CAREER: New Synthetic Approaches to Engineering Topology: from Quantum Many-Body Rydberg Atom Arrays to Classical Mechanical Networks

传输（将某物从一个位置移动到另一个位置）是描述物理科学中许多重要现象的核心。在物理学中，理解物理量，如电荷、热量，甚至信息是如何在许多相互作用的粒子系统中进化和传递的，特别是当量子效应被考虑在内时，仍然存在着开放的挑战。最近，基于“合成维度”和“合成晶格”的概念，出现了研究量子系统中输运的新方法，其中我们在现实空间中的正常输运图像被抽象为由小量子系统（如单个原子或分子）的内部状态所跨越的空间中的人口输运。例如，通过吸收入射激光场的光，粒子群可以在原子（如氢）的电子态之间“移动”。通过这种方式，可以用激光或其他电磁场很好地理解和高度可控的原子集合来“模拟”更复杂的凝聚态系统，并导致我们对复杂系统的理解取得进展。当前项目的实验工作将把这种研究输运的方法扩展到强粒子间相互作用的新体制。该团队将进行基于原子样本的实验，这些原子样本可以在微观水平上单独控制和检测。微波电磁场将被用来精确地控制原子状态之间的居群输运，从而允许对输运现象进行新的探索。此外，该团队将努力扩大本科生研究机会的范围和影响，主要强调增加代表性不足群体成员的参与。这项工作的重点是建立一个新的，由本科生领导的研究项目，研究由“合成”或工程和间接力耦合的机械振荡器网络。这项工作将包括来自不同背景的与新型运输现象相关的前沿研究的本科生，并将使用这些人类尺度的实验来生成可视化视频内容，这些视频内容将用于推广和教学。该项目建立在先前设计中性原子和光子合成晶格的工作基础上，将这些想法扩展到一个新的平台，用于探索基于超冷里德伯原子内部自由度的多体输运现象。通过考虑发生在内部状态空间（由相干微波跃迁和强偶极子-偶极子相互作用驱动）而不是实际空间中的量子输运问题，该方法利用了利用光谱控制操纵内部自由度的能力。这种光谱控制允许具有非平凡带拓扑，动力学挫折和可调无序的合成晶格的精确工程。里德伯原子之间的共振偶极-偶极相互作用将导致与拓扑相互作用和强相互作用相关的新现象，对孤立相互作用无序系统中的弛豫和热化的研究，甚至可能出现全新形式的多体现象。研究小组将探索在里德伯原子的内部状态空间中设计新型合成晶格模型的能力，并将探索共振偶极子-偶极子相互作用如何导致这些合成晶格中的新多体现象。另一项与扩大本科生研究范围和影响相关的努力将导致一个基于合成耦合振荡器网络创建拓扑晶格模型的项目。这项研究工作将使工程机械网络具有新的功能，包括设计非互易性、人工规范场、无序和强非线性的新能力。本科生领导的研究团队将使用这些新开发的方法来研究新型机械振荡器网络中的输运现象。该奖项反映了美国国家科学基金会的法定使命，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。

Transport (moving something from one position to another) is central to describing many important phenomena in the physical sciences. In physics, there remain open challenges to understanding how physical quantities like charge, heat, and even information evolve and undergo transport in systems of many interacting particles, especially when quantum effects are taken into account. Recently, new approaches to the study of transport in quantum systems have emerged based on the concepts of "synthetic dimensions" and "synthetic lattices," in which our normal picture of transport in real space is abstracted to the transport of population in a space spanned by the internal states of small quantum systems such as individual atoms or molecules. For example, population can "move" between the electronic states of an atom (like hydrogen) through the absorption of light from an incident laser field. In this way, a collection of atoms, which is well-understood and highly controllable with lasers or other electromagnetic fields, can be used to "simulate" a more complex condensed matter system, and lead to advances in our understanding of the complex system. The experimental effort in the current project will extend this type of approach to the study of transport to a new regime of strong inter-particle interactions. The team will conduct experiments based on samples of atoms that can be individually controlled and detected at the microscopic level. Microwave electromagnetic fields will be used to precisely control the transport of population between states of the atoms, allowing for new kinds of explorations into transport phenomena. Additionally, the team will lead an effort to broaden the scope and impact of undergraduate research opportunities, with a primary emphasis on increasing the participation of members from underrepresented groups. This effort will focus on building a new, undergraduate student-led research project on networks of mechanical oscillators that are coupled by "synthetic," or engineered and indirect, forces. This effort will incorporate undergraduates from diverse backgrounds in cutting-edge research related to new kinds of transport phenomena, and will use these human-scale experiments to generate visualization video content that will be utilized for outreach and instruction.This project builds on previous work designing synthetic lattices in neutral atoms and photons, extending these ideas to a new platform for the exploration of many-body transport phenomena based on the internal degrees of freedom of ultracold Rydberg atoms. By considering the problem of quantum transport taking place in an internal state space (driven by coherent microwave transitions and strong dipole-dipole interactions) rather than real space, this approach leverages the ability to manipulate internal degrees of freedom with spectroscopic control. This spectroscopic control allows for the precise engineering of synthetic lattices with nontrivial band topology, kinetic frustration, and tunable disorder. Resonant dipole-dipole interactions between Rydberg atoms will lead to new phenomena with relevance to the interplay of topology and strong interactions, to the study of relaxation and thermalization in isolated interacting disordered systems, and perhaps to the emergence of entirely new forms of many-body phenomena. The research team will explore the ability to engineer novel synthetic lattice models in the internal state space of Rydberg atoms, and will explore how resonant dipole-dipole interactions lead to new many-body phenomena in these synthetic lattices. An additional effort related to broadening the scope and impact of undergraduate research will lead a project to create topological lattice models based on synthetically-coupled oscillator networks. This research effort will enable new functionality of engineered mechanical networks, including new capabilities for designing non-reciprocity, artificial gauge fields, disorder, and strong nonlinearities. The undergraduate led research team will use these newly developed methods to study transport phenomena in new classes of mechanical oscillator networks.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.