Quantum matter with anisotropic dipole-dipole interaction

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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.