Topology in Nonequilibrium Quantum Many-Body Dynamics

拓扑相的发现导致了科学家思考物质分类方式的范式转变。从概念上超越传统的朗道范式，拓扑相位的特点是全局拓扑性质，而不是局部序参数，已成为一个广阔的研究前沿，与有前途的应用有关的新形式的信息处理和高精度计量。与此同时，探索热平衡领域之外的动力学性质已被证明是理解关键多体现象的关键。在这个非平衡的背景下，与本项目相关的突出例子包括热化和状态准备作为动力学过程的研究，以及揭示物质相的动力学特征。我们提出的研究桥接领域的非平衡量子动力学和拓扑量子物质的目的是揭示拓扑的作用，在量子多体系统的实时动力学。这项研究不仅具有深刻的理论意义，而且还受到其与正在进行的实验活动的直接相关性的强烈激励，这些实验活动涉及固有的非平衡量子多体系统，例如超冷原子气体和光驱动的固态系统。从一个受控（拓扑平凡）的初始状态开始，在这样的系统中的通用实验协议是通过打开一些外部驱动来实现一些感兴趣的哈密顿量来执行参数淬火。这可能会导致与任何平衡场景在性质上不同的情况，例如，当瞬时哈密顿量和波函数的拓扑性质在猝灭后不同时。尽管它们在正在进行的实验中自然发生，但这种情况的物理后果远未得到最终的理解，特别是对于相关系统-本项目的主要焦点。具体而言，在这个项目中，我们将（A）确定新的方法来动态探测远离平衡的相关系统的拓扑性质，（B）提出和研究方案，以动态地准备在非平衡的方式拓扑相的低温状态。关于（A），我们将分析拓扑性质在相互作用的多体系统中可以动态平衡到什么程度，并寻找没有直接平衡模拟的动态定义的拓扑不变量。关于（B），我们的目标是提出实验上可行的方案，以耗散地制备强相关拓扑相位作为量子主方程的稳态。在这个开放的量子系统的背景下，我们还打算解决自然问题的拓扑分类及其可观察到的后果超出了哈密顿动力学和纯量子态的领域。

The discovery of topological phases has led to a paradigm shift in the way scientists think about the classification of matter. Going conceptually beyond the conventional Landau paradigm, topological phases characterized by global topological properties rather than local order parameters have become a broad frontier of research, with promising applications regarding new forms of information processing and high precision metrology. In parallel, exploring dynamical properties beyond the realm of thermal equilibrium has proven to be key to the understanding of crucial many-body phenomena. Prominent examples in this non-equilibrium context that are of relevance for the present project include the study of thermalization and state preparation as dynamical processes, as well as revealing dynamical signatures of phases of matter. Our proposed research bridging the fields of non-equilibrium quantum dynamics and topological quantum matter is aimed at revealing the role of topology in the real-time dynamics of quantum many-body systems. This research is not only of deep theoretical interest, but is also strongly motivated by its immediate relevance for ongoing experimental activity on inherently non-equilibrium quantum many-body systems, such as ultracold atomic gases and light-driven solid state systems. Starting from a controlled (topologically trivial) initial state, the generic experimental protocol in such systems is to perform a parameter quench by switching on some external driving to realize some Hamiltonian of interest. This may lead to situations which are qualitatively different from any equilibrium scenario, e.g. when the topological properties of the instantaneous Hamiltonian and the wave-function differ after the quench. Despite their natural occurrence in ongoing experiments, the physical consequences of such situations are far from being conclusively understood, in particular for correlated systems – the main focus of the present project. Concretely, in this project we will (A) identify new ways to dynamically probe topological properties far from equilibrium in correlated systems, and (B) propose and study scenarios to dynamically prepare low-temperature states of topological phases in a non-equilibrium fashion. Relating to (A), we will analyze as to what extent topological properties can dynamically equilibrate in interacting many-body systems, and search for dynamically defined topological invariants without a direct equilibrium analog. Regarding (B), we aim at proposing experimentally feasible scenarios to dissipatively prepare strongly correlated topological phases as steady states of a quantum master equation. In this open quantum system context, we also intend to address natural questions regarding the topological classification and its observable consequences beyond the realm of Hamiltonian dynamics and pure quantum states.