Sub-Kilohertz Optical Spectroscopy with a Time Domain Atom Interferometer

We report on the sub-kilohertz optical spectroscopy on the ${}_{}{}^1{}_{}{}^{}S_0^{}{}_{}{}^{}$- ${}_{}{}^3{}_{}{}^{}P_1^{}{}_{}{}^{}$ intercombination transition in magnesium at 457 nm. The spectroscopic signal is probed by a time domain atom interferometer. The realization of this time domain atom interferometer with laser cooled and trapped atoms allows extremely long interaction times and leads to resolutions down to 491 Hz (FWHM). This corresponds to a high line $Q$ factor of $1.3\times {10}^{12}$. Because of the high accuracy in the determination of the line center, applications with respect to an optical frequency standard are possible.