Toward All-Optical Loading of Co-Trapped Be$^+$ and O$_2^+$

Trapped and sympathetically cooled O$_2^+$ ions are a promising system for precision measurements, optical frequency metrology, and searches for new physics. We describe our techniques to load O$_2^+$ along with Be$^+$ coolant ions through resonance-enhanced photoionization. For beryllium, a custom-designed monolithic doubling cavity generates 235 nm light for single-color $1+1$ ionization on the $^1S_0 \rightarrow \, ^1P_1$ transition. In O$_2$, a cold molecular beam is photoionized via single-color $2+1$ REMPI on the $X \, ^3\Sigma_g^- \rightarrow\rightarrow d \, ^1\Pi_g \rightarrow X \, ^2\Pi_g(\mathrm{O}_2^+)$ transition. This transition is vibrationally selective and loads ions in a small number of rotational states. We describe initial work conducting spectroscopy of the molecular transition and plans for integrating the cold beam into our trap.