Abstract
Abstract : Optical lattices are employed to simulate important condensed matter materials, with ultracold atoms playing the role of the electrons in a real material. We have obtained the phase diagram of a one-dimensional (1D) Fermi gas with spin-imbalance in this way. This system features a partially polarized phase which is the 1D analog of the long-sought FFLO state. Current research is focused on direct detection of the FFLO state and explore the 1D-3D dimensional crossover. We have recently detected antiferromagnetic order in the 3D Fermi-Hubbard model using spin-dependent Bragg scattering of light. This was a major goal of our project, enabled by the development of a novel scheme to evaporatively cool atoms in an optical lattice. We have also focused on developing alternative cooling schemes, We have also investigated the connection between quantum integrability and thermalization in a 1D Bose gas, and considered equilibration and thermalization phenomena in optical lattices. Other theoretical issues, such as the effects of spin-orbit coupling, the disordered Bose-Hubbard model, and many-body localization, have also been explored.
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