Experimental Methods for Trapping Ions Using Microfabricated Surface Ion Traps

Monte Carlo simulations of two-component Coulomb gases applied in surface electrodes

In this work, we study the gapped surface electrode (SE), a planar system composed of two-conductor flat regions at different potentials with a gapGbetween both sheets. The computation of the electric field and the surface charge density requires solving Laplace's equation subjected to Dirichlet conditions (on the electrodes) and Neumann boundary conditions over the gap. In this document, the gapless surface electrode is modeled as a two-dimensional classical Coulomb gas having punctual charges +qand -qon the inner and outer electrodes, respectively, interacting with an inverse power law 1/r-potential. The coupling parameter Γ between particles inversely depends on temperature and is proportional toq². Precisely, the density charge arises from the equilibrium states via Monte Carlo (MC) simulations. We focus on the coupling and the gap geometry effect. Mainly on the distribution of particles in the circular and the harmonically-deformed gapped SE. MC simulations differ from electrostatics in the strong coupling regime. The electrostatic approximation and the MC simulations agree in the weak coupling regime where the system behaves as two interacting ionic fluids. That means that temperature is crucial in finite-size versions of the gapped SE where the density charge cannot be assumed fully continuous as the coupling among particles increases. Numerical comparisons are addressed against analytical descriptions based on an electric vector potential approach, finding good agreement.

A New Measurement Method for High Voltages Applied to an Ion Trap Generated by an RF Resonator

A new method is proposed to measure unknown amplitudes of radio frequency (RF) voltages applied to ion traps, using a pre-calibrated voltage divider with RF shielding. In contrast to previous approaches that estimate the applied voltage by comparing the measured secular frequencies with a numerical simulation, we propose using a pre-calibrated voltage divider to determine the absolute amplitude of large RF voltages amplified by a helical resonator. The proposed method does not require measurement of secular frequencies and completely removes uncertainty caused by limitations of numerical simulations. To experimentally demonstrate our method, we first obtained a functional relation between measured secular frequencies and large amplitudes of RF voltages using the calibrated voltage divider. A comparison of measured relations and simulation results without any fitting parameters confirmed the validity of the proposed method. Our method can be applied to most ion trap experiments. In particular, it will be an essential tool for surface ion traps which are extremely vulnerable to unknown large RF voltages and for improving the accuracy of numerical simulations for ion trap experiments.