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

Journal of Experimental and Theoretical Physics

Anomalies in resonant absorption line profiles of atoms with large hyperfine splitting

А. И. Пархоменко, S.P. Pod'yachev, Timofei Privalov, Anatolii M. Shalagin

Published Jan 1, 1997• 2 citations
Publisher

Abstract

We examine a monochromatic absorption line in the velocity-nonselective excitation of atoms when the components of the hyperfine stricture of the electronic ground states are optically pumped. We show that the absorption lines possess unusual substructures for some values of the hyperfine splitting of the ground state (which exceed the Doppler absorption linewidth severalfold). These substructures in the absorption spectrum are most apparent if the hyperfine structure of the excited electronic state is taken into account. We calculate the absorption spectra of monochromatic light near the D 1 and D 2 lines of atomic rubidium 85,87 Rb. With real hyperfine splitting taken into account, the D 1 and D 2 lines are modeled by 4-and 6-level diagrams, respectively. Finally, we show that atomic rubidium vapor can be successfully used to observe the spectral features experimentally.

DOI
10.1134/1.558151

Related papers

Anomalies in the shape of atomic resonant absorption lines under conditions of strong optical pumping of hyperfine structure components of the ground state

А. И. Пархоменко, S.P. Pod'yachev, Timofei Privalov +1 more

The ground electronic state of even such simple atoms as those of alkali elements has the set of sublevels. These sublevels are hyperfine (HF) components and magnetic sublevels. The collisions with particles of nonmagnetic buffer gas or even with walls (when walls have proper coating) do not mix practically the populations of ground state HF sublevels, if the orbital moment of electrons in the ground state is equal to zero. Due to this reason these sublevels may be extremely long lived. Because of this, for instance, the so-called effects of optical orientation and optical pumping are apparent in atoms of alkali metals. The radiation can pump practically all the atoms (with which there is effective interaction) to a single HF component. In a situation in which optical pumping is a minor effect, the monochromatic absorption line consists of separate lines corresponding to intra-atomic transitions. The optical pumping is not significant, for example, if the radiation intensity is so low that now pumping between HF sublevels occurs in the time it takes the atom to traverse the light beam. Under the conditions of optical pumping and when other nonlinear effects are present, the absorption line profile can undergo considerable alteration. Many theoretical and experimental investigations have been done in the laser spectroscopy of resonant transitions of atoms (atoms of alkali metals) under the conditions of optical pumping within ground state HF structure. A characteristic feature of all such investigations is the velocity-selective excitation of absorbing atoms. Also, as a rule, the value of HF splitting is not very big in comparison to Doppler broadening in these experiments. Under such conditions, the absorption spectra consists of Doppler- broadened lines with nonlinear resonances, which emerge when two fields of different frequencies or different propagation directions are employed. When only one monochromatic traveling wave is employed, optical pumping leads to formation of a single smooth absorption line occupying a position between the resonant transitions frequencies associated with HF components. As HF splitting grows, the line profile remains smooth, its width is approximately equal to the size of the HF splitting. The strength of the optical pumping from one ground state HF component to another is greater for greater HF splitting in comparison to the Doppler width. In this regard, Cs and Rb are the most typical of the alkali atoms (the HF splitting exceeds the Doppler width by a factor close to 20). This is the qualitative picture of the absorption line profile (particularly for a monochromatic radiation) under the conditions of optical pumping between the HF sublevels of the electronic ground state, this qualitative picture had formed by now.

Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE•Oct 21, 1998•0 citations

Measuring the Hyperfine Splittings of Lowest Energy Atomic Transitions in Rubidium

Benjamin Graber

The goal of this experiment was to measure the hyperfine energy splittings of the ground to first excited state transitions in rubidium using saturated absorption spectroscopy. Using this technique, we measured these transition energy spectra by taking the difference of two photodiode outputs due to multiple beams of a single laser scanned over a range of frequencies and shone through a cell of Rb vapor. When the laser frequency was resonant with an atomic transition, photons of those frequencies were absorbed, leaving a dip in intensity of the beam measured at the photodiode. One of the two laser beams had its excitations saturated by a more intense, counter-propagating pump beam from the same laser. The pump beam saturated the absorption of the velocity equal zero atoms that the counter-propagating probe beam could have also interacted with due to no Doppler shift. At these frequencies the probe beam experienced less absorption that was measured by a photodiode. The photodiode output was calibrated to the change in frequency of the scanned laser using a Fabry-Pérot interferometer. The output of this interferometer served as a reference for how the laser frequency changed. Final results for the 87Rb F=1 spectrum accounted for the largest error with a maximum of 12.2% deviation from accepted energy spacing values due in part to systematic error. Other spectra measurements were in better agreement, possessing error ranging from 2.1% to 10.1% and some agreeing with accepted values to within our uncertainty.

•Jan 1, 2015•0 citations

Attenuated Total Reflection of the Rubidium D2Line in Optically Dense Vapor

賢 東條, Yuuki Murakami, Masahiro Hasuo +1 more

Absorption spectrum of the evanescent light at a glass/Rb vapor interface has been observed with atom density from 9 ×10 19 m -3 to 5 ×10 20 m -3 . Absorption is as high as 60% at the peak of a hyperfine structure split line. The absorption spectrum of the experiment is compared with that of the calculation based on Fresnel's relation on the assumption of a homogeneous electric susceptibility of the vapor. Near the critical angle the calculation which incorporates the Lorentz–Lorenz local-field correction reproduces the experimental red shift only partly.

Journal of the Physical Society of Japan•May 15, 2003•7 citations

Enhanced absorption in Doppler-free spectroscopy of the Rb atom D 1 line with monochromatic light: Application to laser-frequency stabilization

Peter Yun, Rodolphe Boudot, Qiang Hao +1 more

The detection of narrow and high-amplitude optical resonances in atomic cells is of crucial importance for the development of compact and high-stability lasers or vapor-cell optical references. In this work, using monochromatic light and appropriate polarization settings for the counterpropagating pump and probe beams, we demonstrate the detection of enhanced-absorption sub-Doppler resonances on the ${D}_{1}$ line of the $\mathrm{Rb}$ atom. We report a theoretical model showing that the Zeeman coherence induced between magnetic sublevels---especially in the $F\ensuremath{\rightarrow}{F}^{\ensuremath{'}}=F\ensuremath{-}1$ systems, with $F$ and ${F}^{\ensuremath{'}}$ being the hyperfine quantum numbers of the ground and excited states, respectively---plays a key role in the observed enhanced-absorption process. The theoretically predicted behavior matches the experimental observations well. The impact of light polarization, laser intensity, magnetic field, and cell temperature on the Doppler-free resonance features is experimentally investigated. For application, two identical diode lasers are frequency-stabilized onto enhanced-absorption sub-Doppler resonances. The fractional frequency stability of the laser beatnote is measured to be $1.8\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}12}$ at $1\phantom{\rule{0.1em}{0ex}}\mathrm{s}$ and $8.4\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}12}$ at ${10}^{4}\phantom{\rule{0.1em}{0ex}}\mathrm{s}$. These results demonstrate the potential of this scheme for the implementation of a compact or even chip-scale optical frequency reference, which might find applications in instrumentation, navigation, and metrology.

Physical Review Applied•Mar 25, 2025•4 citations

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

Jason L. Bowie, Jack Boyce, R. Y. Chiao

Using an external cavity-tuned diode laser in Doppler-free saturation spectroscopy, we are able to resolve the weak-field Zeeman splittings in the hyperfine levels of the rubidium D1 line. The number of lines observed in the Zeeman structure of rubidium and their measured energy-level splittings are as expected from theory. The measured amplitudes of the saturated-absorption signals, crossover resonances, and velocity-selective optical pumping signals are used in the analysis of various theories concerning saturated-absorption spectroscopy.

