  The local phonon modes in a Coulomb crystal of trapped ions can represent a
Hubbard system of coupled bosons. We selectively prepare single excitations at
each site and observe free hopping of a boson between sites, mediated by the
long-range Coulomb interaction between ions. We then implement phonon blockades
on targeted sites by driving a Jaynes-Cummings interaction on individually
addressed ions to couple their internal spin to the local phonon mode. The
resulting dressed states have energy splittings that can be tuned to suppress
phonon hopping into the site. This new experimental approach opens up the
possibility of realizing large-scale Hubbard systems from the bottom up with
tunable interactions at the single-site level.
