Interaction Effects on Wannier Functions for Bosons in Optical Lattice

We have numerically calculated the single band Wannier functions for interacting Bose gases in optical lattices with a self-consistent approach. We find that the Wannier function is broadened by repulsive atom interaction. The tunneling parameter J and on-site interaction U computed with the broadened Wannier functions are found to change significantly for different atomic number per site. Our theory can explain the nonuniform atomic clock shift observed in [Campbell et al., Science 313, 649 (2006)].