  We have experimentally observed the dynamics of a single polariton and two
polaritons in a two-ion chain. By driving two trapped ions at a motional
blue-sideband transition, we realize the anti-Jaynes-Cummings-Hubbard model.
When a single polariton exists in a trapped-ion chain, the polariton hops
between the ion sites. On the other hand, when there are single polaritons at
each ion site, the hopping of the polaritons is suppressed because of the
polariton-polariton interaction induced by the nonlinearity of the
anti-Jaynes-Cummings interaction, thereby realizing the blockade of polariton
hopping in the anti-Jaynes-Cummings-Hubbard model with trapped ions. Our work
is a step towards the development of a trapped-ion based quantum simulator for
strongly interacting polaritonic systems.
