Universal Scattering with Ultracold Polar Molecules in Optical Potentials

Interactions between atoms and molecules are controlled by their attractive long-range van-der-Waals potentials as well as their short-range exchange and repulsive potentials. Here, we determine the ultracold inelastic and elastic scattering rate coefficients for a large class of polar molecules in their lowest vibrational state with their constituent atoms using universal scattering theory. Universal scattering is solely determined by the van-der-Waals, dispersion interaction, which in turn is defined by the dynamic polarizability of the atom and molecule as a function of imaginary frequency. We examine two different approaches to calculate the dynamic polarizability: 1) a {\it perturbation-theory-based} method that uses relativistic potentials and transition dipole moments, and 2) a non-relativistic {\it coupled cluster polarization propagator} method. We evaluate the strengths and weaknesses of these methods. Finally, we compare our inelastic rates coefficients with experimental measurements and exact quantum-mechanical calculations, where available. Our goal is to provide a better understanding of the limits of the universal scattering model at ultra-low temperatures and, in particular, the degree to which short-range potentials are important.