Quantum matter with anisotropic dipole-dipole interaction

本课题研究强磁矩原子和极性分子的基态性质。主要重点是各向异性偶极-偶极相互作用的设置，这与本合作研究项目中的实验组密切相关。一个重要的方面是对冷偶极原子气体中量子液滴的微观描述：虽然在低密度气相中很好地理解了超均场校正，但一旦出现对密度更高的量子液滴的不稳定性，目前对超均场校正的描述就会出现一个很小的虚部，这在分析中通常被忽略。因此，在微观分析中推导基态能量是一个开放和具有挑战性的问题，这在量子液体和低密度气相中都是有效的。第二个重要方面是在三维到二维以及三维到一维的空间交叉中超越平均场校正的行为。特别地，建立了这样的分析也将包括偶极相互作用的约束诱导共振的行为，这仍然是当前讨论的主题。最后，本部分的主要目标之一是研究极性分子和/或具有大磁矩的冷原子气体所实现的物质的拓扑状态。我们从利用极性分子实现著名的SSH模型开始，并通过制备半填充体系来研究量子多体基态。粒子的玻色子特性起着重要的作用，与原来的费米子模型相比，它强烈地改变了粒子的行为。然后，我们将研究几个这样的链耦合到准一维的自然扩展，并研究它们的拓扑性质。最后，我们还研究了用极性分子和/或偶极原子气体来实现物质拓扑状态的替代方法。

In this project, we study ground state properties of atoms with strong magnetic moments and polar molecules. The main focus is on setups with anisotropic dipole-dipole interactions, which are in close connection to the experimental groups within this collaborative research project. One important aspect is the microscopic description of the quantum droplets in cold dipolar atomic gases: while the beyond-mean-field corrections are well understood in the low-density gas phase, once the instability towards the quantum droplets with a higher density appears, the current description of the beyond-mean-field correction picks up a small imaginary part, which is generally ignored in the analysis. Therefore, it is an open and challenging problem to derive the ground state energy in a microscopic analysis, which is valid in the quantum liquid as well as the low-density gas phase. A second important aspect is the behavior of the beyond-mean-field correction within the dimensional crossover from three to two dimensions as well as three to one dimension. Especially, it is established that such an analysis will also include the behavior of the confinement-induced resonance for dipolar interactions, which is still a topic of current discussions. Finally, one of the main goals in this part is to study topological states of matter realized with polar molecules and/or cold atomic gases with large magnetic moments.We start with a realization of the famous SSH model using polar molecules and study the quantum many-body ground state by preparing the system at half-filling. The bosonic character of the particles plays a significant role and strongly modifies the behavior compared to the original formulation of the SSH model with fermions. Then, we will study the natural extension into quasi-one dimension by coupling several of such chains together, and study their topological properties. Finally, we also work on alternative methods to realize topological states of matter with polar molecules and/or dipolar atomic gases.