Attractive Bosons in Optical Lattices

We study the theory of attractive bosons in an optical lattice with a hard-core constraint, limiting on-site occupations to 0, 1, or 2 particles per site. Our goal is to investigate the Boson pairing phase transition. We describe how an off-resonant Raman photoassociation transition [C. Ryu, et. al. Cond-mat/0508201] may be used to generate this model. We explore the properties of this system through a mean-field theory that allows short-range correlations. We write a wavefunction that describes both atomic and molecular superfluid phases, and study properties of the system near the phase transition, including the structure of vortices.