Electric field noise above surfaces: A model for heating rate scaling law in ion traps

In this work we present a model where we take explicitly into account the spatial dependence of the electric field noise density above a surface, introducing a characteristic length not yet considered in previous models: the correlation length, zeta of the noisy potential on the surface. In that picture, the noise arise from finite size sources distributed randomly on the surface. We show that this simple model accounts for the behavior of electric field noise scaling on the whole range covered by both ion heating measurements and cantilever-based measurements. We propose that this correlation length could be related to the characteristic size of the patches, opening a way to the control of noise intensity by engineering the material properties.