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

Discrimination of the effects of saturation and optical pumping in velocity-dependent pump-probe spectroscopy of rubidium: A simple analytical study

Heung‐Ryoul Noh, Geol Moon, Wonho Jhe

Published Dec 27, 2010• 14 citations
Publisher

Abstract

This paper presents a simple analytical theory for the velocity-dependent pump-probe laser spectroscopy of $^{87}\mathrm{Rb}$ and $^{85}\mathrm{Rb}$ atoms where the pump and the probe beams are circularly or linearly polarized. The analytical solutions of the line shapes of the velocity-selective optical pumping spectroscopy [G. Moon and H. R. Noh, Phys. Rev. A 78, 032506 (2008)] and saturated absorption spectroscopy [G. Moon and H. R. Noh, J. Opt. Soc. Am. B 25, 701 (2008); 27, 1741 (2010)] obtained in the previous reports, expressed as a sum of several Lorentzian functions, could be approximated as one (or in some cases, two) Lorentzian function(s). In particular, the contributions of the saturation and optical pumping effects could be discriminated explicitly in these simple analytical solutions, which is not possible in existing theories such as Nakayama's model. The simple analytical results for the saturation spectroscopy were compared with experimental results, and good agreement between them was observed.

DOI
10.1103/physreva.82.062517

Related papers

Theoretical Analysis of Rb and Cs D2 Lines in Doppler-Free Spectroscopic Techniques with Optical Pumping

Shigeru Nakayama

The relative intensities of the Doppler-free signals of the 85Rb and Cs D2 lines in saturation spectroscopy, velocity-selective optical pumping (VSOP) spectroscopy, and polarization spectroscopy were calculated theoretically, taking into accont the optical pumping process in the Zeeman sublevels and arbitrary polarization combinations for pump and probe beams. Both circular and linear optical anisotropy induced by the pump beam were considered in the theoretical calculation. The magnitude and sign of the Doppler-free resonances in each spectroscopic method were quite different owing to the polarizations of the pump and probe beams. The theoretical results obtained from a single-cycle optical pumping in a four-level approximation were in good agreement with recent experimental reports.

Japanese Journal of Applied Physics•Jan 1, 1985•57 citations

Effect of optical pumping in saturated absorption spectroscopy: an analytic study for two-level atoms

Heung‐Ryoul Noh

We present the analytic solutions of the saturated absorption spectrum for an atomic medium composed of two-level atoms and describe the effects of saturation and optical pumping on the spectrum. The background-subtracted Doppler-free spectrum is Lorentzian-shaped with an amplitude and width given by 1 − {1 + s 0 [1 + (γ 2 t /2)]} −1/2 and γ t [1 + {1 + s 0 [1 + (γ 2 t /2)]} 1/2 ], respectively, where γ t is the transverse decay rate, γ 2 is the decay rate to energy levels other than the ground state, s 0 is the saturation parameter and t is the interaction time of the atoms with laser beams. Analytic results are compared with numerical results and show good agreement with one another. This paper is intended for graduate students who have started to study basic atomic physics.

European Journal of Physics•Aug 14, 2009•13 citations

Optical pumping spectroscopy of Rb vapour with co-propagating laser beams: line identification by a simple theoretical model

Aleksandar J. Krmpot, Mihailo D. Rabasović, Branislav M. Jelenkovic

In this paper the saturation spectra of rubidium vapour at room temperature, obtained with overlapped co-propagating laser beams, were examined. Unlike the standard saturation spectroscopy, here the transmission of the pump laser beam was detected. The pump laser was locked to an atomic transition of the D2 line, while the probe laser frequency was scanned in a wide frequency range. The pump and probe beams had approximately the same intensities; thus the probe laser can saturate transitions and contribute to optical pumping. This, together with Doppler broadening, leads to rich pump transmission spectra, with many lines appearing due to the interaction of lasers with atoms in different velocity groups. The advantages of this method are well-resolved structures and appearance of spectral lines on a flat, Doppler-free background. Agreement between experimental and theoretical results shows the usefulness of this simple model, based on the rate equations, for identification of lines and determination of relative contribution to the observed line intensity from atoms with different velocities. Theoretical spectra are a useful tool for the calibration of experimental spectra obtained by a nonlinear dependence of the laser frequency on the voltage applied to the piezo used for the laser diode frequency scanning.

