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

规范场是我们现代理解所有尺度物理学的基础。从高能物理到引力和凝聚态物理，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拓扑量子效应的量子模拟打开了一扇大门，在新的，前所未有的良好控制的环境。在这些装置中，原子被适当地耦合到产生有效规范势的激光场。这些系统可以模拟电子在磁场中运动的动力学，也可以模拟非阿贝尔规范场中基本粒子的动力学。它们的多功能性和可调谐性使它们成为研究和测试规范场存在下量子多体系统动力学的理想平台。在这个计划中，我们的目标是从理论上研究和实验上实现的超冷原子在光学晶格中的合成规范场诱导的新的拓扑相的物质。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，工程师和探测拓扑相，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，它们的奇异传输特性和它们的激发的有趣性质。特别强调将给予相互作用和外部规范场之间的相互作用的调查，提供路线的实现和检测相互作用的阶段，如拓扑莫特绝缘体，分数陈省身绝缘体和分数量子霍尔液体。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。我们希望我们的实验和理论相结合的努力，把拓扑物质的理论理解和实验实现到一个新的水平，铺平了道路，在量子信息处理和自旋电子学的未来应用。

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.