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We study the reflection of two counter-propagating modes of the light fieldin a ring resonator by ultracold atoms either in the Mott insulator state or inthe superfluid state of an optical lattice. We obtain exact numerical resultsfor a simple two-well model and carry out statistical calculations appropriatefor the full lattice case. We find that the dynamics of the reflected lightstrongly depends on both the lattice spacing and the state of the matter-wavefield. Depending on the lattice spacing, the light field is sensitive tovarious density-density correlation functions of the atoms. The light field andthe atoms become strongly entangled if the latter are in a superfluid state, inwhich case the photon statistics typically exhibit complicated multimodalstructures.Comment: 10 pages revtex, 13 figure

Cavity QED determination of atomic number statistics in optical lattices