The effects of intrinsic heating on the many-body phases that form in a red detuned optical lattice. (Left) The superfluid state. The upper plot shows the initial superfluid state where atoms are delocalized over the entire system. After absorption of a photon and the subsequent spontaneous emission, the atom can fall back into the lowest band. During this process, the wave function of this atom localizes (blue sphere), leading to a reduction of the coherence in the superfluid (blue transparent). (Right) The Mott insulator state. In the initial state (upper plot), the atoms are already localized on lattice sites. Hence the ground band scattering event of an atom with a lattice photon does not considerably affect the Mott state.