Excitons and cavity polaritons for cold-atoms in an optical lattice

We investigate collective electronic excitations for ultracold atoms in an optical lattice prepared in the Mott insulator phase. Frenkel like-excitons in these artificial crystals can appear when the atomic excited state line width is smaller than the exciton band width. When the optical lattice atoms are placed within a cavity the excitons and the cavity photons get coupled, and in the strong coupling regime they form two branches of cavity polaritons.