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Hybrid traps for the simultaneous confinement of neutrals and ions haverecently emerged as versatile tools for studying interactions between thesespecies at very low temperatures. Such traps rely on the combination ofdifferent types of external fields for the confinement of either speciesraising the question of interactions between the individual traps. Here, theinfluence of a strongly inhomogeneous magnetic field used for trapping neutralson the trapping and laser cooling of a single Ca$^+$ ion in a radiofrequencyion trap is studied theoretically using molecular-dynamics simulations based onmultilevel rate equations. The inhomogeneous magnetic field couples thedifferent components of the ion motion and introduces position-dependent Zeemansplittings. Nonetheless, laser cooling is still found to work efficiently asthe ion samples different magnetic field strengths and directions along itstrajectory. Offsetting the centres of the two traps generates a linearmagnetic-field gradient so that multiple lasers are required to address theresulting range of Zeeman splittings in order to ensure efficient cooling. Thepresent study yields detailed insights into the ion cooling dynamics incombined magnetic and radiofrequency electric fields relevant for thecharacterisation and optimisation of hybrid trapping experiments.

Laser Cooling of Trapped Ions in Strongly Inhomogeneous Magnetic Fields