Doppler-free saturation of the cascade fluorescence that follows excitation of the $5s \to 6p $ transition in atomic rubidium

We present an experimental scheme that produces Doppler-free spectra of the $5s \to 6p $ second resonance transition in atomic rubidium. The experiment uses the saturation of the cascade fluorescence that occurs when thermal rubidium atoms interact with two counterpropagating $420 $ nm laser beams of comparable intensity. Part of the excited atomic population goes through the $5p_{3/2}$ level which then decays by emission of $780$ nm photons. Narrow dips appear in this otherwise broad $780$ nm fluorescence, which allows resolution of the $6p_{3/2}$ hyperfine structure. A rate equation model is used to interpret the spectra. It is also shown that these narrow peaks can be used to lock the frequency of the $420 $ nm laser. Using a second beam modulated in frequency produces three sets of spectra with known frequency spacings that can be used to perform an all-optical measurement of the hyperfine splittings of the $6p_{3/2} $ manifold in rubidium.