Absorption spectra for strong pump and probe in atomic beam of cesium atoms

We calculate the pump and probe absorption spectra for the cycling Fg =4→ Fe =5 transition D2 line of C 133 s in an atomic beam, interacting with a strong resonant σ+ -polarized pump and a probe of comparable intensity and either σ- or π polarization. The aim is to reproduce and analyze the experiments of Dahl who showed for a σ+ -polarized pump and σ- -polarized probe that the pump absorption spectrum switches from an "absorption within transparency" (AWT) structure, when the probe is weaker than the pump, to a "transparency within transparency" (TWT) structure, when the probe is stronger than the pump. For all other polarization combinations, the pump spectrum displays AWT behavior at all probe intensities. We analyze our results by considering the contributions that derive from the individual mg → me transitions. When the σ+ -polarized pump is stronger than the σ- -polarized probe, the population is swept toward the mg → me = mg +1 transitions with the highest values of mg, and the pump absorption spectrum has an AWT structure and resembles that of an N system. However, when the probe is stronger than the pump, the population is swept toward the mg =- Fg → me = mg -1 transition when the probe is near resonance, and to the mg = Fg → me = mg +1 transition when the probe is detuned from resonance. The pump and probe spectra are mirror images of each other and resemble those of a V system where the probe has a peak at line center and the pump spectrum has a TWT structure. For a strong σ+ pump and an even stronger π probe, the population concentrates in the intermediate transitions, and the AWT to TWT changeover does not occur. We also show that the narrow features in the spectra at line center derive from transfer of coherence from the excited to the ground hyperfine levels.