  We theoretically investigate trapped ions interacting with atoms that are
coupled to Rydberg states. The strong polarizabilities of the Rydberg levels
increases the interaction strength between atoms and ions by many orders of
magnitude, as compared to the case of ground state atoms, and may be mediated
over micrometers. We calculate that such interactions can be used to generate
entanglement between an atom and the motion or internal state of an ion.
Furthermore, the ion could be used as a bus for mediating spin-spin
interactions between atomic spins in analogy to much employed techniques in ion
trap quantum simulation. The proposed scheme comes with attractive features as
it maps the benefits of the trapped ion quantum system onto the atomic one
without obviously impeding its intrinsic scalability. No ground state cooling
of the ion or atom is required and the setup allows for full dynamical control.
Moreover, the scheme is to a large extent immune to the micromotion of the ion.
Our findings are of interest for developing hybrid quantum information
platforms and for implementing quantum simulations of solid state physics.
