Programmable light potentials for studying edge states and quantum thermodynamics

光学晶格中的超冷原子为研究多体量子系统提供了独特的量子模拟器，例如与材料科学和其他学科相关。为了进一步增强这些系统的能力，我们使用了可编程的静态和动态变化的光势-这是我们在QCS Hub计划的头几年在WP6中开发的一项技术。我们的方法使用空间光调制器来创建任意势，我们可以通过量子气体显微镜将其投射到亚波长分辨率的原子上。同样的显微镜装置使我们能够以单一晶格位置的分辨率探测二维光学晶格中的原子。在这个PHD项目的第一部分，我们将使用可编程光势来创建所谓的Lieb晶格，方法是用排斥势阻止正方形晶格中每个3x3子单元的中心位置(图2)。Lieb晶格表现出非常有趣的性质，如平带、局域态和边态。基于我们已经在WP6中与局域理论团队合作所做的模型计算，我们将首先使用位置分辨检测来确认边态的存在，并研究它们的动力学演化，然后在更复杂的晶格几何中也这样做。我们将使用另一个定制的光场来准备初始态，该光场可以对选定的原子进行光移，以便在所有其他原子被移除之前，通过微波场将它们转移到不同的超精细状态。在第二个项目中，我们将使用定制的光势来产生微观储集层，例如，具有不同的化学势、原子数和它们之间的耦合连接的强度。我们将专注于量子区域中的观察热力学性质，并研究非平衡动力学和水库之间的传输，以及通过Feshbach共振调节现场相互作用的附加选项。

Ultracold atoms in optical lattices offer unique possibilities as quantum simulators for the study of many-body quantum systems, relevant for example to material science and other disciplines. To further enhance the capabilities of these systems, we use programmable static and dynamically varying light potentials - a technology that we developed in WP6 within the first years of the QCS Hub programme. Our approach uses a spatial light modulator to create arbitrary potentials which we can project onto the atoms with sub-wavelength resolution by our quantum-gas microscope. The same microscope setup enables us to detect the atoms in a two-dimensional optical lattice with single-lattice-site resolution.In the first part of this PhD project, we will use programmable light potentials to create a so-called Lieb lattice, by 'blocking' the central site in each 3x3 sub-cell of a square lattice with a repulsive potential (Fig. 2). Lieb lattices exhibit very interesting properties such as flat bands, localization and edge states. Based on model calculations which we have already done in collaboration with the local theory team in WP6, we would first use the site-resolved detection to confirm the existence of the of edge states, and study their dynamical evolution, and later do so as well in more complex lattice geometries. We will prepare initial states using another tailor-made light field that light-shifts selected atoms such that they can be transferred to a different hyperfine state with a microwave field, before all other atoms are removed. In a second project strand, we will use the tailor-made light-potentials to produce microscopic reservoirs with, e.g., varying chemical potential, atom numbers, and strength of the coupling link between them. We will focus on the observation thermodynamics properties in the quantum regime and investigate out-of-equilibrium dynamics and transport between the reservoirs, with the additional option to tune the onsite-interaction via a Feshbach resonance.