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

Line Shape of the Sub-Doppler Resonance in Alkali-Metal Atomic Vapors in the Field of Counterpropagating Bichromatic Laser Beams

А. М. Михайлов, Rodolphe Boudot, Denis V. Brazhnikov

Published Dec 1, 2021• 7 citations
Publisher

Abstract

Abstract High-contrast sub-Doppler resonances observed in alkali-metal atomic vapors in the field of counterpropagating bichromatic laser beams are perspective in quantum metrology for designing a miniature optical frequency standard. Until now, these nonlinear resonances have been investigated only experimentally or using numerical calculations. In our opinion, the development of a simplified theoretical model of the observed resonances, which would provide explicit compact analytic expressions describing the line shape of the resonance, would be extremely important for further evolution of the theory. In this study, we perform such theoretical analysis based on the three-level Λ scheme of the atom. We investigate two regimes, viz., the regime of a low-intensity standing wave with close intensities of counterpropagating beams (I1 ≈ I2) and the regime of a probe wave, in which one of the beams has a noticeably lower intensity than that of the oppositely propagating beam (I2 ≪ I1). The resulting analytic expressions make it possible to determine qualitative differences between these regimes and to separate explicitly the contributions from different nonlinear effects to the light field absorption, including the terms responsible for the formation of a high-contrast sub-Doppler peak. The expressions derived here are in qualitative agreement with experimental data obtained earlier.

DOI
10.1134/s106377612112013x

Related papers

Theory of Sub-Doppler Spectroscopy of Alkali Metal Vapors in the Field of Counterpropagating Bichromatic Laser Beams: Probe Beam Regime

A. M. Mikhailov, Denis V. Brazhnikov

Sub-Doppler resonances observed in miniature cells ($V \ll 1 cm^3$) with Rb or Cs atoms in the field of counterpropagating bichromatic laser beams are of interest for the creation of a miniature quantum frequency standard (QFS) of the optical range. However, a theory of these resonances that takes into full account the real structure of energy levels in an atom has not yet been constructed, which would make it possible to obtain explicit analytical expressions for the absorption coefficient of the medium. This paper addresses this gap using the density matrix formalism and the algebra of irreducible tensor operators. Namely, we obtained an analytical expression for the absorption coefficient of the probe beam in the presence of a more intense counterpropagating beam (pump-probe regime). Moreover, the calculations were carried out for arbitrary parameters of laser beam polarization, arbitrary angular momenta of optical dipole transitions in the atom and various relaxation processes. The constructed theory allows us to correctly take into account the simultaneous action of various nonlinear optical effects, in contrast to the simplified three-level model of the atom, and also to investigate the partial contribution of each of them to the overall observed resonant circuit. The analysis performed, in particular, made it possible to predict an increase in the amplitude of the sub-Doppler resonance when using counterpropagating light beams with opposite circular polarizations in relation to the configuration of counterpropagating beams with orthogonal linear polarizations, which is often used in practice.

arXiv:2610.18372•Oct 13, 2026•0 citations

Dual-frequency sub-Doppler spectroscopy: Extended theoretical model and microcell-based experiments

Denis V. Brazhnikov, Michael Petersen, Grégoire Coget +4 more

Sub-Doppler spectroscopy in alkali-metal vapor cells using two counterpropagating dual-frequency laser beams allows the detection of high-contrast sign-reversed natural-linewidth sub-Doppler resonances. Previously, a qualitative theory based on a simplified \ensuremath{\Lambda}-scheme model has been reported to explain underlying physics of this phenomenon. In this paper, an extended theoretical model of dual-frequency sub-Doppler spectroscopy (DFSDS) for the Cs ${D}_{1}$ line is reported. Taking into account the real atomic energy structure, main relaxation processes, and various nonlinear effects, this model describes quantitatively the respective contributions of involved physical processes and predicts main properties (height and linewidth) of the sub-Doppler resonances. Experimental tests are performed with a Cs vapor microfabricated cell and results are found to be in correct agreement with theoretical predictions. Spatial oscillations of the sub-Doppler resonance amplitude with translation of the reflection mirror are highlighted. A beat note between two laser systems, including one stabilized with DFSDS on a Cs vapor microcell, yields a fractional frequency stability of $2\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}12}\phantom{\rule{0.16em}{0ex}}{\ensuremath{\tau}}^{\ensuremath{-}1/2}$ until 10-s averaging time. These results demonstrate that DFSDS could be an interesting approach for the development of a high-performance microcell-based optical frequency reference, with applications in various compact quantum devices.

