Quantum dynamics in driven and disordered systems: Floquet topological control and flow methods for many body localization

非技术总结该奖项支持理论研究和教育，以了解和控制量子材料的行为，并将其独特的量子行为用于可能的技术应用。PI将结合从最近发现的新材料中获得的见解和模拟额外维度的想法，即周期性驱动的系统似乎为其所受的每个周期性驱动提供了额外的空间维度。例如，使用这两个想法，一个人可以拿起一个微小的磁铁，用两个调制的光束照射它，然后把它变成一个能量泵，从一个光束中吸取能量，并将其全部提供给另一个光束。PI旨在展示如何将这一原理应用到基于新发现的半导体的固态设备中。此外，PI将为一种新型的相变-多体局域相变-发展一种微观理论，这种相变发生在量子粒子系统(如电子)由于足够的无序存在而不再遵守热力学的共同规则时。研究生和博士后将参与这项研究，并将接受国家重点学科的培训和教育。PI还将完成一本关于如何使用任何物理本科生都已知的基础知识为各种技术和自然现象建模的教科书的编写工作。这本书将提供一个统一的视角，指导初出茅庐的物理学家和工程爱好者如何应用核心物理原理来获得对一系列现象和设备的高级理解，从医疗设备和能源生产到太空旅行、宇宙学和生命系统。技术总结该奖项支持为多体本地化过渡开发新的拓扑量子控制原理和新的分析工具的理论研究和教育。量子动力学是凝聚态物质中最具挑战性的领域之一。实验现在可以在各种环境中观察电子、原子和光的动力学。量子控制理论需要利用这些发展。一方面是拓扑物理，另一方面是无序导致多体局部化，这些平行主题丰富了量子多体动力学。该项目将探索基于拓扑物理的控制电磁辐射的新工具。PI将研究这些拓扑控制工具在相互作用的轻物质系统中实现时的行为。这将需要为多驱动多体量子光学和固态电子系统开发一套全面的理论。这一新兴理论将预测复杂材料在存在电子驰豫和多体相互作用时对强大外部驱动的电子响应。在第二部分的工作中，PI将通过对多体局域跃迁的研究，推导出一种分析无序和相互作用多体量子系统的新方法。该方法结合了么正流方法和强无序重整化群方法，不受相互作用的性质或范围的限制。通过对研究生和博士后的教育和培训，这项工作可能为基于拓扑原理的新的光子器件铺平道路。潜在的技术影响包括控制低太赫兹电磁辐射的新工具，但目前只有很少的控制工具可用。此外，PI将完成一本面向所有物理爱好者的书，描述对现实世界物理问题、自然现象和大学物理课程中技术突破的分析。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。

NONTECHNICAL SUMMARYThis award supports theoretical research and education towards understanding and controlling the behavior of quantum materials, and on using their unique quantum behavior for possible technological applications. The PI will combine insights obtained from the recent discovery of new materials and the idea of simulating extra dimensions, whereby a periodically driven system appears to have an extra spatial dimension for each periodic drive it is subject to. For example, using these two ideas, one can take a microscopic magnet, illuminate it with two modulated light beams, and turn it into an energy pump which draws energy from one beam and gives it in full to another. The PI aims to show how this principle could be implemented into solid-state devices based on newly discovered semiconductors. In addition, the PI will develop a microscopic theory for a new type of phase transition, the many-body localization transition, which occurs when a system of quantum particles, such as electrons, stops obeying the common rules of thermodynamics due to the presence of sufficient disorder. Graduate students and postdocs will participate in the research and will receive training and education in a subject of high national priority. The PI will also conclude the writing of a textbook on how to model a variety of technologies and natural phenomena using fundamentals known to any physics undergraduate. This book will provide a unifying perspective, guiding budding physicists and engineering enthusiasts on how to apply core physics principles to obtain advanced understanding for a range of phenomena and devices, ranging from medical devices and energy production to space travel, cosmology, and living systems. TECHNICAL SUMMARYThis award supports theoretical research and education towards developing new topological quantum control principles and new analysis tools for the many-body localization transition. Quantum dynamics is among the most challenging fields in condensed matter. Experiments can now observe the dynamics of electrons, atoms, and light in a variety of environments. The theory of quantum control needs to harness these developments. Topological physics on the one hand, and disorder leading to many-body localization on the other, present parallel themes that enrich quantum many-body dynamics.The project will explore new tools for controlling electromagnetic radiation that are based on topological physics. The PI will study how these topological control tools behave when realized in interacting light-matter systems. This will require developing a comprehensive theory for multi-driven many-body quantum optics and solid-state electronic systems. The emerging theory will predict the electronic response of complex materials to strong external drives in the presence of electronic relaxation and many-body interactions. In the second part of the work, the PI will derive a new method for analyzing disordered and interacting many-body quantum systems through study of the many-body localization transition. The method envisioned combines unitary flow methods with strong-disorder renormalization group approaches and will not be restricted by the nature or the range of the interactions. It has the potential to lead to the discovery of fundamentally new universality classes.Beyond education and training of graduate students and postdocs, the work could pave the way to new photonic devices based on topological principles. Potential technological impacts include new tools for controlling low THz electromagnetic radiation for which only few control tools are available. In addition, the PI will complete a book addressed to all physics enthusiasts describing an analysis of real-world physics problems, natural phenomena, and technological breakthroughs drawing on college physics curriculum.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.