Spectroscopy of electric dipole and quadrupole transitions in $^{224}$Ra$^+$

We report on spectroscopy of the low-lying electronic transitions in $^{224}$Ra$^+$. The ion's low charge to mass ratio and convenient wavelengths make $^{224}$Ra$^+$ a promising optical clock candidate. We measured the frequencies of the the $^2{S}_{1/2} \ $$\leftrightarrow$$\ ^2{P}_{1/2}$ cooling transition, the $^2{S}_{1/2}\ $$\leftrightarrow$$\ ^2{D}_{5/2}$ clock transition, the $^2{D}_{3/2} \ $$\leftrightarrow$$\ ^2{P}_{3/2}$ electric dipole transition, and the $^2{D}_{5/2} \ $$\leftrightarrow$$\ ^2{P}_{3/2}$ cleanout transition. From these measurements we calculate the frequencies of the $^2{D}_{3/2}\ $$\leftrightarrow$$\ ^2{P}_{1/2}$ repump transition, the $^2{S}_{1/2} \ $$\leftrightarrow$$\ ^2{D}_{3/2}$ electric quadrupole transition, and the $^2{S}_{1/2} \ $$\leftrightarrow$$\ ^2{P}_{3/2}$ electric dipole transition.