Dynamics of a single trapped ion immersed in a buffer gas

TL;DR

This paper develops a detailed theoretical model for the behavior of a single trapped ion interacting with a buffer gas, exploring different cooling regimes and proposing a method to actively reduce ion energy.

Contribution

It extends previous models by incorporating non-homogeneous buffer gases and higher multipole traps, providing analytic and numerical insights into ion cooling dynamics.

Findings

Identifies three regimes of sympathetic cooling based on mass ratio.

Provides analytic expressions for ion energy distribution and cooling rates.

Proposes a method for actively decreasing ion energy via spatial control of buffer gas.

Abstract

We provide a comprehensive theoretical framework for describing the dynamics of a single trapped ion interacting with a neutral buffer gas, thus extending our previous studies on buffer-gas cooling of ions beyond the critical mass ratio [B. H\"oltkemeier et al., Phys. Rev. Lett. 116, 233003 (2016)]. By transforming the collisional processes into a frame, where the ion's micromotion is assigned to the buffer gas atoms, our model allows one to investigate the influence of non-homogeneous buffer gas configurations as well as higher multipole orders of the radio-frequency trap in great detail. Depending on the neutral-to-ion mass ratio, three regimes of sympathetic cooling are identified which are characterized by the form of the ion's energy distribution in equilibrium. We provide analytic expressions and numerical simulations of the ion's energy distribution, spatial profile and cooling rates for these different regimes. Based on these findings, a method for actively decreasing the ion's energy by reducing the spatial expansion of the buffer gas arises (Forced Sympathetic Cooling).