arXiv:1812.09641•Physical Review A•Jun 17, 2019•36 citations

Two-frequency sub-Doppler spectroscopy of the caesium D1 line in various configurations of counterpropagating laser beams

Denis V. Brazhnikov, S M Ignatovich, I. S. Mesenzova +3 more

Abstract Sub-Doppler resonances in caesium vapours are studied in a laser field produced by counterpropagating two-frequency light beams with mutually orthogonal linear polarisations. The beams are in resonance with optical transitions in the D1 line, the frequency difference of the field spectral components being equal to the hyperfine ground-state splitting in the Cs atom (∼9.2 GHz). It has already been shown that in this configuration, the hypercontrast effect can be observed for sub-Doppler resonances, which makes this configuration promising for the employment in new-generation miniature optical frequency standards. In the present work, two different two-frequency configurations are compared with each other and with the single-frequency configuration widely used in practice for observing saturated absorption resonances. The parameters of nonlinear resonances are measured at various temperatures of caesium vapours and at different optical field intensities. The results of the investigations performed make it possible to find an optimal two-frequency scheme for exciting nonlinear resonances and to estimate a potential of the scheme for its applications in quantum metrology.

Quantum Electronics•Oct 26, 2020•10 citations

Dual structure of saturated absorption resonance at an open atomic transition

В. В. Васильев, Vladimir L Velichansky, Sergei A. Zibrov +4 more

Experiments on open transitions of the D 1 line of alkali metals (Cs and Rb isotopes) reveal the dual structure of saturated absorption resonance in the signal of a high-intensity optical wave in the presence of a low-intensity counterpropagating wave. Theoretical analysis shows that the observed shape of the resonance is associated with the openness of the atomic transition as well as with the Doppler effect for atoms in a gas. The results are of general physical significance for nonlinear spectroscopy and can also find application in metrology (frequency and time standards on open transitions).

Journal of Experimental and Theoretical Physics•May 1, 2011•8 citations

Two-frequency sub-Doppler spectroscopy of the caesium D1 line in various configurations of counterpropagating laser beams

Denis V. Brazhnikov, S M Ignatovich, I. S. Mesenzova +3 more

Sub-Doppler resonances in caesium vapours are studied in a laser field produced by counterpropagating two-frequency light beams with mutually orthogonal linear polarisations. The beams are in resonance with optical transitions in the D1 line, the frequency difference of the field spectral components being equal to the hyperfine ground-state splitting in the Cs atom (≈9.2 GHz). It has already been shown that in this configuration, the hypercontrast effect can be observed for sub-Doppler resonances, which makes this configuration promising for the employment in newgeneration miniature optical frequency standards. In the present work, two different two-frequency configurations are compared with each other and with the single-frequency configuration widely used in practice for observing saturated absorption resonances. The parameters of nonlinear resonances are measured at various temperatures of caesium vapours and at different optical field intensities. The results of the investigations performed make it possible to find an optimal two-frequency scheme for exciting nonlinear resonances and to estimate a potential of the scheme for its applications in quantum metrology.