Journal of Physics B Atomic Molecular and Optical Physics•Jun 14, 2010•5 citations

Optical pumping effects in high resolution laser spectroscopy

Shigeru Nakayama

A theoretical analysis of the relative intensities of the Doppler-free signals in saturation spectroscopy, velocity selective optical pumping (VSOP) spectroscopy, polarization spectroscopy and a mixing of saturation and polarization spectroscopies is presented using the approximation of a single cycle of optical pumping in a four-level system. An optical pumping process in the Zeeman sublevels is taken into account owing to the important role of spontaneous emission even if the sublevels are degenerate. Arbitrary polarization combinations are considered for pump and probe beams. The similarities and differences between three kinds of spectroscopy are made clear. Both circular and linear optical anisotropies induced by the pump beam are considered in this theoretical calculation. The magnitude and sign of Doppler-free resonances in each spectroscopy are quite different owing to the polarizations of the pump and probe beams. The four-level system is important as a three-level approximation. The results obtained from the four-level optical pumping theory are in good agreement with experimental reports.

Physica Scripta•Jan 1, 1997•29 citations

Saturated-absorption spectroscopy of weak-field Zeeman splittings in rubidium: comment

J. B. Kim, H.A. Kim, Han Seb Moon +1 more

High-resolution saturated absorption spectroscopy of the 85RbD1 line has been used for observation of the Zeeman effect by use of a diode laser with a narrow linewidth. Experimental results were compared with both Breit–Rabi theory related to shifted resonant frequencies and Nakayama's single-cycle optical pumping theory related to signal magnitudes of signal [J. Opt. Soc. Am. B2, 1431 (1985)]. A comparison of our results with those of Bowie [J. Opt. Soc. Am. B12, 1839 (1995)], who used perturbation theory to obtain the energy-level shifts, yielded experimental results that differ significantly in some respects.

Journal of the Optical Society of America B•Nov 1, 1997•2 citations

Linear polarization spectroscopy in rubidium

Shi-Hao Sun, Yong-Feng Wu, Jiang Bo-Nan

We realize the linear polarization spectroscopy on the D2 transitions of rubidium atoms and investigate the underlying physics with an analytical theory using the Nakayama model. We demonstrate that the strong birefringence in the rubidium atomic gas is induced by the π light optical pumping, which is distinguished from the conventional PS using circularly polarized light. The theory agrees with the experiment reasonably well, except for the upper hyperfine closed transitions where the saturation plays nontrivial roles. The effects of the misalignment of the polarization optics and the miscalibration of the pump intensity are also discussed.

