Superfluid and Supersolid Phases in Optical Lattices in Two Dimensions

This work addresses the study of superfluid and supersolid phases of dipolar Fermi molecules lying in a two dimensional space. The prediction of these phases, performed within a mean field analysis, results from proposing a model in which interacting Fermi molecules are confined in a bilayer array of parallel lattices with square symmetry. As a result of the repulsive intralayer and attractive interlayer interactions between dipolar molecules, a checkerboard pattern and a paired superfluid regimes can emerge. The supersolid phase is identified as the spatial coexistence of density ordered and superfluid phases. The model here proposed can be implemented within the current experimental capabilities as a function of the interlayer separation and the application of an external electric field varying the dipolar interaction between molecules.