Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Physical Review A

Calculation of line shapes in double-resonance optical pumping

Heung‐Ryoul Noh, Han Seb Moon

Published Aug 14, 2009• 29 citations
Publisher

Abstract

A theoretical study on double-resonance optical pumping for the transitions $5{S}_{1/2}\text{\ensuremath{-}}5{P}_{3/2}\text{\ensuremath{-}}4{D}_{3/2,5/2}$ of $^{87}\text{R}\text{b}$ atoms is presented. The full-density-matrix equations in the presence the probe and the coupling laser beams for all relevant magnetic sublevels of the hyperfine levels were solved numerically, and the absorption of a probe beam was calculated as a function of the detuning of the coupling beam. The calculated results were compared with experimental data, and they showed an excellent agreement. The results were also compared with the approximate results calculated when the coherence between the ground and the highest excited levels was neglected. We found that the dominant operating mechanism for double-resonance signals was the optical pumping rather than the two-photon coherence, although the latter affected the signals significantly.

DOI
10.1103/physreva.80.022509

Related papers

Double-resonance optical pumping of Rb atoms

Han Seb Moon, Lim Lee, Jung Bog Kim

We have studied double-resonance optical pumping (DROP) as a function of the polarization combination of lasers, laser power, and the alignment of lasers in the 5S1/2-5P3/2-D3/2,5/2 ladder-type system of Rb87 atoms. By considering the two-photon transition probability and optical pumping effects, the changes in the relative magnitude of the DROP hyperfine structures as a function of the polarization combination of the lasers were analyzed theoretically. The theoretical results are in good agreement with the experimental results. Owing to the low optical pumping effect in the cycling transition, we could see the dependence of the spectrum on the laser power in the 5P3/2-4D5/2 transition distinctly. Also, the spectral linewidths as a function of the alignment between the lasers were measured 12.2 MHz for copropagating beams and 6.9 MHz for counterpropagating beams.

Journal of the Optical Society of America B•Aug 7, 2007•47 citations

Line-shape study of two-color–three-photon ionization of Rb atoms

Ivo Cacelli, A. Fioretti, C. Gabbanini +2 more

We report on the analysis of the line shapes in a two-color, three-photon ionization process of rubidium atoms in a magneto-optical trap. A cw and a pulsed laser are tuned almost at resonance with the ${5}^{2}{S}_{1/2}{\ensuremath{-}5}^{2}{P}_{3/2}$ and the ${5}^{2}{P}_{3/2}{\ensuremath{-}6}^{2}{D}_{5/2}$ transitions, respectively. The line shapes, recorded as functions of the pulsed laser wavelength, are strongly asymmetric with respect to the near resonance peak positions: in fact, they present long tails only on one side, according to the sign of the detuning of the cw laser. Moreover, the signal is overall stronger for negative than for positive detunings. Theoretical considerations based on the Autler-Townes scheme and computer simulations of the excitation-ionization dynamics show that the main source of asymmetry is the coupling of the two ionization pathways going through the ${6}^{2}{D}_{3/2}$ and ${6}^{2}{D}_{5/2}$ levels. In order to reproduce the experimental line shapes one must take into account the variability of the pulsed laser intensity and its finite coherence time.

Physical Review A•Aug 21, 2002•0 citations

Polarization dependence of double-resonance optical pumping and electromagnetically induced transparency in the 5S1/2−5P3/2−5D5/2 transition of 87 Rb atoms

