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

arXiv:0909.5081 · Physical Review A

Nonlinear magneto-optical resonances at D1 excitation of Rb85 and Rb87 in an extremely thin cell

Marcis P. Auzinsh, R. Ferber, F. Gahbauer, Andrey Jarmola, L. Kalvāns, A. Papoyan, David G. Sarkisyan

Published Mar 17, 2010• 10 citations
arXivHTMLPDF

Abstract

Nonlinear magneto-optical resonances have been measured in an extremely thin cell (ETC) for the ${D}_{1}$ transition of rubidium in an atomic vapor of natural isotopic composition. All hyperfine transitions of both isotopes have been studied for a wide range of laser power densities, laser detunings, and ETC wall separations. Dark resonances in the laser induced fluorescence (LIF) were observed as expected when the ground-state total angular momentum ${F}_{g}$ was greater than or equal to the excited-state total angular momentum ${F}_{e}$. Unlike the case of ordinary cells, the width and contrast of dark resonances formed in the ETC dramatically depended on the detuning of the laser from the exact atomic transition. A theoretical model based on the optical Bloch equations was applied to calculate the shapes of the resonance curves. The model, which had been developed previously for ordinary vapor cells, averaged over the contributions from different atomic velocity groups, considered all neighboring hyperfine transitions, took into account the splitting and mixing of magnetic sublevels in an external magnetic field, and included a detailed treatment of the coherence properties of the laser radiation. Such a theoretical approach had successfully described nonlinear magneto-optical resonances in ordinary vapor cells. However, to describe the resonances in the ETC, key parameters such as the ground-state relaxation rate, excited-state relaxation rate, Doppler width, and Rabi frequency had to be modified significantly in accordance with the ETC's unique features. The level of agreement between the measured and calculated resonance curves achieved for the ETC was similar to what could be accomplished for ordinary cells. However, in the case of the ETC, it was necessary to fine-tune parameters such as the background and the Rabi frequency for different transitions, whereas for the ordinary cells, these parameters were identical for all transitions.

DOI
10.1103/physreva.81.033408

Related papers

Nonlinear magneto-optical resonances at D1 excitation of R85b and R87b for partially resolved hyperfine F levels

Marcis P. Auzinsh, R. Ferber, F. Gahbauer +2 more

Experimental signals of nonlinear magneto-optical resonances at ${D}_{1}$ excitation of natural rubidium in a vapor cell have been obtained and described with experimental accuracy by a detailed theoretical model based on the optical Bloch equations. The ${D}_{1}$ transition of rubidium is a challenging system to analyze theoretically because it contains transitions that are only partially resolved under Doppler broadening. The theoretical model took into account all nearby transitions, the coherence properties of the exciting laser radiation, and the mixing of magnetic sublevels in an external magnetic field and also included averaging over the Doppler profile. The experimental signals were reproduced very well at each hyperfine transition and over a wide range of laser power densities, beam diameters, and laser detunings from the exact transition frequency. The bright resonance expected at the ${F}_{g}=1\ensuremath{\rightarrow}{F}_{e}=2$ transition of $^{87}\text{R}\text{b}$ has been observed. A bright resonance was observed at the ${F}_{g}=2\ensuremath{\rightarrow}{F}_{e}=3$ transition of $^{85}\text{R}\text{b}$, but displaced from the exact position of the transition due to the influence of the nearby ${F}_{g}=2\ensuremath{\rightarrow}{F}_{e}=2$ transition, which is a dark resonance whose contrast is almost 2 orders of magnitude larger than the contrast of the bright resonance at the ${F}_{g}=2\ensuremath{\rightarrow}{F}_{e}=3$ transition. Even in this very delicate situation, the theoretical model described in detail the experimental signals at different laser detunings.

arXiv:0903.0524•Physical Review A•May 6, 2009•32 citations

Conversion of bright magneto-optical resonances into dark resonances at fixed laser frequency for D2 excitation of atomic rubidium

