  We propose to sympathetically slow and cool polar molecules in a cold,
low-density beam using laser-cooled Rydberg atoms. The elastic collision cross
sections between molecules and Rydberg atoms are large enough to efficiently
thermalize the molecules even in a low density environment. Molecules traveling
at 100 m/s can be stopped in under 30 collisions with little inelastic loss.
Our method does not require photon scattering from the molecules and can be
generically applied to complex species for applications in precision
measurement, quantum information science, and controlled chemistry.
