Title: In-situ Doppler-free spectroscopy and laser frequency stabilization based on time-division multiplexing differential saturated absorption

Abstract: We introduce a novel time-division multiplexing differential saturated absorption spectroscopy (TDMDSAS) approach, providing superior accuracy and stability in Doppler-free spectroscopy. By distinguishing probe and reference fields in the temporal domain, TDMDSAS efficiently suppresses Doppler broadening and common-mode optical noise. We utilized this technology to determine the absolute frequency of diverse neutral Yb isotopes across its $6s^2\ ^{1}S_0\to 6s6p ^{1}P_1$ transitions. Furthermore, the first-ever observation of in-situ Doppler-free Zeeman sub-level spectra was accomplished, enabling the determination of magnetic field gradients. We stabilized a UV diode laser at 399 nm using an error signal derived from the spectral first-derivative demodulated signal of $^{174}\mathrm{Yb}$. This technique yielded a frequency stability of up to 15 kHz with a 40 s averaging time and a standard deviation of around 180 kHz over a half-hour period. Given its low cost, straightforward, and scalable nature, TDMDSAS holds excellent potential in metrology and quantum applications.