<i>In situ</i> Doppler-free spectroscopy with pulsed optical fields

We propose a novel pulsed optical method based on saturated absorption spectroscopy, where the pump beam is periodically switched on and off using pulse amplitude modulation. This periodic alternation enables time-division multiplexing of the same probe beam into both probe and reference signals, achieving differential Doppler-free spectroscopy with a deterministic zero background. This method effectively mitigates Doppler broadening and common-mode optical noise by addressing disturbances such as nonuniform background absorption and environmental noise, thereby offering enhanced accuracy and robustness. Using this technique, we measured the transition frequency of ${\mathrm{Yb}}^{+}$ isotopes in the $^{2}S_{1/2}\ensuremath{\rightarrow}^{2}P_{1/2}$ transition. By employing an error signal derived from the dispersive signal of $^{174}\mathrm{Yb}^{+}$, we achieved efficient stabilization of a 369.5-nm ultraviolet diode laser, demonstrating a frequency stability of $3\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}11}$ (26 kHz) over a 1500-s averaging period and a locking point standard deviation of 850 kHz sustained over 10 days. Furthermore, we report the first in situ observation of Doppler-free Zeeman sublevel spectra in a hot ion system, highlighting the precision of this method and its potential application in measuring magnetic field gradients.