Dispersive interactions between atoms and non planar surfaces

We calculate the dispersive force between a ground state atom and a non planar surface. We present explicit results for a corrugated surface, derived from the scattering approach at rst order in the corrugation amplitude. A variety of analytical results are derived in di erent limiting cases, including the van der Waals and Casimir-Polder regimes. We compute numerically the exact rstorder dispersive potential for arbitrary separation distances and corrugation wavelengths, for a Rubidium atom on top of a silicon or gold corrugated surface. We discuss in detail the inadequacy of the proximity force approximation, and present a simple but adequate approximation for computing the potential.