# Doppler cooling thermometry of a multi-level ion in the presence of micromotion

## TL;DR

This paper presents an analytical model for Doppler cooling thermometry of multi-level ions in RF traps, accounting for micromotion effects, and validates it with experiments on different energy distributions.

## Contribution

The novel model extends Doppler thermometry to multi-level ions and includes micromotion effects, improving initial energy estimation accuracy.

## Key findings

- Model accurately describes fluorescence during Doppler cooling.
- Experimental validation with various energy distributions.
- Effective initial energy extraction from fluorescence data.

## Abstract

We study the time-dependent fluorescence of an initially hot, multi-level, single atomic ion trapped in a radio-frequency Paul trap during Doppler cooling. We have developed an analytical model that describes the fluorescence dynamics during Doppler cooling which is used to extract the initial energy of the ion. While previous models of Doppler cooling thermometry were limited to atoms with a two-level energy structure and neglected the effect of the trap oscillating electric fields, our model applies to atoms with multi-level energy structure and takes into account the influence of micromotion on the cooling dynamics. This thermometry applies to any initial energy distribution. We experimentally test our model with an ion prepared in a coherent, thermal and Tsallis energy distributions.