<p>We have investigated the detailed line shapes of modulation transfer spectroscopy (MTS) for the <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="41598_2025_92562_Article_IEq1.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="138" /> </InlineMediaObject> <EquationSource Format="TEX">\(F_g=2 \rightarrow F_e=1, 2\)</EquationSource> </InlineEquation>, and 3 transitions of <sup>85</sup>Rb due to neighboring hyperfine transitions. This analysis has been conducted under four different polarization configurations: linear parallel, linear perpendicular, circular parallel, and circular perpendicular configurations. To the best of our knowledge the effects of neighboring transitions have been applied to MTS for the first time. The dependencies in the asymmetric MTS spectra resulting from the neighboring effects on the <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="41598_2025_92562_Article_IEq2.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="122" /> </InlineMediaObject> <EquationSource Format="TEX">\(F_g=2 \rightarrow F_e=1\)</EquationSource> </InlineEquation> transition of <sup>85</sup>Rb are accounted for by artificially adjusting the hyperfine energy separations in the excited state. We also investigate the detailed MTS line shapes for the <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="41598_2025_92562_Article_IEq3.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="153" /> </InlineMediaObject> <EquationSource Format="TEX">\(F_g = 1 \rightarrow F_e = 0, 1, 2\)</EquationSource> </InlineEquation> transitions of <sup>87</sup>Rb, considering circular polarization configurations. The significant strength of the MTS spectra for the crossover lines involving the <InlineEquation ID="IEq4"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="41598_2025_92562_Article_IEq4.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="48" /> </InlineMediaObject> <EquationSource Format="TEX">\(F_e = 0\)</EquationSource> </InlineEquation> and 1 states of <sup>87</sup>Rb in the <InlineEquation ID="IEq5"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="41598_2025_92562_Article_IEq5.gif" Format="GIF" Height="17" Rendition="HTML" Resolution="72" Type="Linedraw" Width="64" /> </InlineMediaObject> <EquationSource Format="TEX">\(\sigma ^+ - \sigma ^-\)</EquationSource> </InlineEquation> polarization configuration can be explained through a MTS signal mediated by spontaneous emission. Theoretical line shapes of these transitions, calculated using the density matrix equations, show good agreement with the observed spectra.</p>

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Neighboring and polarization effects on line shape of the modulation transfer spectroscopy in lower ground hyperfine state of Rb atoms

  • Shabraz Khan,
  • Heung-Ryoul Noh,
  • Jin-Tae Kim

摘要

We have investigated the detailed line shapes of modulation transfer spectroscopy (MTS) for the \(F_g=2 \rightarrow F_e=1, 2\) , and 3 transitions of 85Rb due to neighboring hyperfine transitions. This analysis has been conducted under four different polarization configurations: linear parallel, linear perpendicular, circular parallel, and circular perpendicular configurations. To the best of our knowledge the effects of neighboring transitions have been applied to MTS for the first time. The dependencies in the asymmetric MTS spectra resulting from the neighboring effects on the \(F_g=2 \rightarrow F_e=1\) transition of 85Rb are accounted for by artificially adjusting the hyperfine energy separations in the excited state. We also investigate the detailed MTS line shapes for the \(F_g = 1 \rightarrow F_e = 0, 1, 2\) transitions of 87Rb, considering circular polarization configurations. The significant strength of the MTS spectra for the crossover lines involving the \(F_e = 0\) and 1 states of 87Rb in the \(\sigma ^+ - \sigma ^-\) polarization configuration can be explained through a MTS signal mediated by spontaneous emission. Theoretical line shapes of these transitions, calculated using the density matrix equations, show good agreement with the observed spectra.