  We propose and demonstrate a scalable scheme for the simultaneous
determination of internal and motional states in trapped ions with single-site
resolution. The scheme is applied to the study of polaritonic excitations in
the Jaynes- Cummings Hubbard model with trapped ions, in which the internal and
motional states of the ions are strongly correlated. We observe quantum phase
transitions of polaritonic excitations in two ions by directly evaluating their
variances per ion site. Our work establishes an essential technological method
for large-scale quantum simulations of polaritonic systems.
