Measurement of the Land\'{e} g factor of the 5D$_{5/2}$ state of Ba II with a single trapped ion

We present a terrestrial measurement of the Land\'{e} g factor of the 5D$_5/2$ state of singly ionized barium. Measurements were performed on single Doppler-cooled $^{138}$Ba$^+$ ions in a linear Paul trap. A frequency-stabilized fiber laser with a nominal wavelength of 1.762 $\mu$m was scanned across the 6S$_{1/2}\leftrightarrow$5D$_{5/2}$ transition to spectroscopically resolve transitions between Zeeman sublevels of the ground and excited states. From the relative positions of the four narrow transitions observed at several different values for the applied magnetic field, we find a value of 1.2020$\pm$0.0005 for g(5D$_{5/2}$), a considerable improvement over the previously quoted value.