Non-ergodic dynamics in tunable Bose-Hubbard models

在这个项目中，我们将完成一个基于超冷Cs原子独特性质的可调实验平台的开发和建设，该平台结合了双色超晶格、依赖态晶格、Feshbach共振和量子气体显微镜，以研究超越传统多体定域化和标准Bose-Hubbard模型的非遍历动力学。最近，在没有无序的齐次平移不变系统中预测了新的局部化形式。一个例子是所谓的碎片模型，其中多体希尔伯特空间分裂成指数级的许多不连通的子空间或碎片，这些子空间或碎片与底层哈密顿量的任何明显对称性无关。在这个项目中，我们将研究倾斜玻色-哈伯德模型在一维和二维中丰富的弛豫动力学。倾斜的Hubbard模型预计会在大倾斜的极限内微扰地显示碎裂。碎裂最显著的标志之一是弛豫动力学对初始态的强烈依赖性，这可以用量子气体显微镜直接观察到。由于多体光谱的碎片化性质，需要针对单个碎片来定义热化。这导致了特征行为，例如，对于在片段内热正化的初始状态，纠缠熵迅速饱和到由其所在的片段的尺寸确定的值。这与传统的多体局部化系统呈现对数增长的行为形成了鲜明对比。我们将通过测量局部可观测数据来揭示这种差异，例如两点关联和局部电流，这是由量子气体显微镜和光学超晶格促进的。有趣的是，碎片化在不止一个维度上为稳定的非遍历阶段铺平了道路。作为扩展，我们将开发具有相当大的近邻相互作用和次近邻跳跃的依赖于状态的光学晶格。这些项提供了额外的微观参数的可调性，这对于在光学晶格中探索不同形式的无无序遍历破缺的新型约束动力学的工程将是非常有价值的。

Within this project, we are going to complete the development and construction of a tunable experimental platform based on the unique properties of ultracold Cs atoms, which combines bichromatic superlattices, state-dependent lattices, Feshbach resonances and quantum-gas microscopy in order to study non-ergodic dynamics beyond conventional many-body localization and standard Bose-Hubbard models. Recently, novel forms of localization have been predicted in homogeneous translationally-invariant systems without disorder. One example are so-called fragmented models, where the many-body Hilbert-space fragments into exponentially many disconnected subspaces or fragments that are not related to any obvious symmetry of the underlying Hamiltonian. Within this project, we are going to investigate the rich relaxation dynamics of tilted Bose-Hubbard models in one- and two-dimensions. Tilted Hubbard models are expected to perturbatively exhibit fragmentation in the limit of large tilts. One of the most striking signatures of fragmentation is the strong initial-state dependence of the relaxation dynamics, which can be directly observed using quantum gas microscopes. Due to the fragmented nature of the many-body spectrum, thermalization needs to be defined with respect to individual fragments. This results in characteristic behavior, e.g., for initial states that thermalize within a fragment the entanglement entropy quickly saturates to a value that is determined by the dimension of the fragment it lives in. This is in stark contrast to the behavior of conventional many-body-localized systems that exhibit a logarithmic growth. We are going to reveal this difference by measuring local observables, such as two-point correlations and local currents, facilitated by quantum gas microscopy and optical superlattices. Intriguingly, fragmentation paves the way towards stable non-ergodic phases in more than one dimension. As an extension, we are going to develop state-dependent optical lattices with sizable nearest-neighbor interactions and next-nearest-neighbor hopping. These terms offer additional tunability of the microscopic parameters, which will be extremely valuable for the engineering of novel constrained dynamics in optical lattices to explore different forms of disorder-free ergodicity breaking.