Marcis P. Auzinsh, Andris Bērziņš, R. Ferber +4 more

Nonlinear magneto-optical resonances on the hyperfine transitions belonging to the ${D}_{2}$ line of rubidium were changed from bright to dark resonances by changing the laser power density of the single exciting laser field or by changing the vapor temperature in the cell. In one set of experiments atoms were excited by linearly polarized light from an extended cavity diode laser with polarization vector perpendicular to the light's propagation direction and magnetic field, and laser-induced fluorescence was observed along the direction of the magnetic field, which was scanned. A low-contrast bright resonance was observed at low laser power densities when the laser was tuned to the ${F}_{g}=2\ensuremath{\rightarrow}{F}_{e}=3$ transition of ${}^{87}$Rb and near to the ${F}_{g}=3\ensuremath{\rightarrow}{F}_{e}=4$ transition of ${}^{85}$Rb. The bright resonance became dark as the laser power density was increased above 0.6 mW/cm${}^{2}$ or 0.8 mW/cm${}^{2}$, respectively. When the ${F}_{g}=2\ensuremath{\rightarrow}{F}_{e}=3$ transition of ${}^{87}$Rb was excited with circularly polarized light in a second set of experiments, a bright resonance was observed, which became dark when the temperature was increased to around 50${}^{\phantom{\rule{0.16em}{0ex}}\ensuremath{\circ}}$C. The experimental observations at room temperature could be reproduced with good agreement by calculations based on a theoretical model, although the theoretical model was not able to describe measurements at elevated temperatures, where reabsorption was thought to play a decisive role. The model was derived from the optical Bloch equations and included all nearby hyperfine components, averaging over the Doppler profile, mixing of magnetic sublevels in the external magnetic field, and a treatment of the coherence properties of the exciting radiation field.

arXiv:1111.6432•Physical Review A•Mar 16, 2012•22 citations

Relaxation mechanisms affecting magneto-optical resonances in an extremely thin cell: Experiment and theory for the cesium D1 line

Marcis P. Auzinsh, Andris Bērziņš, R. Ferber +5 more

We have measured magneto-optical signals obtained by exciting the ${D}_{1}$ line of cesium atoms confined to an extremely thin cell (ETC), whose walls are separated by less than $1\ensuremath{\mu}\text{m}$, and developed an improved theoretical model to describe these signals with experimental precision. The theoretical model was based on the optical Bloch equations and included all neighboring hyperfine transitions, the mixing of the magnetic sublevels in an external magnetic field, and the Doppler effect, as in previous studies. However, in order to model the extreme conditions in the ETC more realistically, the model was extended to include a unified treatment of transit relaxation and wall collisions with relaxation rates that were obtained directly from the thermal velocities of the atoms and the length scales involved. Furthermore, the interactions of the atoms with different regions of the laser beam were modeled separately to account for the varying laser beam intensity over the beam profile as well as saturation effects that become important near the center of the beam at the relatively high laser intensities used during the experiments in order to obtain measurable signals. The model described the experimentally measured signals for laser intensities for magnetic fields up to 55 G and laser intensities up to $1{\text{W/cm}}^{2}$ with excellent agreement.

arXiv:1411.2750•Physical Review A•Feb 10, 2015•7 citations

F -resolved magneto-optical resonances in the D1 excitation of cesium: Experiment and theory

Marcis P. Auzinsh, R. Ferber, F. Gahbauer +2 more

Bright and dark nonlinear magneto-optical resonances associated with the ground state Hanle effect have been studied experimentally and theoretically for ${D}_{1}$ excitation of atomic cesium. This system offers the advantage that the separation between the different hyperfine levels exceeds the Doppler width, and hence transitions between individual levels can be studied separately. At the same time, the system retains the advantages offered by ordinary glass cells, including simplicity and subnatural width Hanle resonances. Experimental measurements for various laser power densities and transit relaxation times are compared with a model based on the optical Bloch equations, which averages over the Doppler contour of the absorption line and simultaneously takes into account all hyperfine levels, as well as mixing of magnetic sublevels in an external magnetic field. In contrast to previous studies, which could not resolve the hyperfine transitions because of Doppler broadening, in this study there is excellent agreement between experiment and theory regarding the sign (bright or dark), contrast and width of the resonance. The results support the traditional theoretical interpretation, according to which these effects are related to the relative strengths of transition probabilities between different magnetic sublevels in a given hyperfine transition.