Han Seb Moon, Heung‐Ryoul Noh

The polarization dependence of double-resonance optical pumping (DROP) in the ladder-type electromagnetically induced transparency (EIT) of the $5{S}_{1/2}\ensuremath{-}5{P}_{3/2}\ensuremath{-}5{D}_{5/2}$ transition of ${}^{87}$Rb atoms is studied. The transmittance spectra in the $5{S}_{1/2}(F=2)\ensuremath{-}5{P}_{3/2}({F}^{\ensuremath{'}}=3)\ensuremath{-}5{D}_{5/2}({F}^{\ensuremath{'}\ensuremath{'}}=2,3,4)$ transition were observed as caused by EIT, DROP, and saturation effects in the various polarization combinations between the probe and coupling lasers. The features of the double-structure transmittance spectra in the $5{S}_{1/2}(F=2)\ensuremath{-}5{P}_{3/2}({F}^{\ensuremath{'}}=3)\ensuremath{-}5{D}_{5/2}({F}^{\ensuremath{'}\ensuremath{'}}=4)$ cycling transition were attributed to the difference in saturation effect according to the transition routes between the Zeeman sublevels and the EIT according to the two-photon transition probability.

Physical Review A•Sep 15, 2011•21 citations

Comparison between transparencies of 5S_1/2-5P_3/2-4D_5/2 and 5S_1/2-5P_3/2-5D_5/2 transitions of ^87Rb atoms

Han Seb Moon, Heung‐Ryoul Noh

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.

Journal of the Optical Society of America B•Jun 7, 2012•15 citations

Theory of Optical-Microwave Double Resonance I. Fundamentals and Double Resonance of Microwave Detection

Michio Takami

The effect of optical pumping on the lineshapes and the peak values of microwave absorption line is calculated by a density matrix method in the Doppler limit approximation. The calculated double resonance signal consists of two terms. One is proportional to the unperturbed population difference of the optical transition and has a Lorentzian lineshape at weak microwave saturation. In this term the two-photon processes cause broadening of the line. The other is proportional to the population difference of the microwave transition and gives the higher-order dynamic Stark effect. At moderate optical saturation the former term is much greater than the latter. At strong optical saturation the latter term becomes noticeable and lineshape anomaly occurs. The peak values of the double resonance signals are also calculated and compared with an experimental result.

Japanese Journal of Applied Physics•Jun 1, 1976•41 citations

Theoretical calculation of saturated absorption spectra for multi-level atoms

Liam Maguire, Rick van Bijnen, Emine Meşe +1 more

We have developed a model for calculating saturated absorption spectra for dipole transitions in multi-level atoms. Using a semiclassical density matrix formalism, we derive a set of coupled differential equations for the internal state of the atom in a standing wave light field. The equations are solved using standard integration techniques. The absorption at each laser detuning is found from an average of the absorption for a number of velocities along the laser field, thermally weighted. The method is relatively efficient computationally yet quantitatively predicts important details of saturated absorption spectra including saturation, crossover resonances, merging of absorption lines at high intensity and optical pumping between hyperfine levels. We have measured saturated absorption and fluorescence spectra of 85 Rb, and compare to our computational results for a 36-level model.

