Spectroscopy of $^1$S$_0 \leftrightarrow ^3$P$_0$ transition in In$^+$

We report spectroscopy of the $^1$S$_0 \leftrightarrow ^3$P$_0$ transition at 237~nm in single indium ions confined in a Paul- Straubel trap. The indium ion is among candidates for optical frequency references because of the high quality factor (Q $\sim 1.5 \cdot 10^{15}$) and the small quadrupole and blackbody shifts of its ground-state to $^3$P$_0$ transition. Using a frequency- quadrupled diode laser to cool the ion on the stronger $^1$S$_0 \leftrightarrow ^3$P$_1$ transition, we report sub-kHz linewidths in exciting the narrow $^3$P$_0$ transition using a frequency-quadrupled Nd:YAG nonplanar ring oscillator (NPRO) at 946~nm stabilized to a vertically-mounted high-finesse ULE cavity.