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

Abstract

We present a model for the scaling laws of the electric field noise spectral density as a function of the distance $d$ above a conducting surface. Our analytical approach models the patch potentials by introducing a correlation length $\ensuremath{\zeta}$ of the electric potential on the surface. The predicted scaling laws are in excellent agreement with two different classes of experiments (cold trapped ions and cantilevers), for which the $d$ parameter differs by four orders of magnitude. According to this model, heating rate in miniature ion traps could be greatly reduced by proper material engineering.