Quantum simulation of mesoscopic systems with highly excited atoms and ions

在超低温（绝对零度的几十亿分之一）和非常小的尺度（纳米）上，量子效应支配着物理系统的性质。即使是组件相对较少的系统也可能非常复杂，以至于它们的性质既不能用分析方法计算，也不能用数值方法计算。此外，即使是实验也可能产生很少关于系统的信息。如果考虑到许多粒子系统，例如金属中的电子等凝聚态系统，这就变得更加引人注目。特别是，如果粒子之间的相互作用很强，量子性质是很难确定和表征实验和理论。获取复杂量子系统信息的一种方法是模拟它们，而这些信息是不容易获取的。在这里，原始的系统参数被可以更精确地监测和操纵的参数所取代。近年来，人们发现由超冷原子组成的气体对完成这项任务特别有用。电场、磁场和光场被用来创造原子运动发生的潜在景观。例如，反向传播的激光束产生周期势，这相当于电子在结晶固体中遇到的情况。此外，原子之间的相互作用可以通过施加小磁场（使用所谓的费什巴赫共振）来调节。在这里，吸引、排斥甚至没有相互作用都是可以实现的。因此，超冷原子可以作为凝聚态系统的量子模拟器的构建块，其中原子承担电子的角色。这种模拟器的一个主要成就是研究了光学晶格中超冷原子气体从莫特绝缘体到超流体的相变。在前一种情况下，原子被紧紧地困在单个晶格中，而在后一种情况下，形成了一个扩展到整个晶格的非经典态。在本文提出的工作中，我们从理论上研究了一个在快时间尺度上模拟介观系统的量子模拟器。这个跨学科的研究项目与凝聚态物理、分子物理和超冷化学直接相关。它将加深我们对发生在分子、团簇和小自旋链中的物理过程的理解。量子模拟器的基本组成部分是由原子或离子组成的，这些原子或离子被放置在间距为几微米的陷阱中，这个陷阱足够大，激光束可以与（定位）单个原子相互作用。在这个模拟器中，超冷原子定义了一个潜在的晶格结构，电子动力学在其中发生。这直接类似于结晶固体或分子。然而，与“传统”分子不同的是，单个原子核可以被操纵。该项目的目的是探索这些系统，表征它们的性质，并阐明它们模拟介观系统的潜力。这为直接监测基本物理过程打开了一扇大门，例如电荷转移，这些过程通常是隐藏在观察者的眼睛之外的。该方案的一个关键特征是与实验有很强的相互作用。

At ultracold temperatures (within a few billionths of a degree of Absolute Zero) and on very small scales (nanometres) quantum effects dominate the properties of physical systems. Even systems with relatively few components might be so complex that their properties can be calculated neither analytically nor numerically. Moreover, even experiments may yield little information about the systems. This becomes even more dramatic if many particle systems are considered, e.g. condensed matter systems such as electrons in a metal. In particular, if interactions between the particles are strong, the quantum properties are very difficult to determine and to characterize experimentally and theoretically.One approach to gain information about complex quantum systems which are not easily accessible is to mimic - or simulate - them. Here, the original system parameters are replaced by ones which can be more precisely monitored and manipulated. In recent years it has turned out that gases of ultracold atoms are particularly useful to perform this task. Electric, magnetic and optical fields are used to create potential landscapes in which the atomic motion takes place. For example, counter propagating laser beams give rise to a periodic potential which is equivalent to the scenario encountered by electrons in a crystalline solid. Moreover, the interaction between the atoms is tunable by applying small magnetic fields (using the so-called Feshbach resonances). Here, attraction, repulsion or even no interaction is achievable. Ultracold atoms thus can serve as a building block for a quantum simulator of condensed matter systems where the atoms assume the role of the electrons. One major achievement of such a simulator was the study of a phase transition in a gas of ultracold atoms in an optical lattice from a Mott-insulator to a superfluid. In the former case the atoms are tightly trapped in the individual lattice sites whereas in the latter case a non-classical state is formed which extends over the entire lattice.In the proposed work we theoretically investigate a quantum simulator which mimics mesoscopic systems on fast timescales. This interdisciplinary research project is of direct relevance to condensed matter physics, molecular physics and ultracold chemistry. It will deepen our understanding of physical processes that take place in molecules, clusters and small spin chains. The basic building-block of the quantum simulator comprises atoms or ions held in traps with a spacing of several micrometers - large enough for laser beams to intreract with (address) individual atoms. In this simulator, the ultracold atoms define an underlying lattice structure in which the electronic dynamics takes place. This is directly analogous to a crystalline solid or a molecule. However, unlike in a 'conventional' molecule individual nuclei can be manipulated.The aim of the project is to explore these systems, to characterize their properties and to illuminate their potential to simulate mesoscopic systems. This opens a doorway to direct monitoring of fundamental physical processes, such as charge transfer, which normally take place hidden from the observer's eye. A key feature of the proposal is a strong interaction with the experiments.