  We describe a new type of spatially periodic structure (lattice models): a
polaritonic crystal (PolC) formed by a two-dimensional lattice of trapped
two-level atoms interacting with quantised electromagnetic field in a cavity
(or in a one-dimensional array of tunnelling-coupled microcavities), which
allows polaritons to be fully localised. Using a one-dimensional polaritonic
crystal as an example, we analyse conditions for quantum degeneracy of a
low-branch polariton gas and those for quantum optical information recording
and storage.
