  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.
