Cold polar molecules in two-dimensional traps: Tailoring interactions with external fields for novel quantum phases

We discuss techniques to engineer effective long-range interactions between polar molecules using external static electric and microwave fields. We consider a setup where molecules are trapped in a two-dimensional pancake geometry by a far-off-resonance optical trap, which ensures the stability of the dipolar collisions. We detail how to modify the shape and the strength of the long-range part of interaction potentials, which can be utilized to realize interesting quantum phases in the context of cold molecular gases.