Impact of Zeeman sub-level pumping on saturated absorption spectra of thermal atomic vapor

Abstract

We propose ab-initio reduced rate equation models (with maximum 7 levels) to calculate the saturated absorption spectra (SAS) of thermal atomic vapor for linearly polarized pump and probe beams. We also experimentally validate our simplified models, that consume $\sim 100\times$ lower computational resources than full multi-level models, for all four hyperfine dips of the Rb D$_2$ line with residual error $\lesssim 3\%$ and no fitting parameters with various pump-probe intensities and beam diameters. Our 5-level model, which considers hyperfine pumping but ignores Zeeman pumping, accurately predicts enhanced saturated probe transmission at all the resonances and crossovers. However, this model is unable to predict reduced probe transmission induced by the Zeeman ($m_\textrm{F}$) sub-level pumping at the crossover $X_{10}$, comprising hyperfine transitions $F_\textrm{g}=1\rightarrow F_\textrm{e}=0$ and $F_\textrm{e}=1$ of $^{87}$Rb. In this case, our 7-level model, which accounts for both hyperfine and Zeeman pumping, faithfully reproduces all the SAS features corresponding to the hyperfine transitions $F_\textrm{g}=1\rightarrow F_\textrm{e}=0,1,2$ of $^{87}$Rb. In addition, both our models account for the transit-relaxation (depending on beam diameter) of atoms traversing the laser beam for an accurate computation. Finally, we also present theoretical and experimental evidence demonstrating the significance of probe-induced hyperfine pumping even at intensities $\sim 10\times$ smaller than that required for two-level saturation.