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Scientific Reports

Optical pumping effect on modulation transfer spectroscopy of the $$D_1$$ line of $$^{85}$$Rb atoms with non-cycling transition

Shabraz Khan, Heung‐Ryoul Noh, Jin‐Tae Kim

Published Mar 11, 2026• 0 citations
Publisher

Abstract

The [Formula: see text] line of [Formula: see text]Rb exhibits non-cycling transitions; therefore, only weak modulation transfer spectroscopy (MTS) signals could be obtained. In this study, however, strong MTS spectra were obtained for the [Formula: see text] line via optical pumping (OP) of the [Formula: see text] line of [Formula: see text]Rb. Four linear parallel (lin ∥ lin) and linear perpendicular (lin⊥lin), [Formula: see text], and [Formula: see text] polarization configurations were investigated using an OP laser with four different polarizations such as linear horizontal (P), linear vertical (S), [Formula: see text], and [Formula: see text] polarizations. Under the linear perpendicular configuration, the MTS signal for the [Formula: see text] transition of the [Formula: see text] line exhibited approximately a 41-fold increase in the signal slope in the presence of a linearly-polarized OP beam, compared with the signal slope obtained without OP. The calculated MTS spectra for the [Formula: see text] configuration in the presence of [Formula: see text]- or [Formula: see text]-polarized OP beam as an example matched well with experimental observations.

