Sympathetic cooling of O₂⁺ with co-trapped Ca^+ for a two-photon optical clock

We explore the use of ⁴⁰Ca⁺ ions to sympathetically cool ¹⁶O₂⁺ ions in a linear radiofrequency trap for a two-photon optical clock based on a vibrational transition. In previous work, ⁹Be⁺ ions were used for sympathetic cooling and fluorescence-based detection. ^[1]  The lighter ⁹Be⁺ ions formed the core of a Coulomb crystal with the heavier ¹⁶O₂⁺ displaced towards the periphery. For heavier coolant ions such as ⁴⁰Ca⁺, the mass-dependent radial confinement inverts this order, placing the ¹⁶O₂⁺ ions near the trap center. This reordering offers several improvements for clock operation. The number of trapped ¹⁶O₂⁺ ions can be inferred from fluorescence images with bright ⁴⁰Ca⁺ ions surrounding the non-fluorescing ¹⁶O₂⁺ core. Placing the ¹⁶O₂⁺ ions near the trap axis provides a more uniform laser intensity for vibrational spectroscopy, reducing inhomogeneous transition rates and AC Stark shifts compared to the ⁹Be⁺ case. This positioning also reduces micromotion and hence smaller systematic shifts from the second-order Doppler effect. This work will be useful for high-precision molecular spectroscopy, optical frequency metrology and fundamental physics tests such as searches for time variations in the proton-to-electron mass ratio.