•Jan 1, 2020•1 citation

Nonlinear enhanced-absorption resonances in compact alkali-vapor cells for applications in quantum metrology

Denis V. Brazhnikov, S M Ignatovich, I. S. Mesenzova +10 more

Abstract We review three laser spectroscopy schemes developed recently for observation of high-contrast enhanced-absorption nonlinear resonances in small alkali-vapor cells. In our experiments, optical transitions within the cesium D1 line are involved and a probe beam transmission is analyzed. The first spectroscopy method is based on the configuration with two-frequency counter propagating beams, which are linearly polarized in orthogonal directions. This configuration provides observation of high-contrast natural-linewidth resonances superimposed on broad Doppler profiles when the laser frequency is scanned. These resonances have good prospects for developing a miniature optical frequency reference. The second scheme involves two-frequency counter propagating beams with equal circular polarizations and provides observation of subnatural-linewidth resonances when the Raman frequency detuning is scanned. We use these resonances for stabilizing the microwave frequency of a local oscillator (≈ 4.6 GHz). Frequency stability of around 6 × l0-12 is achieved at 1-s averaging using a 5-mm length cell. This result makes the technique attractive for developing a miniature frequency standard in thr microwave range. The third configuration exploits single-frequency counter-propagating beams with linear orthogonal polarizations. The ultrahigh-contrast subnatural-linewidth resonances can be observed when the longitudinal magnetic field is scanned around zero. The possible application is discussed of these resonances in vector atomic magnetometry.

