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Optics Express

Magnetic-field enhanced modulation transfer spectroscopy: theory and experiment

Sanglok Lee, Jeongwon Kang, Subin Kim, Jeongyoun Jeong, Geol Moon, Heung‐Ryoul Noh

Published Oct 4, 2021• 7 citations
Publisher

Abstract

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.

DOI
10.1364/oe.440270

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Journal of the Optical Society of America B•Jun 7, 2012•15 citations
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.
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.
Active frequency stabilization of a laser to an atomic or molecular resonance underpins many modern-day AMO physics experiments. With a flat background and high signal-to-noise ratio, modulation transfer spectroscopy (MTS) offers an accurate and stable method for laser locking. Despite its benefits, however, the four-wave mixing process that is inherent to the MTS technique entails that the strongest modulation transfer signals are only observed for closed transitions, excluding MTS from numerous applications. Here, we report for the first time the observation of a magnetically tunable MTS error signal. Using a simple two-magnet arrangement, we show that the error signal for the 87Rb F = 2 → F' = 3 cooling transition can be Zeeman-shifted over a range of ~10 GHz to any arbitrary point on the rubidium D2 spectrum. Modulation transfer signals for locking to the 87Rb F = 1 → F' = 2 repumping transition as well as 1 GHz red-detuned to the cooling transition are presented to demonstrate the versatility of this technique, which can readily be extended to the locking of Raman and lattice lasers.
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.
Theoretical study and computer modeling results of the spectra of coherent dark resonances resulted from excitation of Zeeman sublevels of the Fg=2→Fe=1 transition of the D1 line in 87Rb atoms by a frequency-modulated laser field are presented and discussed in detail. The influence of the nonlinear Zeeman effect on the structure of the coherent dark resonances is observed. It is shown that calculated for different values of the magnetic field spectra are in a good agreement with the experimental data.
We have experimentally and theoretically studied the causes of the transparency spectra of the 5S1/2-5P3/2-4D5/2 and 5S1/2-5P3/2-5D5/2 transitions of 87Rb atoms. Although, the two-photon resonance of the 5S1/2-5P3/2-4D5/2 transition was not Doppler-free in an Rb vapor, we observed the transparency phenomenon in this transition. The main cause of the transparency of the 5S1/2-5P3/2-4D5/2 transition was double-resonance optical pumping (DROP) due to two-step excitation, and that of the 5S1/2-5P3/2-5D5/2 transition was DROP and electromagnetically induced transparency due to two-photon coherence. We confirmed the experimental results with theoretical results calculated using the density matrix equations considering all the degenerate magnetic sublevels of both transitions of the 87Rb atoms.