Journal of the Optical Society of America B•Oct 1, 1995•11 citations

Optical Study of the Hyperfine Structure of the Rubidium Resonance Lines*

James R. Beacham, Kenneth L. Andrew

We have developed a rubidium atomic-beam light source that emits Rb lines with a Doppler width of only 0.0015 cm−1. When the light from this source was measured with a scanning Fabry–Perot interferometer and the data were reduced by digital computer utilizing numerical deconvolution techniques, we were able to determine a hyperfine level splitting in natural rubidium as small as 0.0014 cm−1 with an uncertainty of 0.0001 cm−1. We have measured the relative intensities and positions of 19 of the 20 hfs components of the two resonance lines, 7800 and 7974 Å, of natural Rb. From these data, we calculate isotope shifts σ87−σ85 = 0.00268 cm−1 for 52P32 and σ87′−σ85′ = 0.00259 cm−1 for 52P12.

Journal of the Optical Society of America•Feb 1, 1971•41 citations
We examine a monochromatic absorption line in the velocity-nonselective excitation of atoms when the components of the hyperfine stricture of the electronic ground states are optically pumped. We show that the absorption lines possess unusual substructures for some values of the hyperfine splitting of the ground state (which exceed the Doppler absorption linewidth severalfold). These substructures in the absorption spectrum are most apparent if the hyperfine structure of the excited electronic state is taken into account. We calculate the absorption spectra of monochromatic light near the D 1 and D 2 lines of atomic rubidium 85,87 Rb. With real hyperfine splitting taken into account, the D 1 and D 2 lines are modeled by 4-and 6-level diagrams, respectively. Finally, we show that atomic rubidium vapor can be successfully used to observe the spectral features experimentally.
The ground electronic state of even such simple atoms as those of alkali elements has the set of sublevels. These sublevels are hyperfine (HF) components and magnetic sublevels. The collisions with particles of nonmagnetic buffer gas or even with walls (when walls have proper coating) do not mix practically the populations of ground state HF sublevels, if the orbital moment of electrons in the ground state is equal to zero. Due to this reason these sublevels may be extremely long lived. Because of this, for instance, the so-called effects of optical orientation and optical pumping are apparent in atoms of alkali metals. The radiation can pump practically all the atoms (with which there is effective interaction) to a single HF component. In a situation in which optical pumping is a minor effect, the monochromatic absorption line consists of separate lines corresponding to intra-atomic transitions. The optical pumping is not significant, for example, if the radiation intensity is so low that now pumping between HF sublevels occurs in the time it takes the atom to traverse the light beam. Under the conditions of optical pumping and when other nonlinear effects are present, the absorption line profile can undergo considerable alteration. Many theoretical and experimental investigations have been done in the laser spectroscopy of resonant transitions of atoms (atoms of alkali metals) under the conditions of optical pumping within ground state HF structure. A characteristic feature of all such investigations is the velocity-selective excitation of absorbing atoms. Also, as a rule, the value of HF splitting is not very big in comparison to Doppler broadening in these experiments. Under such conditions, the absorption spectra consists of Doppler- broadened lines with nonlinear resonances, which emerge when two fields of different frequencies or different propagation directions are employed. When only one monochromatic traveling wave is employed, optical pumping leads to formation of a single smooth absorption line occupying a position between the resonant transitions frequencies associated with HF components. As HF splitting grows, the line profile remains smooth, its width is approximately equal to the size of the HF splitting. The strength of the optical pumping from one ground state HF component to another is greater for greater HF splitting in comparison to the Doppler width. In this regard, Cs and Rb are the most typical of the alkali atoms (the HF splitting exceeds the Doppler width by a factor close to 20). This is the qualitative picture of the absorption line profile (particularly for a monochromatic radiation) under the conditions of optical pumping between the HF sublevels of the electronic ground state, this qualitative picture had formed by now.
