Determination of transition frequencies in a single ¹³⁸Ba⁺ ion

Transition frequencies between low-lying energy levels in a single trapped $^{138}$Ba$^{+}$ ion have been measured with laser spectroscopy referenced to an optical frequency comb. By extracting the frequencies of one-photon and two-photon components of the line shape using an eight-level optical Bloch model, we achieved 0.1 MHz accuracy for the 5d $^{2}$D$_{3/2}$ - 6p $^{2}$P$_{1/2}$ and 6s $^{2}$S$_{1/2}$ - 5d $^{2}$D$_{3/2}$ transition frequencies, and 0.2 MHz for the 6s $^{2}$S$_{1/2}$ - 6p $^{2}$P$_{1/2}$ transition frequency.