Non-ergodic dynamics in tunable Bose-Hubbard models

在这个项目中，我们将完成基于超冷Cs原子独特性质的可调实验平台的开发和构建，该平台结合了双色超晶格，状态依赖晶格，Feshbach共振和量子气体显微镜，以研究超越传统多体局域化和标准Bose-Hubbard模型的非遍历动力学。最近，新形式的本地化已被预测在均匀的无无序的几何不变系统。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基础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的丰富的弛豫动力学。倾斜的哈伯德模型预计将扰动地表现出大倾斜极限的碎片。碎裂的最显著的特征之一是弛豫动力学的强初始态依赖性，这可以使用量子气体显微镜直接观察到。由于多体光谱的碎片性质，热化需要相对于单个碎片来定义。这导致特征行为，例如，对于在碎片内热化的初始状态，纠缠熵迅速饱和到由其所处的碎片的尺寸确定的值。这与表现出对数增长的传统多体局域系统的行为形成鲜明对比。我们将通过测量局部可观测量来揭示这种差异，例如量子气体显微镜和光学超晶格促进的两点相关和局部电流。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。作为一个扩展，我们将发展具有相当大的最近邻相互作用和次最近邻跳跃的状态相关光学晶格。这些条款提供了额外的可调性的微观参数，这将是非常有价值的工程的新的约束动力学的光学晶格，探索不同形式的无无序遍历性打破。

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.