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

TL;DR

This paper introduces an analytical model for electric field noise scaling laws near conducting surfaces, explaining experimental data and suggesting material engineering to reduce heating in ion traps.

Contribution

The model incorporates surface patch potential correlations to accurately predict electric field noise scaling, aligning with diverse experimental results.

Findings

Excellent agreement with experiments over four orders of magnitude

Scaling laws depend on correlation length of surface potentials

Material engineering can significantly reduce heating rates

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, $\zeta$, 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), that span at least four orders of magnitude of $d$. According to this model, heating rate in miniature ion traps could be greatly reduced by proper material engineering.