  State-of-the-art experiments using Rydberg atoms can now operate with large
numbers of trapped particles with tunable geometry and long coherence time. We
propose a way to utilize this in a hybrid setup involving neutral ground state
atoms to efficiently simulate condensed matter models featuring electron-phonon
coupling. Such implementation should allow for controlling the coupling
strength and range as well as the band structure of both the phonons and atoms,
paving the way towards studying both static and dynamic properties of extended
Hubbard-Holstein models.