The goal of this experiment was to measure the hyperfine energy splittings of the ground to first excited state transitions in rubidium using saturated absorption spectroscopy. Using this technique, we measured these transition energy spectra by taking the difference of two photodiode outputs due to multiple beams of a single laser scanned over a range of frequencies and shone through a cell of Rb vapor. When the laser frequency was resonant with an atomic transition, photons of those frequencies were absorbed, leaving a dip in intensity of the beam measured at the photodiode. One of the two laser beams had its excitations saturated by a more intense, counter-propagating pump beam from the same laser. The pump beam saturated the absorption of the velocity equal zero atoms that the counter-propagating probe beam could have also interacted with due to no Doppler shift. At these frequencies the probe beam experienced less absorption that was measured by a photodiode. The photodiode output was calibrated to the change in frequency of the scanned laser using a Fabry-Pérot interferometer. The output of this interferometer served as a reference for how the laser frequency changed. Final results for the 87Rb F=1 spectrum accounted for the largest error with a maximum of 12.2% deviation from accepted energy spacing values due in part to systematic error. Other spectra measurements were in better agreement, possessing error ranging from 2.1% to 10.1% and some agreeing with accepted values to within our uncertainty.
Absorption spectrum of the evanescent light at a glass/Rb vapor interface has been observed with atom density from 9 ×10 19 m -3 to 5 ×10 20 m -3 . Absorption is as high as 60% at the peak of a hyperfine structure split line. The absorption spectrum of the experiment is compared with that of the calculation based on Fresnel's relation on the assumption of a homogeneous electric susceptibility of the vapor. Near the critical angle the calculation which incorporates the Lorentz–Lorenz local-field correction reproduces the experimental red shift only partly.
The detection of narrow and high-amplitude optical resonances in atomic cells is of crucial importance for the development of compact and high-stability lasers or vapor-cell optical references. In this work, using monochromatic light and appropriate polarization settings for the counterpropagating pump and probe beams, we demonstrate the detection of enhanced-absorption sub-Doppler resonances on the D1{D}_{1}D1​ line of the Rb\mathrm{Rb}Rb atom. We report a theoretical model showing that the Zeeman coherence induced between magnetic sublevels---especially in the $F\ensuremath{\rightarrow}{F}^{\ensuremath{'}}=F\ensuremath{-}1$ systems, with FFF and ${F}^{\ensuremath{'}}$ being the hyperfine quantum numbers of the ground and excited states, respectively---plays a key role in the observed enhanced-absorption process. The theoretically predicted behavior matches the experimental observations well. The impact of light polarization, laser intensity, magnetic field, and cell temperature on the Doppler-free resonance features is experimentally investigated. For application, two identical diode lasers are frequency-stabilized onto enhanced-absorption sub-Doppler resonances. The fractional frequency stability of the laser beatnote is measured to be $1.8\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}12}$ at 1s1\phantom{\rule{0.1em}{0ex}}\mathrm{s}1s and $8.4\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}12}$ at 104s{10}^{4}\phantom{\rule{0.1em}{0ex}}\mathrm{s}104s. These results demonstrate the potential of this scheme for the implementation of a compact or even chip-scale optical frequency reference, which might find applications in instrumentation, navigation, and metrology.
Using an external cavity-tuned diode laser in Doppler-free saturation spectroscopy, we are able to resolve the weak-field Zeeman splittings in the hyperfine levels of the rubidium D1 line. The number of lines observed in the Zeeman structure of rubidium and their measured energy-level splittings are as expected from theory. The measured amplitudes of the saturated-absorption signals, crossover resonances, and velocity-selective optical pumping signals are used in the analysis of various theories concerning saturated-absorption spectroscopy.
We have developed a rubidium atomic-beam light source that emits Rb lines with a Doppler width of only 0.0015 cm−1. When the light from this source was measured with a scanning Fabry–Perot interferometer and the data were reduced by digital computer utilizing numerical deconvolution techniques, we were able to determine a hyperfine level splitting in natural rubidium as small as 0.0014 cm−1 with an uncertainty of 0.0001 cm−1. We have measured the relative intensities and positions of 19 of the 20 hfs components of the two resonance lines, 7800 and 7974 Å, of natural Rb. From these data, we calculate isotope shifts σ87−σ85 = 0.00268 cm−1 for 52P32 and σ87′−σ85′ = 0.00259 cm−1 for 52P12.