Quantum simulations with fermionic ultracold atoms in optical lattices

量子模拟试图从根本上洞察复杂微观系统的行为，这些系统构成了从材料科学到化学和生物学等不同领域的基础。现在可以通过在微观、量子力学水平上可控的实验来模拟(或模拟)这一行为，从而获得新的理解。这提供了一种革命性的方法，可以解决目前即使是最快的超级计算机也无法解决的问题。光学晶格中的超冷原子为在我们的实验室中研究多体量子系统的这种行为提供了独特的可能性。特别是，量子气体显微镜使我们能够实现对光学晶格中费米子的单位和单原子分辨检测。这一激动人心的新工具将为研究光学晶格中的强关联费米子量子系统开辟道路，以前所未有的洞察力了解其局域性质，这是该项目的核心主题。在该项目中，将解决以下具体目标：-空间光调制器的建立和表征：使用激光场操纵原子需要在时间和空间上非常精确地控制光势。我们计划使用位相调制空间光调制器(SLM)在原子位置创建全息图案。项目工作包括建立SLM，在一个独立的装置中包括所有激光系统和相应的光学装置，旨在创建针对所需特性优化的光势，例如高对比度和空间均匀性。-不平衡动力学：一个关键的科学目标是研究多体费米子量子系统的非平衡动力学。由空间光调制器产生的量身定制的光场将在系统中引入局部微扰，目标是解决和理解随后的动态演化。一维系统中的输运现象、猝灭后的准粒子传播或自旋-电荷分离等现象都可以用Luttinger液体理论来研究，这些现象可以用高分辨率成像系统观察到。-低熵量子相的新技术：动态变化的光势也可以用来实施从陷阱中确定性地移除高熵区域的方案。在一种理论上提出的冷却方案中，建议通过分离晶格中的低和高熵区域来冷却费米子。晶格中心的电势首先被降低到一个凹坑，以产生低熵(带状绝缘体)相。然后，由于酒窝和边缘之间的差动光移，通过选择性寻址，高熵边缘(金属相)被推开或移除。酒窝被绝热移除，以达到半填满的低熵相。

Quantum Simulation seeks to gain fundamental insight into the behaviour of complex microscopic systems, which underlie diverse fields ranging from materials science to chemistry and biology. New understanding can now be achieved by modelling (or simulating) this behaviour with experiments that are controllable on a microscopic, quantum-mechanical level. This provides a revolutionary approach that could solve problems that are currently intractable for even the fastest supercomputer.Ultracold atoms in optical lattices offer the unique possibility to study such behaviour of many-body quantum systems in our laboratories. In particular, a quantum gas microscope has enabled us to achieve single-site and single-atom resolved detection of fermions in an optical lattice. This exciting new tool will open the path to the study of strongly correlated fermionic quantum systems in optical lattices with unprecedented insight into their local properties, which is the core subject of the project.The following specific objectives will be addressed during the project: - Setup and characterisation of a spatial light modulator: the manipulation of atoms using laser field requires a very precise control of light potentials in both time and space. We plan to use a phase modulating spatial light modulator (SLM) to create holographic patterns at the position of the atoms. Project work comprises the setup of the SLM including all laser systems and corresponding optics in an independent setup aiming at the creation of light potentials optimised towards the desired properties, such as high contrast and spatial homogeneity.- Out-of equilibrium dynamics: A key scientific goal is to study the out-of-equilibrium dynamics of many-body fermionic quantum systems. The tailor-made light fields created by spatial light modulators will introduce local perturbations to the system, and the goal is to resolve and understand the ensuing dynamical evolution. A vast range of phenomena can be investigated, such as transport phenomena, quasiparticle propagation after quenches or spin-charge separation in a 1D system, as predicted within the theory of Luttinger liquids, which would be observable with the high resolution imaging system. - Novel techniques towards low-entropy quantum phases: Dynamically varying light potentials could also be used to implement schemes to deterministically remove high-entropy regions from the trap. In a theoretically proposed cooling scheme, it is suggested to cool fermions by separating regions of low and high-entropy in the lattice. The potential in the centre of the lattice is first lowered to a dimple to create a low-entropy (band insulator) phase. The high-entropy edges (metallic phase) are then pushed away or removed by selective addressing, thanks to the differential light shifts between the dimple and the edges. The dimple is adiabatically removed to reach a low-entropy phase with half-filling.