  We demonstrate the site-dependent control of polaritons in the Jaynes
Cummings Hubbard (JCH) model with trapped ions. In a linear ion crystal under
illumination by optical beams nearly resonant to the red-sideband (RSB)
transition for the radial vibrational direction, quasiparticles called
polaritonic excitations or polaritons, each being a superposition of one
internal excitation and one vibrational quantum (phonon), can exist as
conserved particles. Polaritons can freely hop between ion sites in a
homogeneous configuration, while their motion can be externally controlled by
modifying the parameters for the optical beams site-dependently. We demonstrate
the blockade of polariton hopping in a system of two ions by the individual
control of the frequency of the optical beams illuminating each ion. A JCH
system consisting of polaritons in a large number of ion sites can be
considered an artificial many-body system of interacting particles and the
technique introduced here can be used to exert fine local control over such a
system, enabling detailed studies of both its quasi-static and dynamic
properties.
