# Sideband cooling of the radial modes of motion of a single ion in a Penning trap

## TL;DR

This paper demonstrates the extension of Doppler and sideband cooling techniques to simultaneously cool both radial modes of a single ion in a Penning trap, achieving near-ground state cooling through numerical and experimental methods.

## Contribution

It introduces a method to cool both radial modes of a single ion in a Penning trap using combined Doppler and sideband cooling, supported by simulations and experimental validation.

## Key findings

- Achieved mean phonon numbers of 0.35 and 1.7 after 68 ms of sideband cooling.
- Demonstrated effective cooling of both radial modes in a Penning trap.
- Supported experimental results with numerical simulations.

## Abstract

Doppler and sideband cooling are long standing techniques that have been used together to prepare trapped atomic ions in their ground state of motion. In this paper we study how these techniques can be extended to cool both radial modes of motion of a single ion in a Penning trap. We numerically explore the prerequisite experimental parameters for efficient Doppler cooling in the presence of an additional oscillating electric field to resonantly couple the radial modes. The simulations are supported by experimental data for a single $^{40}$Ca$^+$ ion Doppler cooled to $\sim$100 phonons in both modes at a magnetron frequency of 52 kHz and a modified cyclotron frequency of 677 kHz. For these frequencies, we then show that mean phonon numbers of $0.35(5)$ for the modified cyclotron and $1.7(2)$ for the magnetron motions are achieved after 68 ms of sideband cooling.