Precision Measurement of the Saturation Intensity in Rubidium at 420 nm

arXiv:2606.30871v2 Announce Type: new Abstract: The $5S_{1/2} \rightarrow 6P_{3/2}$ transition of rubidium at 420 nm is a promising candidate for a portable warm-vapor all-optical atomic clock. Despite recent precision spectroscopy studies at 420 nm in Rb, an experimental determination of the saturation intensity of this transition has not yet been reported. The saturation intensity is a fundamental parameter that influences the identification of a potential clock transition frequency in terms of optimizing various intensity-dependent parameters and connected systematics. In this work, we report the first experimental measurement of the saturation intensity of the 420 nm transition in Rb, obtaining $(23.18 \pm 0.28)$ mW/cm$^2$ for the $^{87}$Rb $F=2\rightarrow F'=3$ transition and $(25.56 \pm 0.37)$ mW/cm$^2$ for the $^{85}$Rb $F=3\rightarrow F'=4$ transition, in excellent agreement with theoretical predictions. We further investigate the temperature dependence of the Doppler-free Lamb-dip amplitude and linewidth over 59.03$~\pm~0.37$ - 91.20$~\pm~0.90^\circ$C in a 100 mm commercial vapor cell, identifying around 82.02$~\pm~ 0.73^\circ$C as the optimal operating temperature, where the signal-to-noise ratio of the Lamb-dip amplitude with temperature reaches a maximum and the observed Lamb-dip linewidth exhibits a minimum. We also present precise measurements of the magnetic-dipole ($A$) and electric-quadrupole ($B$) hyperfine constants of the $6P_{3/2}$ state for both isotopes, with the measured values being consistent with previously reported values for the hyperfine constants.