Journal of Physics B Atomic Molecular and Optical Physics•May 24, 2006•50 citations
A theoretical study on double-resonance optical pumping for the transitions 5S1/2\ensuremath-5P3/2\ensuremath-4D3/2,5/25{S}_{1/2}\text{\ensuremath{-}}5{P}_{3/2}\text{\ensuremath{-}}4{D}_{3/2,5/2}5S1/2​\ensuremath-5P3/2​\ensuremath-4D3/2,5/2​ of 87Rb^{87}\text{R}\text{b}87Rb atoms is presented. The full-density-matrix equations in the presence the probe and the coupling laser beams for all relevant magnetic sublevels of the hyperfine levels were solved numerically, and the absorption of a probe beam was calculated as a function of the detuning of the coupling beam. The calculated results were compared with experimental data, and they showed an excellent agreement. The results were also compared with the approximate results calculated when the coherence between the ground and the highest excited levels was neglected. We found that the dominant operating mechanism for double-resonance signals was the optical pumping rather than the two-photon coherence, although the latter affected the signals significantly.
We have studied double-resonance optical pumping (DROP) as a function of the polarization combination of lasers, laser power, and the alignment of lasers in the 5S1/2-5P3/2-D3/2,5/2 ladder-type system of Rb87 atoms. By considering the two-photon transition probability and optical pumping effects, the changes in the relative magnitude of the DROP hyperfine structures as a function of the polarization combination of the lasers were analyzed theoretically. The theoretical results are in good agreement with the experimental results. Owing to the low optical pumping effect in the cycling transition, we could see the dependence of the spectrum on the laser power in the 5P3/2-4D5/2 transition distinctly. Also, the spectral linewidths as a function of the alignment between the lasers were measured 12.2 MHz for copropagating beams and 6.9 MHz for counterpropagating beams.
We report on the analysis of the line shapes in a two-color, three-photon ionization process of rubidium atoms in a magneto-optical trap. A cw and a pulsed laser are tuned almost at resonance with the ${5}^{2}{S}_{1/2}{\ensuremath{-}5}^{2}{P}_{3/2}$ and the ${5}^{2}{P}_{3/2}{\ensuremath{-}6}^{2}{D}_{5/2}$ transitions, respectively. The line shapes, recorded as functions of the pulsed laser wavelength, are strongly asymmetric with respect to the near resonance peak positions: in fact, they present long tails only on one side, according to the sign of the detuning of the cw laser. Moreover, the signal is overall stronger for negative than for positive detunings. Theoretical considerations based on the Autler-Townes scheme and computer simulations of the excitation-ionization dynamics show that the main source of asymmetry is the coupling of the two ionization pathways going through the 62D3/2{6}^{2}{D}_{3/2}62D3/2​ and 62D5/2{6}^{2}{D}_{5/2}62D5/2​ levels. In order to reproduce the experimental line shapes one must take into account the variability of the pulsed laser intensity and its finite coherence time.
The polarization dependence of double-resonance optical pumping (DROP) in the ladder-type electromagnetically induced transparency (EIT) of the $5{S}_{1/2}\ensuremath{-}5{P}_{3/2}\ensuremath{-}5{D}_{5/2}$ transition of 87{}^{87}87Rb atoms is studied. The transmittance spectra in the $5{S}_{1/2}(F=2)\ensuremath{-}5{P}_{3/2}({F}^{\ensuremath{'}}=3)\ensuremath{-}5{D}_{5/2}({F}^{\ensuremath{'}\ensuremath{'}}=2,3,4)$ transition were observed as caused by EIT, DROP, and saturation effects in the various polarization combinations between the probe and coupling lasers. The features of the double-structure transmittance spectra in the $5{S}_{1/2}(F=2)\ensuremath{-}5{P}_{3/2}({F}^{\ensuremath{'}}=3)\ensuremath{-}5{D}_{5/2}({F}^{\ensuremath{'}\ensuremath{'}}=4)$ cycling transition were attributed to the difference in saturation effect according to the transition routes between the Zeeman sublevels and the EIT according to the two-photon transition probability.
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.
The effect of optical pumping on the lineshapes and the peak values of microwave absorption line is calculated by a density matrix method in the Doppler limit approximation. The calculated double resonance signal consists of two terms. One is proportional to the unperturbed population difference of the optical transition and has a Lorentzian lineshape at weak microwave saturation. In this term the two-photon processes cause broadening of the line. The other is proportional to the population difference of the microwave transition and gives the higher-order dynamic Stark effect. At moderate optical saturation the former term is much greater than the latter. At strong optical saturation the latter term becomes noticeable and lineshape anomaly occurs. The peak values of the double resonance signals are also calculated and compared with an experimental result.
We have developed a model for calculating saturated absorption spectra for dipole transitions in multi-level atoms. Using a semiclassical density matrix formalism, we derive a set of coupled differential equations for the internal state of the atom in a standing wave light field. The equations are solved using standard integration techniques. The absorption at each laser detuning is found from an average of the absorption for a number of velocities along the laser field, thermally weighted. The method is relatively efficient computationally yet quantitatively predicts important details of saturated absorption spectra including saturation, crossover resonances, merging of absorption lines at high intensity and optical pumping between hyperfine levels. We have measured saturated absorption and fluorescence spectra of 85 Rb, and compare to our computational results for a 36-level model.