Broadening and intensity redistribution in the Na($3p$) hyperfine excitation spectra due to optical pumping in the weak excitation limit

摘要

Detailed analysis of spectral line broadening and variations in relativeintensities of hyperfine spectral components due to optical pumping ispresented. Hyperfine levels of sodium $3p_{1/2}$ and $3p_{3/2}$ levels areselectively excited in a supersonic beam at various laser intensities under theconditions when optical pumping time is shorter than transit time of atomsthrough the laser beam. The excitation spectra exhibit significant linebroadening at laser intensities well below the saturation intensity, andredistribution of intensities of hyperfine spectral components is observed,which in some cases is contradicting with intuitive expectations. Theoreticalanalysis of the dynamics of optical pumping shows that spectral line broadeningdepends sensitively on branching coefficient of the laser-driven transition.Analytical expressions for branching ratio dependent critical Rabi frequencyand critical laser intensity are derived, which give the threshold for onset ofnoticeable line broadening by optical pumping. Transitions with larger andsmaller branching coefficients are relatively less affected. The theoreticalexcitation spectra were calculated numerically by solving density matrixequations of motion using the split propagation technique, and they wellreproduce the observed effects of line broadening and peak intensityvariations. The calculations also show that presence of dark (i.e., not laser-coupled) Zeeeman sublevels in the lower state results in effective branchingcoefficients which vary with laser intensity and differ from those implied bythe sum rules, and this can lead to peculiar changes in peak ratios ofhyperfine components of the spectra.