Determination of transition frequencies in a single \(^{138}\)Ba\(^{+}\) 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.