Strongly Correlated 2D Quantum Phases with Cold Polar Molecules: Controlling the Shape of the Interaction Potential

We discuss techniques to tune and shape the long-range part of the interaction potentials in quantum gases of polar molecules by dressing rotational excitations with static and microwave fields. This provides a novel tool towards engineering strongly correlated quantum phases in combination with low dimensional trapping geometries. As an illustration, we discuss a 2D crystalline phase, and a superfluid-crystal quantum phase transition.Physic