Microscopic Description of Strongly Correlated Bose and Fermi Gases

在过去的几年里，冷原子物理领域进入了一个新的领域。不同分波通道中原子-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比提供了可能性。此外，这些最新的突破对于将冷原子系统用于量子计算应用和作为量子模拟器至关重要。虽然在实现这些目标方面取得了很大进展，但仍有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关联系统的准确描述。将使用一种多方面的微观方法，旨在高精度地处理强关联的少数粒子和多粒子系统。在过去的一到两年中，我们将研究三个系统：i)三组分费米气体，ii)p波相互作用的费米气体，以及ii)偶极玻色和费米气体。理论结果将直接与工作在低隧道区域的光学晶格实验相关。此外，还将考虑由多个晶格点组成的系统。两点体系的预期结果将为均匀和非均匀体系的多体研究提供指导。这项多主体研究预计将提供一系列基准结果，理论家和实验者都会对此感兴趣。这项工作将在许多重要方面惠及科学教育基础设施，而不仅仅是直接改善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.