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.
