Controlling the scattering length of ultracold dipolar molecules

By applying a circularly polarized and slightly blue-detuned microwave field with respect to the first excited rotational state of a dipolar molecule, one can engineer a long-range, shallow potential well in the entrance channel of the two colliding partners. As the applied microwave ac-field is increased, the long-range well becomes deeper and can support a certain numbers of bound states, which in turn bring the value of the molecule-molecule scattering length from a large negative value to a large positive one. We adopt an adimensional approach where the molecules are described by a rescaled rotational constant $\tilde{B} = B/s_{E_3} $ where $s_{E_3}$ is a characteristic dipolar energy. We found that molecules with $\tilde{B} > 10^8$ are immune to any quenching losses when a sufficient ac-field is applied, the ratio elastic to quenching processes can reach values above $10^3$, and that the value and sign of the scattering length can be tuned. The ability to control the molecular scattering length opens the door for a rich, strongly correlated, many-body physics for ultracold molecules, similar than that for ultracold atoms.