Synthetic magnetism in strongly-correlated lattice gases

中性量子气体合成磁性的实现是冷原子物理学中最活跃的研究领域之一，因为它为研究规范场存在下强相关多体系统的非平凡物理学开辟了迷人的前景。这个项目是根据与这个快速发展的领域相关的两个互补目标来组织的。项目的第一部分分析了合成规范场存在时粒子间相互作用的作用。项目的这一部分主要关注目前正在进行的实验中可用的现实场景，特别是具有所谓合成维度的系统，有可能在短期内直接影响实验。该项目的第二个目标是探索一条现实的探索路径，以模拟光学晶格中冷原子的动态规范场。我们将着重于从具有合成尺寸的费米气体开始，使用调制晶格创建与密度相关的规范场，这可能在当前最先进的技术中实现。在后面的阶段，我们将继续探索动态规范场，研究实现密度相关的非阿贝尔场，以及费米-玻色混合物中的密度相关规范场。

The realization of synthetic magnetism in neutral quantum gases constitutes one of the most active research fields in the physics of cold atoms, since it opens fascinating perspectives towards the study of the non-trivial physics of strongly-correlated many-body systems in the presence of gauge fields. This project is organized along two complementary goals related to this rapidly-growing field. The first part of the project analyzes the role of inter-particle interactions in the presence of synthetic gauge fields.Primarily focusing on realistic scenarios currently available in on-going experiments, in particular on systems with so-called synthetic dimensions, this part of the project has the potential to directly impact experiments in the short-term.The second goal of this project is to investigate a realistic exploration path towards the simulation of dynamical gauge fields with cold atoms in optical lattices.We will focus on the creation of density-dependent gauge fields using modulated lattices starting with Fermi gases with synthetic dimensions, which may be implemented within the current state-of-the-art. In a later stage we will move forward in the exploration of dynamical gauge fields, with the study of the realization of density-dependent non-Abelian fields, and of density-dependent gauge fields in Fermi-Bose mixtures.