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Optics Express

Modulation transfer spectroscopy mediated by spontaneous emission

Sang Eon Park, Heung‐Ryoul Noh

Published Jun 5, 2013• 18 citations
Publisher

Abstract

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.

DOI
10.1364/oe.21.014066

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We herein present a theoretical and experimental study on magnetic-field enhanced modulation transfer spectroscopy (MTS) for the 5S1/2 (F = 1) → 5P3/2 (F′ = 0, 1, and 2) transitions of 87Rb atoms. The density matrix equations are solved numerically to obtain the MTS spectra and an excellent agreement is found between the experimental and calculated results. In particular, the enhancement of the MTS signal for the F = 1 → F′ = 0 transition in the presence of the magnetic field is directly verified based on the comparison of the results calculated by neglecting with those calculated including the Zeeman coherences in the F = 1 ground state. The unexpected behaviors of the F = 1 → F′ = 1 transition are also examined.

Optics Express•Oct 4, 2021•7 citations
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.
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.
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.
We conducted a theoretical and experimental study of lineshape in modulation transfer spectroscopy for ⁸⁷Rb atoms. When a linearly polarized pump beam, modulated at an angular frequency of Ω, overlaps in parallel with an unmodulated linearly polarized probe beam, combined modulated probe beams are generated via nonlinear interaction with atoms. The detected modulation transfer signals are calculated by numerically solving the complete optical Bloch equations for the ⁸⁷Rb atoms without the use of any phenomenological parameters. We find that the calculated results are in good agreement with experimental results.
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.
We herein present a theoretical and experimental study on magnetic-field enhanced modulation transfer spectroscopy (MTS) for the 5S1/2 (F = 1) → 5P3/2 (F′ = 0, 1, and 2) transitions of 87Rb atoms. The density matrix equations are solved numerically to obtain the MTS spectra and an excellent agreement is found between the experimental and calculated results. In particular, the enhancement of the MTS signal for the F = 1 → F′ = 0 transition in the presence of the magnetic field is directly verified based on the comparison of the results calculated by neglecting with those calculated including the Zeeman coherences in the F = 1 ground state. The unexpected behaviors of the F = 1 → F′ = 1 transition are also examined.