Journal of Physics Conference Series•Mar 1, 2021•6 citations
Abstract High-contrast sub-Doppler resonances observed in alkali-metal atomic vapors in the field of counterpropagating bichromatic laser beams are perspective in quantum metrology for designing a miniature optical frequency standard. Until now, these nonlinear resonances have been investigated only experimentally or using numerical calculations. In our opinion, the development of a simplified theoretical model of the observed resonances, which would provide explicit compact analytic expressions describing the line shape of the resonance, would be extremely important for further evolution of the theory. In this study, we perform such theoretical analysis based on the three-level Λ scheme of the atom. We investigate two regimes, viz., the regime of a low-intensity standing wave with close intensities of counterpropagating beams (I1 ≈ I2) and the regime of a probe wave, in which one of the beams has a noticeably lower intensity than that of the oppositely propagating beam (I2 ≪ I1). The resulting analytic expressions make it possible to determine qualitative differences between these regimes and to separate explicitly the contributions from different nonlinear effects to the light field absorption, including the terms responsible for the formation of a high-contrast sub-Doppler peak. The expressions derived here are in qualitative agreement with experimental data obtained earlier.
Sub-Doppler resonances observed in miniature cells (V≪1cm3V \ll 1 cm^3V≪1cm3) with Rb or Cs atoms in the field of counterpropagating bichromatic laser beams are of interest for the creation of a miniature quantum frequency standard (QFS) of the optical range. However, a theory of these resonances that takes into full account the real structure of energy levels in an atom has not yet been constructed, which would make it possible to obtain explicit analytical expressions for the absorption coefficient of the medium. This paper addresses this gap using the density matrix formalism and the algebra of irreducible tensor operators. Namely, we obtained an analytical expression for the absorption coefficient of the probe beam in the presence of a more intense counterpropagating beam (pump-probe regime). Moreover, the calculations were carried out for arbitrary parameters of laser beam polarization, arbitrary angular momenta of optical dipole transitions in the atom and various relaxation processes. The constructed theory allows us to correctly take into account the simultaneous action of various nonlinear optical effects, in contrast to the simplified three-level model of the atom, and also to investigate the partial contribution of each of them to the overall observed resonant circuit. The analysis performed, in particular, made it possible to predict an increase in the amplitude of the sub-Doppler resonance when using counterpropagating light beams with opposite circular polarizations in relation to the configuration of counterpropagating beams with orthogonal linear polarizations, which is often used in practice.
Sub-Doppler spectroscopy in alkali-metal vapor cells using two counterpropagating dual-frequency laser beams allows the detection of high-contrast sign-reversed natural-linewidth sub-Doppler resonances. Previously, a qualitative theory based on a simplified \ensuremath{\Lambda}-scheme model has been reported to explain underlying physics of this phenomenon. In this paper, an extended theoretical model of dual-frequency sub-Doppler spectroscopy (DFSDS) for the Cs D1{D}_{1}D1​ line is reported. Taking into account the real atomic energy structure, main relaxation processes, and various nonlinear effects, this model describes quantitatively the respective contributions of involved physical processes and predicts main properties (height and linewidth) of the sub-Doppler resonances. Experimental tests are performed with a Cs vapor microfabricated cell and results are found to be in correct agreement with theoretical predictions. Spatial oscillations of the sub-Doppler resonance amplitude with translation of the reflection mirror are highlighted. A beat note between two laser systems, including one stabilized with DFSDS on a Cs vapor microcell, yields a fractional frequency stability of $2\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}12}\phantom{\rule{0.16em}{0ex}}{\ensuremath{\tau}}^{\ensuremath{-}1/2}$ until 10-s averaging time. These results demonstrate that DFSDS could be an interesting approach for the development of a high-performance microcell-based optical frequency reference, with applications in various compact quantum devices.
Abstract Sub-Doppler resonances in caesium vapours are studied in a laser field produced by counterpropagating two-frequency light beams with mutually orthogonal linear polarisations. The beams are in resonance with optical transitions in the D1 line, the frequency difference of the field spectral components being equal to the hyperfine ground-state splitting in the Cs atom (∼9.2 GHz). It has already been shown that in this configuration, the hypercontrast effect can be observed for sub-Doppler resonances, which makes this configuration promising for the employment in new-generation miniature optical frequency standards. In the present work, two different two-frequency configurations are compared with each other and with the single-frequency configuration widely used in practice for observing saturated absorption resonances. The parameters of nonlinear resonances are measured at various temperatures of caesium vapours and at different optical field intensities. The results of the investigations performed make it possible to find an optimal two-frequency scheme for exciting nonlinear resonances and to estimate a potential of the scheme for its applications in quantum metrology.
Experiments on open transitions of the D 1 line of alkali metals (Cs and Rb isotopes) reveal the dual structure of saturated absorption resonance in the signal of a high-intensity optical wave in the presence of a low-intensity counterpropagating wave. Theoretical analysis shows that the observed shape of the resonance is associated with the openness of the atomic transition as well as with the Doppler effect for atoms in a gas. The results are of general physical significance for nonlinear spectroscopy and can also find application in metrology (frequency and time standards on open transitions).
Sub-Doppler resonances in caesium vapours are studied in a laser field produced by counterpropagating two-frequency light beams with mutually orthogonal linear polarisations. The beams are in resonance with optical transitions in the D1 line, the frequency difference of the field spectral components being equal to the hyperfine ground-state splitting in the Cs atom (≈9.2 GHz). It has already been shown that in this configuration, the hypercontrast effect can be observed for sub-Doppler resonances, which makes this configuration promising for the employment in newgeneration miniature optical frequency standards. In the present work, two different two-frequency configurations are compared with each other and with the single-frequency configuration widely used in practice for observing saturated absorption resonances. The parameters of nonlinear resonances are measured at various temperatures of caesium vapours and at different optical field intensities. The results of the investigations performed make it possible to find an optimal two-frequency scheme for exciting nonlinear resonances and to estimate a potential of the scheme for its applications in quantum metrology.
Abstract We review three laser spectroscopy schemes developed recently for observation of high-contrast enhanced-absorption nonlinear resonances in small alkali-vapor cells. In our experiments, optical transitions within the cesium D1 line are involved and a probe beam transmission is analyzed. The first spectroscopy method is based on the configuration with two-frequency counter propagating beams, which are linearly polarized in orthogonal directions. This configuration provides observation of high-contrast natural-linewidth resonances superimposed on broad Doppler profiles when the laser frequency is scanned. These resonances have good prospects for developing a miniature optical frequency reference. The second scheme involves two-frequency counter propagating beams with equal circular polarizations and provides observation of subnatural-linewidth resonances when the Raman frequency detuning is scanned. We use these resonances for stabilizing the microwave frequency of a local oscillator (≈ 4.6 GHz). Frequency stability of around 6 × l0-12 is achieved at 1-s averaging using a 5-mm length cell. This result makes the technique attractive for developing a miniature frequency standard in thr microwave range. The third configuration exploits single-frequency counter-propagating beams with linear orthogonal polarizations. The ultrahigh-contrast subnatural-linewidth resonances can be observed when the longitudinal magnetic field is scanned around zero. The possible application is discussed of these resonances in vector atomic magnetometry.