Manipulating Ultracold Atoms --- from One to Many

在物理学和自然科学的许多领域中，还原论- 然而，也有许多例子，其中还原方法不能提供完整的图片。 随着越来越多的部分被添加进来，新的现象可能会在不同的阶段出现，而这些新的现象不能完全从之前更简单的系统的特性中理解。 冷原子系统是研究涌现现象的理想平台。 在实验上，几个实验室已经开发出精确控制原子阱中原子数量的技术，从一个到几个，再到许多。 这是由于冷原子的精确可控性而成为可能的。 这项研究旨在提供对各种冷原子系统的理论理解。 中心主题是研究单个原子的性质如何影响少原子或多原子系统的物理。这项研究是基础性的-冷原子的基础科学。 将解决的基本问题包括：一个原子或原子系综如何与光的量子场相互作用？ 一个相互作用的原子系综会达到平衡吗？ 如果是，如何做到？ 当原子间的相互作用变得非常强时，会出现什么奇异的性质？ 其中许多问题处于冷原子和量子多体系统领域的前沿。 因此，这项工作将大大推动相关领域的发展。 本项目以冷原子为平台，研究了单体物理、少体物理和多体物理之间的联系。有四个主要的主题领域：光腔内的冷原子，耦合原子的内部和外部自由度;冷原子受合成自旋轨道耦合;量子磁性与一维量子气体;和远离平衡的量子动力学。每个主题都代表了一个相对独立的研究方向，尽管不同主题之间也有很强的联系。 许多不同的理论技术将被用来解决这些问题，包括平均场方法，变分方法，微扰计算，精确对角化，时间演化块抽取（TEBD）的例子。

In the realm of physics and many other fields of natural science, reductionism --- a complicated system can be reduced to simpler constituents and the properties of the whole can be inferred from the study of each constituent parts --- has played an important role. However, there also exist many examples where a reductionistic method does not provide a complete picture. As more and more parts are added, new phenomena may emerge at different stages and these new phenomena cannot be fully understood from the properties of the simpler system that precedes it. Such emergent behavior is well known in science. The system of cold atoms represents an ideal platform to investigate the emergent phenomena. Experimentally, several labs have developed techniques to accurately control the number of atoms in their atom traps, from one, to a few, to many. This is made possible by the exquisite controllability of cold atoms. The proposed research aims to provide a theoretical understanding of various cold atomic systems. The central theme is to study how the properties of single atoms affect the physics of a few-atom or a many-atom system. This research is of fundamental nature --- the basic science of cold atoms. Fundamental issues that will be addressed include: How does an atom or an ensemble of atoms interact with a quantum field of light? Will an ensemble of atoms that are interacting with each other and prepared out of equilibrium reach equilibrium? If so, how? When the inter-atomic interaction becomes very strong, what exotic properties will emerge? Many of these issues are at the forefront of the field of cold atoms and quantum many-body systems. This work will therefore significantly advance the relevant fields. In this project, the connection among single-body, few-body and many-body physics using the platform of cold atoms is investigated. There are four main topic areas: cold atoms inside an optical cavity, coupling both the internal and the external degrees of freedom of the atoms; cold atoms subject to synthetic spin-orbit coupling; quantum magnetism with 1D quantum gases; and far-off-equilibrium quantum dynamics. Each of these topics represents a relatively independent research direction, though there also are strong connections among different topics. A number of different theoretical techniques will be used to tackle these problems, including the mean-field method, the variational method, perturbation calculations, exact diagonalization, time-evolving block decimation (TEBD) for example.