Dynamics of correlated many-body quantum systems

量子模拟旨在获得对复杂微观系统行为的基本见解，这些系统是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）这种行为，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难以解决的问题。光学晶格中的超冷原子为我们在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，我们建立了量子气体显微镜平台，使我们能够实现光学晶格中原子的单位点和单原子分辨检测。这个令人兴奋的新工具将为研究光学晶格中的强相关费米子量子系统开辟道路，并对其局部特性有前所未有的了解，这是该项目的核心主题。*量子自旋模型。该项目的第一部分将致力于改进单原子成像系统，并实施第二原子物种的激光冷却，以实现光学晶格中的双组分超冷量子气体。这种双组分玻色子原子系统可以模拟不同的自旋模型，这在凝聚态物理中具有重要意义。可调整的散射长度将使实现S=1/2和S=1模型具有（近）海森堡对称性成为可能。我们还可以通过控制一个物种内部的相互作用来设计反铁磁交换，使这种相互作用强度与系统中其他相互作用强度的尺度明显不同：另一种方法是通过将系统准备成一个高度激发的初始状态，该初始状态是由突然施加交错的现场能量产生的，这样莫特绝缘体就处于亚稳态，交换能量改变符号。另一种可以测试的技术是Floquet调制技术。玻色子原子的猝灭动力学。一个关键的目标是研究多体费米子量子系统的非平衡动力学。我们计划将一维相关动力学的先前研究扩展到均匀二维系统，其中现有的数值和分析方法受到限制。例如，我们正在计划使用定制的光势创建电荷密度波，并观察其松弛到平衡状态，我们将特别研究作为物种间相互作用函数的动力学。单站点或多站点寻址也将允许我们执行本地淬灭。单原子成像将使我们能够监测多体系统中相关性的直接传播，不仅在一维，而且在二维或不同的晶格几何形状，如三角形晶格中。此外，当有效相互作用强度缓慢调整过临界点时，激发的产生速率和磁畴的形成可以直接在现场成像，以探索Kibble-Zurek-like物理。

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, we have setup quantum-gas microscope platforms, which have enabled us to achieve single-site and single-atom resolved detection of atoms 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. *Quantum spin models. The first part of the of the project will be devoted to improve the single-atom imaging systems and implement the laser cooling of a second atomic species to realise two-component ultracold quantum gases in an optical lattice. Such a system of two-component bosonic atoms can mimic different spin models, which are of importance in condensed matter physics. The tailorable scattering lengths will make it possible to implement S=1/2 and S=1 models with (near) Heisenberg symmetry. We can also engineer, antiferromagnetic exchange by control over the interactions within one species, so that this interaction strength becomes markedly different to the other scales of interaction strength in the system: Another way of doing so is by preparation of the system into a highly excited initial state generated by the sudden imposition of staggered onsite energies such that the Mott insulator is a metastable state, and exchange energies change sign. A further technique which may be tested are Floquet modulation techniques. *Quench dynamics with bosonic atoms. A key goal is to study the out-of-equilibrium dynamics of many-body fermionic quantum systems. We are planning to extend the previous studies of correlation dynamics in 1D to uniform 2D systems, where existing numerical and analytical approaches suffer from limitations. We are planning for example create a charge-density wave using tailored light potentials and observe its relaxation to equilibrium, and we will in particular study the dynamics as a function of the interspecies interaction. Single or multi-site addressing will also allow us to perform local quenches. Single-atom imaging will enable us to monitor the direct spreading of correlations in many-body systems not only in one dimension but also in 2D or in different lattice geometries, such as triangular lattices. Furthermore, the production rate of excitations and the formation of magnetic domains when tuning the effective interaction strength slowly across the critical point can be directly imaged in-situ to explore Kibble-Zurek-like physics.