  By means of analytical and numerical methods we analyze the phase diagram of
polaritons in one-dimensional coupled cavities. We locate the phase boundary,
discuss the behavior of the polariton compressibility and visibility fringes
across the critical point, and find a non-trivial scaling of the phase boundary
as a function of the number of atoms inside each cavity. We also predict the
emergence of a polaritonic glassy phase when the number of atoms fluctuates
from cavity to cavity.