DOI
10.1038/s41598-026-43427-6

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Optical pumping effect on modulation transfer spectroscopy of the D1D_1D1​ line of 85^{85}85Rb atoms with non-cycling transition
The [Formula: see text] line of [Formula: see text]Rb exhibits non-cycling transitions; therefore, only weak modulation transfer spectroscopy (MTS) signals could be obtained. In this study, however, strong MTS spectra were obtained for the [Formula: see text] line via optical pumping (OP) of the [Formula: see text] line of [Formula: see text]Rb. Four linear parallel (lin ∥ lin) and linear perpendicular (lin⊥lin), [Formula: see text], and [Formula: see text] polarization configurations were investigated using an OP laser with four different polarizations such as linear horizontal (P), linear vertical (S), [Formula: see text], and [Formula: see text] polarizations. Under the linear perpendicular configuration, the MTS signal for the [Formula: see text] transition of the [Formula: see text] line exhibited approximately a 41-fold increase in the signal slope in the presence of a linearly-polarized OP beam, compared with the signal slope obtained without OP. The calculated MTS spectra for the [Formula: see text] configuration in the presence of [Formula: see text]- or [Formula: see text]-polarized OP beam as an example matched well with experimental observations.
The D_1 line of ^{85}Rb exhibits non-cycling transitions; therefore, only weak modulation transfer spectroscopy (MTS) signals could be obtained \cite{Khan2024}. In this study, however, strong MTS spectra were obtained for the D_1 line via optical pumping (OP) of the D_2 line of 85^{85}85Rb. Four linear parallel (lin \parallel lin) and linear perpendicular (lin\perplin), \sigma^+ - \sigma^+, and \sigma^+ - \sigma^- polarization configurations were investigated using an OP laser with four different polarizations such as linear horizontal (P), linear vertical (S), \sigma^+, and \sigma^- polarizations. Under the linear perpendicular configuration, the MTS signal for the F_g=3 \rightarrow F_e=2 transition of the D_1 line exhibited approximately a 41-fold increase in the signal slope in the presence of a linearly-polarized OP beam, compared with the signal slope obtained without OP. The calculated MTS spectra for the \sigma^+ \sigma^- configuration in the presence of \sigma^+- or \sigma^--polarized OP beam as an example matched well with experimental observations.
The D_1 line of ^{85}Rb exhibits non-cycling transitions; therefore, only weak modulation transfer spectroscopy (MTS) signals could be obtained \cite{Khan2024}. In this study, however, strong MTS spectra were obtained for the D_1 line via optical pumping (OP) of the D_2 line of 85^{85}85Rb. Four linear parallel (lin \parallel lin) and linear perpendicular (lin\perplin), \sigma^+ - \sigma^+, and \sigma^+ - \sigma^- polarization configurations were investigated using an OP laser with four different polarizations such as linear horizontal (P), linear vertical (S), \sigma^+, and \sigma^- polarizations. Under the linear perpendicular configuration, the MTS signal for the F_g=3 \rightarrow F_e=2 transition of the D_1 line exhibited approximately a 41-fold increase in the signal slope in the presence of a linearly-polarized OP beam, compared with the signal slope obtained without OP. The calculated MTS spectra for the \sigma^+ \sigma^- configuration in the presence of \sigma^+- or \sigma^--polarized OP beam as an example matched well with experimental observations.
Modulation transfer spectroscopy (MTS) is widely used in an optical laboratory for laser frequency stabilization. There have been many theoretical and experimental papers on this spectroscopic method. However, most of the works focus on the cycling transitions like the D2 line of rubidium. In this paper, the MTS for noncycling transitions is investigated. We consider the D1 line of rubidium whose modulation transfer spectrum has been determined and compared to the polarization spectrum. It is found that the slope of the modulation transfer signal is sharper than the polarization spectrum. The performance of laser frequency locking based on the MTS method is better than that of the polarization spectroscopy method. The dependence of the signal amplitude on the temperature of the vapor cell was analyzed, and the high signal-to-noise-ratio spectra are achieved for D1 open transitions. The obtained results provide an effective spectroscopic method for the robust frequency locking of a laser at a wavelength of 795 nm.
We have investigated the detailed line shapes of modulation transfer spectroscopy (MTS) for the Fg=2→Fe=1,2F_g=2 \rightarrow F_e=1, 2Fg​=2→Fe​=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 Fg=2→Fe=1F_g=2 \rightarrow F_e=1Fg​=2→Fe​=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 Fg=1→Fe=0,1,2F_g = 1 \rightarrow F_e = 0, 1, 2Fg​=1→Fe​=0,1,2 transitions of 87Rb, considering circular polarization configurations. The significant strength of the MTS spectra for the crossover lines involving the Fe=0F_e = 0Fe​=0 and 1 states of 87Rb in the σ+−σ−\sigma ^+ - \sigma ^-σ+−σ− 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.
We report the polarization dependence of the spectrum in modulation transfer spectroscopy for the transitions from the lower ground state (F(g) = 1) of (87)Rb atoms. We measured the spectra for the two polarization configurations where the carrier and probe beams were linearly polarized in parallel or perpendicular directions. The measured spectra were in excellent agreement with calculated results. The spectra were strongly dependent on the polarization configurations. In particular, the signal for parallel polarization configuration was generated via an incoherent process mediated by spontaneous emission.
In a spin-exchange relaxation-free (SERF) atomic magnetometer, the pump and probe laser frequencies are tuned to the D 1 transition line of alkali metal atoms to enhance measurement sensitivity. The D 1 line, a non-cycling transition, exhibits a low absorption coefficient. This study theoretically analyzes the influence of different parameters on the absorption coefficient of the D 1 line and proposes a polarization-dependent approach to enhance it. A frequency stabilization method based on modulation transfer spectroscopy (MTS) with an enhanced absorption coefficient is introduced. Compared with the conventional method, optimizing the probe beam’s polarization increases the absorption coefficient, raising the amplitude of the MTS signal. The results show that using a stronger MTS signal for frequency stabilization reduces the laser's frequency noise. Using heterodyne measurement, we characterize the linewidth-narrowing effect of MTS locking and evaluate the frequency stability of the locked laser. The linewidth of each laser is reduced from the free-running 2.2 MHz to 885 kHz after MTS stabilization. The Allan deviation measurements of the beat signal between two locked lasers are 2.6 × 10 −11 / τ . This work provides a stable optical frequency reference for SERF atomic magnetometers and offers potential applications in extracting spatial information from optically pumped atoms.