Microscopic Description of Strongly Correlated Bose and Fermi Gases

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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.