topological order. While Fermionic fractional quantum Hall states of electrons have been previously observed in 2D electron materials, the work supported by this grant work aims to experimentally realize and explore fractional quantum Hall states with small ensembles of strongly interacting bosonic atoms that quickly rotate in a two-dimensional harmonic trap. Such ensembles experience a gauge field, and are expected to adiabatically transition into the bosonic fractional quantum Hall state. While the particle number in such ensembles is small, on the order of 4-10 particles, the quantum gas microscope will enable the researchers to detect every single particle with near unity fidelity. Therefore, they can carry out a complete quantum limited measurement of the mesoscopic many- body system. In particular they seek to directly measure particle correlation functions in momentum space, which would give very direct evidence of the highly entangled many-body states.