Laser Cooling of Trapped Ions in Strongly Inhomogeneous Magnetic Fields

TL;DR

This study theoretically investigates how a strongly inhomogeneous magnetic field affects laser cooling of a trapped calcium ion, revealing that efficient cooling is still possible despite the complex magnetic environment, which is crucial for hybrid trap experiments.

Contribution

It provides a detailed theoretical analysis of ion laser cooling dynamics in inhomogeneous magnetic fields within hybrid traps, informing experimental optimization.

Findings

Laser cooling remains effective despite magnetic inhomogeneity.

Multiple lasers are needed to address varying Zeeman splittings.

Magnetic field gradients influence ion motion and cooling efficiency.

Abstract

Hybrid traps for the simultaneous confinement of neutrals and ions have recently emerged as versatile tools for studying interactions between these species at very low temperatures. Such traps rely on the combination of different types of external fields for the confinement of either species raising the question of interactions between the individual traps. Here, the influence of a strongly inhomogeneous magnetic field used for trapping neutrals on the trapping and laser cooling of a single Ca$^+$ ion in a radiofrequency ion trap is studied theoretically using molecular-dynamics simulations based on multilevel rate equations. The inhomogeneous magnetic field couples the different components of the ion motion and introduces position-dependent Zeeman splittings. Nonetheless, laser cooling is still found to work efficiently as the ion samples different magnetic field strengths and directions along its trajectory. Offsetting the centres of the two traps generates a linear magnetic-field gradient so that multiple lasers are required to address the resulting range of Zeeman splittings in order to ensure efficient cooling. The present study yields detailed insights into the ion cooling dynamics in combined magnetic and radiofrequency electric fields relevant for the characterisation and optimisation of hybrid trapping experiments.