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

运输（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，理解电荷、热量甚至信息等物理量如何在许多相互作用粒子的系统中演化和传输仍然存在挑战，特别是当考虑量子效应时。近年来，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，其中我们在真实的空间中的正常输运图像被抽象为由单个原子或分子等小量子系统的内部状态所跨越的空间中的布居输运。例如，通过吸收入射激光场的光，粒子数可以在原子（如氢）的电子态之间“移动”。 通过这种方式，原子的集合，这是很好地理解和高度可控的激光或其他电磁场，可以用来“模拟”一个更复杂的凝聚态系统，并导致我们对复杂系统的理解的进步。在目前的项目中的实验工作将扩展这种类型的方法来研究传输到一个新的制度的强粒子间的相互作用。该团队将基于可以在微观水平上单独控制和检测的原子样本进行实验。微波电磁场将被用来精确控制原子状态之间的人口传输，从而允许对传输现象进行新的探索。此外，该团队将努力扩大本科生研究机会的范围和影响，主要重点是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，本科生主导的研究项目，对机械振荡器的网络，耦合的“合成”，或工程和间接的力量。这项工作将把来自不同背景的本科生纳入与新型传输现象相关的前沿研究中，并将使用这些人类规模的实验来生成可视化视频内容，用于推广和教学。该项目建立在以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传输现象。通过考虑发生在内部状态空间（由相干微波跃迁和强偶极-偶极相互作用驱动）而不是真实的空间中的量子输运问题，这种方法利用了利用光谱控制操纵内部自由度的能力。这种光谱控制允许精确工程的合成晶格与非平凡的带拓扑结构，动力学挫折，和可调的障碍。里德伯原子之间的共振偶极-偶极相互作用将导致与拓扑学和强相互作用的相互作用相关的新现象，研究孤立相互作用无序系统中的弛豫和热化，也许会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-偶极相互作用如何在这些合成晶格中导致新的多体现象。与扩大本科研究的范围和影响有关的额外努力将导致一个项目，以创建基于合成耦合振荡器网络的拓扑晶格模型。这项研究工作将使工程机械网络的新功能，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类别的机械振荡器网络中的传输现象。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。

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.