We discuss an AMO toolbox for designing Hubbard and spin Hamiltonians with cold atoms and molecules, which realize strongly correlated condensed matter models with controllable parameters. We will focus in particular on polar molecules in optical lattices, and selfassembled lattices. Examples to be discussed range from the realization of the Kitaev model to Hubbard models with (only) three-body interactions.
In addition, we present a few new atomic and molecular physics ideas, from novel cooling methods to obtain the required ultralow temperatures to _sub_-wavelength optical lattices which maybe essential prerequisites for an experimental realization.
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