Microscopic Description of Strongly Correlated Bose and Fermi Gases

在过去的几年中，冷原子物理领域进入了一个新的领域。在不同的部分波通道中原子-原子相互作用的强度和限制几何现在基本上可以随意控制。这些发展为回答紧迫的原子物理问题和利用冷原子系统研究凝聚态物质和核物理类似物提供了可能性。此外，这些最近的突破对于在量子计算应用和量子模拟器中利用冷原子系统至关重要。虽然在实现这些目标方面取得了很大进展，但仍存在许多悬而未决的问题。从理论的角度来看，一个关键的挑战在于开发强相关系统的准确描述。将使用多方面的微观方法，旨在以高精度处理强相关的少粒子和多粒子系统。在过去的一到两年里，我们将研究三种实验上可行的系统：i)三组分费米气体，ii) p波相互作用费米气体，以及ii)偶极玻色和费米气体。理论结果将直接关系到在低隧穿状态下操作的光学晶格实验。此外，将考虑由多个点阵点组成的系统。两点系统的预期结果将为均匀和非均匀系统的多体研究提供指导。多体研究有望提供一系列理论学家和实验学家都感兴趣的基准结果。这项工作将在许多重要方面有益于科学教育基础设施，而不仅仅是直接提高对冷原子气体的理解。

Over the past few years the field of cold atom physics has entered a new regime. The strength of the atom-atom interactions in different partial wave channels and the confining geometry can now be controlled essentially at will. These developments open the possibility to answer pressing atomic physics questions and to exploit cold atom systems for the study of condensed matter and nuclear physics analogs. Furthermore, these recent break-throughs are crucial for utilizing cold atom systems in quantum computation applications and as quantum simulators. While much progress has been made towards these goals, many open questions remain. From the theoretical point of view, a key challenge consists in developing accurate descriptions of strongly-correlated systems. A multi-faceted microscopic approach will be used that aims at treating strongly-correlated few- and many-particle systems with high accuracy. Three systems that have become experimentally accessible during the past one or two years will be investigated: i) three-component Fermi gases,ii) p-wave interacting Fermi gases, andiii) dipolar Bose and Fermi gases.The theoretical results will be directly relevant to optical lattice experiments that operate in the low-tunneling regime. Additionally, systems consisting of multiple lattice sites will be considered. The anticipated results for two-site systems will provide guidance for many-body studies of homogeneous and inhomogeneous systems. The many-body studies are expected to provide a host of benchmark results that will be of interest to theorists and experimentalists alike. The work will benefit science education infrastructure in a number of important ways beyond the direct improvements to the understanding of cold atom gases.