Tunable defect interactions and supersolidity in dipolar quantum gases on a lattice potential

Point defects in self-assembled crystals, such as vacancies and interstitials, attract each other and form stable clusters. This leads to a phase separation between perfect crystalline structures and defect conglomerates at low temperatures. We propose a method that allows one to tune the effective interactions between point defects from attractive to repulsive by means of external periodic fields. In the quantum regime, this allows one to engineer strongly correlated many-body phases. We exemplify the microscopic mechanism by considering dipolar quantum gases of ground-state polar molecules and weakly bound molecules of strongly magnetic atoms trapped in a weak optical lattice in a two-dimensional configuration. By tuning the lattice depth, defect interactions turn repulsive, which allows us to deterministically design a novel supersolid phase in the continuum limit.