Spontaneous-emission-induced transition rates between atomic states in optical lattices

We derive a general expression for the spontaneous-emission-induced transition rates between the atomic states of atoms trapped in far-detuned optical potentials, taking into account both their internal and external degrees of freedom. We apply this result to atoms trapped in deep optical lattices. For one- and two-dimensional lattices, we quantify the correlations among excitations in the tightly confined directions, the loosely trapped directions, and the internal state of the atom. We emphasize the differences in excitations between red- and blue-detuned lattices.