Spin-orbit coupling in interacting bosonic systems: density-dependent gauge fields and flux ladders

拓扑学是物理学中的一个关键概念，涉及高能物理和凝聚态物理等多个领域。在这种情况下，拓扑有序导致了高度违反直觉的现象，例如量子霍尔系统中任意子激发的存在，或者强关联材料中规范理论的出现。人工规范场作用下的超冷原子气体构成了拓扑系统受控模拟的理想平台。在过去的几年里，实验已经证明了对单粒子拓扑性质的令人印象深刻的控制水平，使得能够设计聚合的拓扑哈密顿量，并达到在固态样品中无法获得的极端参数状态和观察到的结果。然而，将这些实验研究扩展到多体系统是一项极具挑战性的任务。因此，在超冷原子背景下，多体拓扑相在很大程度上仍然没有被探索。在这个项目中，我们将在第一个资助期积累的经验的基础上，利用自旋-轨道耦合的超冷玻色气体来研究拓扑和相互作用的相互作用。我们的研究将沿着两条主线进行。在连续体中，我们将实现和研究依赖于密度的人工规范场，其中原子间相互作用产生物质对规范场的反向作用，并实现相互作用规范理论。在光学晶格中，我们将在多体区域实现磁通梯-著名的Hofstadter模型的带状版本-，表征它们的相图，并研究相互作用对它们失超动力学的影响。这项工作将与本研究股的理论小组密切合作，以便在实验和理论计算之间进行直接比较。

Topology is a key concept in physics, with implications in areas as diverse as high-energy and condensed-matter physics. There, topological order gives rise to highly counterintuitive phenomena such as the existence of anyonic excitations in quantum Hall systems or the emergence of gauge theories in strongly-correlated materials. Ultracold atomic gases subjected to artificial gauge fields constitute an ideal platform for the controlled simulation of topological systems. During the last years, experiments have demonstrated an impressive level of control over single-particle topological properties,allowing to engineer paradigmatic topological Hamiltonians and to reach extreme parameter regimes and observables not accessible in solid-state samples. However, extending these experimental studies to the many-body regime is a highly challenging task. As a consequence, many-body topological phases remain largely unexplored in the ultracold atom context. In this project, we will study the interplay of topology and interactions using spin-orbit coupled ultracold bosonic gases, building on the experience accumulated during the first funding period. Our research will be structured along two lines. In the continuum we will implement and study density-dependent artificial gaugefields where the interatomic interactions produce a back-action of matter on the gauge field and realize an interacting gauge theory. In optical lattices we will realize flux ladders – ribbon versions of the celebrated Hofstadter model – in the many-body regime, characterize their phase diagram and study the effect of interactions on their quench dynamics. This work will be carried out in close collaboration with theory teams of this Research Unit, allowing for a direct comparison between experiments and theoretical calculations.