Journal of the Optical Society of America B•Jun 1, 2026•0 citations
This paper presents a simple analytical theory for the velocity-dependent pump-probe laser spectroscopy of 87Rb^{87}\mathrm{Rb}87Rb and 85Rb^{85}\mathrm{Rb}85Rb atoms where the pump and the probe beams are circularly or linearly polarized. The analytical solutions of the line shapes of the velocity-selective optical pumping spectroscopy [G. Moon and H. R. Noh, Phys. Rev. A 78, 032506 (2008)] and saturated absorption spectroscopy [G. Moon and H. R. Noh, J. Opt. Soc. Am. B 25, 701 (2008); 27, 1741 (2010)] obtained in the previous reports, expressed as a sum of several Lorentzian functions, could be approximated as one (or in some cases, two) Lorentzian function(s). In particular, the contributions of the saturation and optical pumping effects could be discriminated explicitly in these simple analytical solutions, which is not possible in existing theories such as Nakayama's model. The simple analytical results for the saturation spectroscopy were compared with experimental results, and good agreement between them was observed.
The relative intensities of the Doppler-free signals of the 85Rb and Cs D2 lines in saturation spectroscopy, velocity-selective optical pumping (VSOP) spectroscopy, and polarization spectroscopy were calculated theoretically, taking into accont the optical pumping process in the Zeeman sublevels and arbitrary polarization combinations for pump and probe beams. Both circular and linear optical anisotropy induced by the pump beam were considered in the theoretical calculation. The magnitude and sign of the Doppler-free resonances in each spectroscopic method were quite different owing to the polarizations of the pump and probe beams. The theoretical results obtained from a single-cycle optical pumping in a four-level approximation were in good agreement with recent experimental reports.
We present the analytic solutions of the saturated absorption spectrum for an atomic medium composed of two-level atoms and describe the effects of saturation and optical pumping on the spectrum. The background-subtracted Doppler-free spectrum is Lorentzian-shaped with an amplitude and width given by 1 − {1 + s 0 [1 + (γ 2 t /2)]} −1/2 and γ t [1 + {1 + s 0 [1 + (γ 2 t /2)]} 1/2 ], respectively, where γ t is the transverse decay rate, γ 2 is the decay rate to energy levels other than the ground state, s 0 is the saturation parameter and t is the interaction time of the atoms with laser beams. Analytic results are compared with numerical results and show good agreement with one another. This paper is intended for graduate students who have started to study basic atomic physics.
In this paper the saturation spectra of rubidium vapour at room temperature, obtained with overlapped co-propagating laser beams, were examined. Unlike the standard saturation spectroscopy, here the transmission of the pump laser beam was detected. The pump laser was locked to an atomic transition of the D2 line, while the probe laser frequency was scanned in a wide frequency range. The pump and probe beams had approximately the same intensities; thus the probe laser can saturate transitions and contribute to optical pumping. This, together with Doppler broadening, leads to rich pump transmission spectra, with many lines appearing due to the interaction of lasers with atoms in different velocity groups. The advantages of this method are well-resolved structures and appearance of spectral lines on a flat, Doppler-free background. Agreement between experimental and theoretical results shows the usefulness of this simple model, based on the rate equations, for identification of lines and determination of relative contribution to the observed line intensity from atoms with different velocities. Theoretical spectra are a useful tool for the calibration of experimental spectra obtained by a nonlinear dependence of the laser frequency on the voltage applied to the piezo used for the laser diode frequency scanning.
A theoretical analysis of the relative intensities of the Doppler-free signals in saturation spectroscopy, velocity selective optical pumping (VSOP) spectroscopy, polarization spectroscopy and a mixing of saturation and polarization spectroscopies is presented using the approximation of a single cycle of optical pumping in a four-level system. An optical pumping process in the Zeeman sublevels is taken into account owing to the important role of spontaneous emission even if the sublevels are degenerate. Arbitrary polarization combinations are considered for pump and probe beams. The similarities and differences between three kinds of spectroscopy are made clear. Both circular and linear optical anisotropies induced by the pump beam are considered in this theoretical calculation. The magnitude and sign of Doppler-free resonances in each spectroscopy are quite different owing to the polarizations of the pump and probe beams. The four-level system is important as a three-level approximation. The results obtained from the four-level optical pumping theory are in good agreement with experimental reports.
High-resolution saturated absorption spectroscopy of the 85RbD1 line has been used for observation of the Zeeman effect by use of a diode laser with a narrow linewidth. Experimental results were compared with both Breit–Rabi theory related to shifted resonant frequencies and Nakayama's single-cycle optical pumping theory related to signal magnitudes of signal [J. Opt. Soc. Am. B2, 1431 (1985)]. A comparison of our results with those of Bowie [J. Opt. Soc. Am. B12, 1839 (1995)], who used perturbation theory to obtain the energy-level shifts, yielded experimental results that differ significantly in some respects.
We realize the linear polarization spectroscopy on the D2 transitions of rubidium atoms and investigate the underlying physics with an analytical theory using the Nakayama model. We demonstrate that the strong birefringence in the rubidium atomic gas is induced by the π light optical pumping, which is distinguished from the conventional PS using circularly polarized light. The theory agrees with the experiment reasonably well, except for the upper hyperfine closed transitions where the saturation plays nontrivial roles. The effects of the misalignment of the polarization optics and the miscalibration of the pump intensity are also discussed.