Second-order Doppler frequency shifts of trapped ions in a linear Paul trap

TL;DR

This paper presents a new model to accurately evaluate the second-order Doppler frequency shift in trapped ions within a linear Paul trap, validated through experiments and simulations, particularly for cold ion ensembles.

Contribution

A novel model for calculating SODFS in ion traps that accounts for ion excess micromotion and assumes uniform radial ion density, validated by experiments and simulations.

Findings

Model accurately predicts SODFS for ions below 100 mK.

Experimental and simulation results confirm the model's effectiveness.

Improves evaluation of SODFS in large ion cloud microwave clocks.

Abstract

The accurate evaluation of the second-order Doppler frequency shift (SODFS) of trapped ions in a linear Paul trap has been studied with experiments and molecular dynamics (MD) simulations. The motion of trapped ions in the trap has three contributions, and we focus on the ion excess micromotion, which is rarely discussed when evaluating the SODFS. Based on the hypothesis that the ion density is uniformly distributed in the radial direction, we propose a new model to accurately evaluate the total SODFS for ion microwave clocks. The effectiveness of the model has been verified both in simulation and experiment, especially for ion ensemble with temperature less than 100 mK. We believe that our new model offers advantages in accurately evaluating the SODFS for the ion trap, especially those of laser-cooled ion microwave clocks based on large ion clouds.