CAREER: Topology and symmetry in non-equilibrium quantum systems

非技术总结这个职业奖项支持在远离平衡的复杂量子系统动力学方面的理论研究和教育。激光物理学的最新实验进展使人们能够在超快的时间尺度上控制材料中的电子，然后它们才能达到平衡。同样，与周围环境完全隔离的原子产生的超冷气体使人们能够实时观察它们的量子动力学。这些进展开启了量子力学研究的新领域。这项研究旨在阐明特定环境下的复杂量子动力学。在这一背景下，最意想不到的发现是，即使是极高能量的量子粒子，在广泛的实验条件下也可以保持空间局域化。这与经典力学通常的直觉形成鲜明对比：如果一个人快速摇动一个装满弹珠的盒子，它们不会静止不动。当量子粒子局部化时，它们不仅保持静止，而且还有可能用于受控的量子计算。该项目旨在澄清这种局部化现象产生的准确条件，确定近期的实验观测数据，并建立对这一鲜为人知的现象的完整理论。在快速驱动单摆的支承时，重力的影响是可以取消的：摆锤可以落在支撑点上方的倒置位置。最近的电子系统实验表明，强激光辐射同样可以稳定非正常超导材料中的奇异量子效应，例如短时间的超导效应。该项目的另一个目标是开发一种动态稳定状态的理论，以便为计算和其他应用程序控制和设计它们。除了指导和培训参与研究计划的研究生和本科生外，PI还旨在通过包括实验室参观、演示和教师互动的“物理日”激励当地的初中生和高中生探索STEM的职业生涯。此外，这个奖项将支持PI在一个新的公开讲座系列中的作用，该系列讲座旨在让更广泛的波士顿社区参与日常物理和研究前沿。随着非平衡物理的未来越来越依赖于具有跨学科技能的物理学家，PI建议开发一门新的课程，将量子、光学和生物环境中的非平衡物理的方法统一起来。技术总结这个职业奖项支持在远离平衡的多体系统中发现、表征和控制量子有序的理论研究和教育。通过多管齐下的方法，包括对模型系统的研究、发展量子稳态的一般定理、微扰理论和数值计算，该项目提出了以下基本问题：1)强猝灭无序可以无限期地阻止良好隔离系统中的局部平衡，这一显著现象被称为多体局域化。PI将研究在高维、准周期环境中多体局域化的基本方面，以及局域化和拓扑学的相互作用。2)在受驱动的量子系统中可以出现没有平衡对应的奇异的非平衡有序，这为研究健壮的量子相干多体现象提供了一个独特的窗口。PI将发现和分类可通过多音驱动获得的复杂有序，并研究其稳定性。3)环境性质在状态准备和稳定脆弱拓扑态方面至关重要。PI将研究非常规环境的性质，包括实验相关系统中的任意子浴和有记忆的浴，并提取它们的普遍特征。过去十年来，在相关材料的超快光谱以及在构建隔离良好的超冷原子和分子气体方面取得的显著实验进展，使多体量子系统的实时动力学成为人们关注的焦点。与此同时，在超导量子比特和囚禁离子等实验平台上建立量子计算机的努力，引发了许多关于驱动耗散系统相干性的有趣问题，并导致量子信息理论和凝聚态之间进行了丰富的思想交流。从理论上讲，对远离平衡的系统的理解仍然具有挑战性，因为统计力学背后的假设通常无法应用。这项拟议的研究旨在广泛地促进我们对封闭、驱动和开放环境下量子多体动力学的理解，并将其具体应用于在动力学环境中观察新的量子秩序。开发新的计算方法和对现实实验系统中微观时间尺度的理解也将是优先事项。除了指导和培训参与研究计划的研究生和本科生外，PI旨在通过包括实验室参观、演示和教师互动的“物理日”激励当地初中生和高中生探索STEM的职业生涯。此外，这个奖项将支持PI在一个新的公开讲座系列中的作用，该系列讲座旨在让更广泛的波士顿社区参与日常物理和研究前沿。随着非平衡物理的未来越来越依赖于具有跨学科技能的物理学家，PI建议开发一门新的课程，统一量子、光学和生物环境中非平衡物理的方法。这一奖项反映了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 CAREER award supports theoretical research and education in the dynamics of complex quantum systems away from equilibrium. Recent experimental advances in laser physics have enabled the control of electrons in materials at ultrafast time scales, before they can equilibrate. Likewise, the production of ultracold gases of atoms that are well isolated from their surroundings has enabled the real-time observation of their quantum dynamics. These developments have opened up a new regime of inquiry within quantum mechanics. This research seeks to elucidate complex quantum dynamics in specific settings.The most unexpected discovery in this context is that even extremely energetic quantum particles can remain spatially localized under a broad range of experimental conditions. This is in striking contrast with usual intuition from classical mechanics: if one rapidly shakes a box full of marbles, they do not stay still. When quantum particles localize, not only do they stay still, but they also become potentially usable for controlled quantum computation. The project aims to clarify the precise conditions under which this localization arises, determine near-term experimental observables, and build towards a complete theory of this poorly understood phenomenon. On driving the support of a simple pendulum quickly, the effects of gravity can be undone: the pendulum bob can settle in the inverted position above the point of support. Recent experiments in electronic systems suggest that strong laser radiation can similarly stabilize exotic quantum effects, such as superconductivity at short times, in materials which do not normally superconduct. Another aim of the project is to develop a theory of such dynamically stabilized states so as to control and engineer them for computation and other applications.In addition to mentoring and training graduate and undergraduate students participating in the research program, the PI aims to inspire local middle- and high-school students to explore careers in STEM through "Physics days" involving lab