Title: Direct laser cooling of Rydberg atoms with an isolated-core transition

Abstract: We propose a scheme to directly laser cool Rydberg atoms by laser cooling the residual ion core within the Rydberg-electron orbit. The scheme is detailed for alkaline-earth-metal Rydberg atoms, whose ions can be easily laser cooled. We demonstrate that a closed optical cooling cycle can be found despite the perturbations caused by the Rydberg electron, and that this cycle can be driven over more than $100~\mu$s to achieve laser cooling. The cooling dynamics with and without the presence of magnetic fields are discussed in detail.