Modelling atoms trapped in ordered and disordered two-dimensional geometries

量子模拟器的加速发展导致了新的物理模型的创建，这些模型允许进一步了解多体量子系统。最有趣的模拟器之一是量子气体显微镜，它允许对单个原子进行操作和成像。因此，有可能在囚禁势中控制冷原子，从而探索该系统可能具有的性质。此外，量子气体显微镜与光学数字镜设备的结合允许对潜在陷阱的几何形状进行更高程度的控制，从而允许探索更复杂的条件。该项目将专注于开发理论和数值方法，以研究这种新的量子模拟器技术的影响。这将通过概括用于描述量子气体显微镜的概念和计算技术来实现，因为它们是研究任意形状晶格势的效应的基础。因此，该项目将专注于对我们实验室目前实施的量子气体显微镜进行建模，并通过控制晶格势来探索中性原子量子模拟器可以探索的新物理。因此，本项目的主要目标是将理论研究和实验研究结合起来，以推动两者的进步。

The accelerating development of quantum simulators has led to the creation of new physical models that permit further understanding of many-body quantum systems. One of the most interesting simulators is the quantum gas microscope, which allows for the manipulation and imaging of single atoms. It is hence possible to control cold atoms in trapping potentials, and thus explore the properties the system can have. Furthermore, the combination of quantum gas microscopes with optical digital mirror devices allows for a higher degree of control over the geometry of the potential traps, allowing for more complex conditions to be explored. The project will focus on the development of theoretical and numerical methods for investigating the effects of this new quantum simulator technology. This will be done by generalising concepts and computational techniques used to describe quantum gas microscopes, as they are fundamental for studying the effects of arbitrarily shaped lattice potentials. Thus, the project will concentrate on both modelling the current quantum gas microscopes implemented in our lab and exploring the new physics that can be probed by neutral atom quantum simulators through the control of lattice potentials. Thus, the main objective of this project is to connect theoretical and experimental investigations, so to push forward the advancement of both.