Precision Measurement of the Saturation Intensity in Rubidium at 420 nm
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.