Optical pumping of alkali-metal vapor with hyperfine-resolved buffer gas pressure

Optical pumping is fundamental to high-precision measurement using thermal alkali-metal atoms in vapor cells. In applications such as spin-exchange-relaxation-free magnetometers, buffer gases e.g., $N₂$ or $He$ are commonly employed to quench fluorescence and mitigate wall relaxation. In the high-pressure limit e.g., the $N₂$ pressure $p_{rm{N}₂}> 1$ atm, where collisional broadening exceeds the hyperfine splitting of the alkali-metal atoms, optical pumping theory provides a clear description of the angular momentum exchange between photons and atomic spins. However, in many magnetic sensing scenarios, this high-pressure condition is not strictly satisfied, rendering the high-pressure approximation inaccurate. Consequently, a precise quantitative understanding of optical pumping under realistic pressures is critical for determining optimal buffer gas parameters, selecting operating points (e.g., pump frequency and intensity), and enhancing system reliability and stability. To address this, we develop a theory of optical pumping in the quasi-high-pressure regime, where collisional broadening is comparable to the ground-state hyperfine splitting. We demonstrate that optical absorption, spin polarization, and magnetic resonance linewidth in this regime differ significantly from those predicted by the high-pressure limit. Our study extends conventional modeling and offers critical guidance for atomic magnetometry operating under realistic buffer gas pressures.