Direct spectroscopy of Rubidium using a narrow-line transition at 420 nm

The 5S$\to$6P transition in Rubidium (Rb) at 420 nm offers the advantage of a narrower linewidth and diverse applications in quantum technologies. However, the direct spectroscopy at this transition is challenging due to its weak transition strength. In this paper, we have discussed the saturated absorption spectroscopy (SAS) of Rb using the narrow-line transition at 420 nm. We have studied the effect of the temperature of the Rb cell, pump power and the beam size on the SAS dip heights and their linewidths. Additionally, our study offers a comprehensive examination, encompassing all eight error signals of Rb for the 5S$\to$6P transition at 420 nm and 421 nm. These findings contribute valuable insights to the field of laser frequency stabilization of Rb at blue transition and can be useful in quantum technologies based on this transition.