Numerical studies of exotic paired states in optical lattices

Ultracold atoms are a unique tool that allows the exploration of phases of matter not easily accessible in condensed matter systems. Two interesting possibilities are spin-imbalanced systems and spin dependent optical lattices with Fermi surfaces that differ for the two hyperfine species. We use mean-field theory and quantum Monte Carlo simulations of Hubbard-like models with an attractive contact interaction to study the FFLO state and, by rotating the two Fermi surfaces by 90 degrees with respect to each other, a recently proposed exotic paired state [Feiguin and Fisher, 2009].