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We study electronic excitations of a degenerate gas of atoms trapped in pairsin an optical lattice. Local dipole-dipole interactions produce a long livedantisymmetric and a short lived symmetric superposition of individual atomicexcitations as the lowest internal on-site excitations. Due to the much largerdipole moment the symmetric states couple efficiently to neighbouring latticesites and can be well represented by Frenkel excitons, while the antisymmetricdark states stay localized. Within a cavity only symmetric states couple tocavity photons inducing long range interactions to form polaritons. Wecalculate their dispersion curves as well as cavity transmission and reflectionspectra to observe them. For a lattice with aspherical sites bright and darkstates get mixed and their relative excitation energies depend on photonpolarizations. The system should allow to study new types of solid statephenomena in atom filled optical lattices.

Bright and dark excitons in an atom--pair filled optical lattice within a cavity