Testing fundamental constants with trapped indium ions

The $^1$S$_0 \leftrightarrow ^3$P$_0$ transition in the In$^+$ ion at 237 nm has a natural linewidth of .8 Hz and is a promising candidate for the development of an optical clock. Since this transition is J=0 $\rightarrow$ J=0, the states are not perturbed by the quadrupole trapping potential. We report trapping and spectroscopy of single indium ions using a Paul-Straubel trap and a laser system on the $^1$S$_0 \leftrightarrow ^3$P$_1$ transition at 230 nm and the development of a frequency quadrupled stabilized Nd:YAG laser to excite the narrow $^1$S$_0 \leftrightarrow ^3$P$_0$ transition. We describe prospects for measuring the time-variation of the electromagnetic coupling constant by comparing the frequency of an oscillator locked to the In$^+$ transition to those of other optical clocks.