tours, demonstrations, and faculty interactions. Furthermore, this award will support the PI's role in a new public lecture series, which aims to engage the broader Boston community on everyday physics and the frontiers of research. As the future of nonequilibrium physics increasingly relies on physicists with interdisciplinary skills, the PI proposes to develop a new course unifying the approaches to out-of-equilibrium physics in quantum, optical, and biological settings. TECHNICAL SUMMARYThis CAREER award supports theoretical research and education in discovering, characterizing, and controlling quantum orders in many-body systems far from equilibrium. Through a multipronged approach that includes studies in model systems, developing general theorems about quantum steady states, perturbation theory and numerical computation, this project proposes to address the following fundamental issues:1) Strong quenched disorder can indefinitely prevent local equilibration in a well-isolated system, a remarkable phenomenon known as many-body localization. The PI will investigate foundational aspects of many-body localization in higher dimensions, in quasiperiodic settings, and the interplay of localization and topology.2) Exotic nonequilibrium orders with no equilibrium counterpart can arise in driven quantum systems, offering a unique window into robust quantum coherent many-body phenomena. The PI will discover and classify the complex orders accessible with multitone driving and investigate their stability.3) Environmental properties are crucial in state preparation and stabilizing fragile topological states. The PI will investigate the properties of unconventional environments, including anyon baths and baths with memory in experimentally relevant systems and extract their universal features.Remarkable experimental advances in the past decade in the ultrafast spectroscopy of correlated materials and in the construction of well-isolated ultracold atomic and molecular gases have brought real-time dynamics of many-body quantum systems into sharp focus. Concurrently, the quest to build a quantum computer in experimental platforms like superconducting qubits and trapped ions has raised many interesting questions about coherence in driven dissipative systems and has led to a rich exchange of ideas between quantum information theory and condensed matter. Theoretically, the understanding of far-from-equilibrium systems remains challenging because the assumptions underlying statistical mechanics typically fail to apply. The proposed research seeks to broadly advance our understanding of quantum many-body dynamics in closed, driven, and open settings, and to specifically apply it to the observation of novel quantum orders in dynamical settings. The development of new computational methods and the understanding of microscopic time scales in realistic experimental systems will also be a priority.In addition to mentoring and training graduate and undergraduate students participating in the research program, the PI aims to inspire local middle- and high-school students to explore careers in STEM through "Physics days" involving lab tours, demonstrations, and faculty interactions. Furthermore, this award will support the PI's role in a new public lecture series, which aims to engage the broader Boston community on everyday physics and the frontiers of research. As the future of nonequilibrium physics increasingly relies on physicists with interdisciplinary skills, the PI proposes to develop a new course unifying the approaches to out-of-equilibrium physics in quantum, optical, and biological settings.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.