FOR 2414: Artificial Gauge Fields and Interacting Topological Phases in Ultracold Atoms

规范场是我们在所有尺度上理解现代物理学的基础。从高能物理到重力和凝聚态物理，它们构成了成功描述物理现象的核心工具。最近，中性超冷原子人工规范场的实验实现，为在新颖的、前所未有的良好控制环境中进行拓扑量子效应的量子模拟打开了一扇门。在这些装置中，原子适当地耦合到产生有效规范电位的激光场。这些系统可以模拟电子在磁场中运动的动力学，也可以模拟基本粒子在非阿贝尔规范场中的动力学。它们的多功能性和可调性使它们成为在规范场存在下研究和测试量子多体系统动力学的理想平台。在本研究中，我们旨在从理论上研究和实验上实现由光学晶格中超冷原子的合成规范场诱导的物质的新拓扑相。通过利用实验、分析和数值技术的最新发展，我们将尝试表征、设计和探测拓扑相，如拓扑绝缘体和超流体，设计协议来测试它们的拓扑不变量、它们的奇特输运性质和它们的激发的有趣性质。特别强调的是相互作用和外部规范场之间的相互作用的研究，为实现和检测相互作用相，如拓扑莫特绝缘子，分数陈恩绝缘子和分数量子霍尔液体提供途径。此外，我们将研究规范场存在下的非平衡动力学，探索实现驱动非平衡拓扑相的途径。我们期望通过实验和理论的结合，将拓扑物质的理论认识和实验实现提升到一个新的水平，为未来在量子信息处理和自旋电子学中的应用铺平道路。

Gauge fields are fundamental for our modern understanding of physics at all scales. From high-energy physics to gravity and condensed matter physics, they constitute a central tool for successfully describing physical phenomena. Recently, the experimental realization of artificial gauge fields for neutral ultracold atoms has opened a door to the quantum simulation of topological quantum effects in novel, unprecedentedly well controlled environments. In these setups, atoms are suitably coupled to laser fields that generate effective gauge potentials. These systems can mimic the dynamics of electrons moving in a magnetic field, but also, the dynamics of elementary particles in non-Abelian gauge fields. Their versatility and tunability make them ideal platforms for investigating and testing the dynamics of quantum many-body systems in the presence of gauge fields. In this proposal we aim to theoretically investigate and experimentally realize novel topological phases of matter induced by synthetic gauge fields in ultracold atoms in optical lattices. By exploiting the latest developments in experimental, analytical and numerical techniques, we will attempt to characterize, engineer and probe topological phases such as topological insulators and superfluids, designing protocols to test their topological invariants, their exotic transport properties and the intriguing nature of their excitations. Special emphasis will be given to the investigation of the interplay between interactions and external gauge fields, providing routes to the realization and detection of interacting phases, such as topological Mott insulators, fractional Chern insulators and fractional quantum Hall liquids. Moreover, we will investigate out-of-equilibrium dynamics in the presence of gauge fields, exploring paths towards the realization of driven non-equilibrium topological phases. We expect our combined experimental and theoretical effort to bring both the theoretical understanding and the experimental realization of topological matter to a new level, paving the way towards future applications in quantum information processing and spintronics.