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We study the coupling of internal electronic excitations to vibrational modesof the external motion of ultracold atoms in an optical lattice. For differentground and excited state potentials the on-site coupling of excitations andvibrations term renormalizes the effective electronic transition energy, whichappears e.g. in clock transitions. In addition in the Mott state with fillingfactor one, the dipole-dipole coupling between neighbouring sites includesemission and absorption of vibrational quanta. Such processes create asignificant mechanism for excitation of vibrations leading to motional heatingof the lattice atoms by resonant light interaction. We calculate estimates ofthe corresponding parameters from a perturbation expansion in small atomicdisplacements.

Coupling of Electronic and Motional Dynamics in a Cold Atom Optical Lattice