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

运输(将物体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由许多相互作用的粒子组成的系统中演化和传输仍然是一个悬而未决的挑战，特别是在考虑量子效应的情况下。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输运的新方法，在这些概念中，我们对真实空间中输运的正常图景被抽象为人口在由单个原子或分子等小量子系统的内态跨越的空间中的输运。例如，粒子数可以通过吸收来自入射激光场的光在原子的电子态(如氢)之间“移动”。通过这种方式，一组用激光或其他电磁场很好地理解并高度可控的原子，可以用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的进步。目前项目中的实验工作将把这种类型的方法扩展到研究输运的一种新的强粒子间相互作用制度。该团队将基于原子样本进行实验，这些原子样本可以在微观层面上进行单独控制和检测。微波电磁场将被用来精确地控制原子态之间的布居传输，从而允许对传输现象的新类型的探索。此外，该团队将领导一项努力，以扩大本科生研究机会的范围和影响，主要重点是增加来自代表性不足群体的成员的参与。这项工作将集中在建立一个由本科生领导的新的研究项目，该项目是关于机械振荡器网络的，这些网络由“合成”或工程和间接的力耦合。这项工作将吸收来自不同背景的本科生参与与新型输运现象相关的前沿研究，并将利用这些人体尺度的实验来生成可视化视频内容，用于扩展和教学。该项目建立在之前设计中性原子和光子合成晶格的基础上，将这些想法扩展到一个新的平台，基于超冷里德堡原子的内部自由度来探索多体输运现象。通过考虑发生在内态空间(由相干微波跃迁和强偶极-偶极相互作用驱动)而不是真实空间中的量子输运问题，该方法利用了通过光谱控制来操纵内部自由度的能力。这种光谱控制允许精确设计具有非平凡带拓扑、动力学受挫和可调谐无序的合成晶格。Rydberg原子之间的共振偶极-偶极相互作用将导致与拓扑和强相互作用相互作用相关的新现象，导致孤立相互作用无序系统的驰豫和热化的研究，并可能导致全新形式的多体现象的出现。研究小组将探索在里德堡原子的内态空间中设计新的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。与扩大本科生研究范围和影响有关的另一项工作将导致一个基于合成耦合振荡器网络创建拓扑格子模型的项目。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、人造规范场、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智力优势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.