arXiv:0803.0201•Physical Review A•Jul 23, 2008•26 citations

Ground-state magneto-optical resonances in cesium vapor confined in an extremely thin cell

C. Andreeva, Aigars Atvars, Marcis P. Auzinsh +4 more

Experimental and theoretical studies are presented related to the ground-state magneto-optical resonance observed in cesium vapor confined in an extremely thin cell (ETC), with thickness equal to the wavelength of the irradiating light. It is shown that utilization of the ETC allows one to examine the formation of a magneto-optical resonance on the individual hyperfine transitions, thus distinguishing processes resulting in dark (reduced absorption) or bright (enhanced absorption) resonance formation. We report experimental evidence of bright magneto-optical resonance sign reversal in Cs atoms confined in an ETC. A theoretical model is proposed based on the optical Bloch equations that involves the elastic interaction processes of atoms in the ETC with its walls, resulting in depolarization of the Cs excited state, which is polarized by the exciting radiation. This depolarization leads to the sign reversal of the bright resonance. Using the proposed model, the magneto-optical resonance amplitude and width as a function of laser power are calculated and compared with the experimental ones. The numerical results are in good agreement with those of experiment.

arXiv:0704.3010•Physical Review A•Dec 10, 2007•17 citations

Dependence of the shapes of nonzero-field level-crossing signals in rubidium atoms on the laser frequency and power density

Marcis P. Auzinsh, Andris Bērziņš, R. Ferber +4 more

We studied magneto-optical resonances caused by excited-state level crossings in a nonzero magnetic field. Experimental measurements were performed on the transitions of the ${D}_{2}$ line of rubidium. These measured signals were described by a theoretical model that takes into account all neighboring hyperfine transitions, the mixing of magnetic sublevels in an external magnetic field, the coherence properties of the exciting laser radiation, and the Doppler effect. Good agreement between the experimental measurements and the theoretical model could be achieved over a wide range of laser power densities. We further showed that the contrasts of the level-crossing peaks can be sensitive to changes in the frequency of the exciting laser radiation as small as several tens of megahertz when the hyperfine splitting of the exciting state is larger than the Doppler broadening.

arXiv:1301.0548•Physical Review A•Mar 12, 2013•9 citations
Nonlinear magneto-optical resonances have been measured in an extremely thin cell (ETC) for the D1{D}_{1}D1​ transition of rubidium in an atomic vapor of natural isotopic composition. All hyperfine transitions of both isotopes have been studied for a wide range of laser power densities, laser detunings, and ETC wall separations. Dark resonances in the laser induced fluorescence (LIF) were observed as expected when the ground-state total angular momentum Fg{F}_{g}Fg​ was greater than or equal to the excited-state total angular momentum Fe{F}_{e}Fe​. Unlike the case of ordinary cells, the width and contrast of dark resonances formed in the ETC dramatically depended on the detuning of the laser from the exact atomic transition. A theoretical model based on the optical Bloch equations was applied to calculate the shapes of the resonance curves. The model, which had been developed previously for ordinary vapor cells, averaged over the contributions from different atomic velocity groups, considered all neighboring hyperfine transitions, took into account the splitting and mixing of magnetic sublevels in an external magnetic field, and included a detailed treatment of the coherence properties of the laser radiation. Such a theoretical approach had successfully described nonlinear magneto-optical resonances in ordinary vapor cells. However, to describe the resonances in the ETC, key parameters such as the ground-state relaxation rate, excited-state relaxation rate, Doppler width, and Rabi frequency had to be modified significantly in accordance with the ETC's unique features. The level of agreement between the measured and calculated resonance curves achieved for the ETC was similar to what could be accomplished for ordinary cells. However, in the case of the ETC, it was necessary to fine-tune parameters such as the background and the Rabi frequency for different transitions, whereas for the ordinary cells, these parameters were identical for all transitions.
Experimental signals of nonlinear magneto-optical resonances at D1{D}_{1}D1​ excitation of natural rubidium in a vapor cell have been obtained and described with experimental accuracy by a detailed theoretical model based on the optical Bloch equations. The D1{D}_{1}D1​ transition of rubidium is a challenging system to analyze theoretically because it contains transitions that are only partially resolved under Doppler broadening. The theoretical model took into account all nearby transitions, the coherence properties of the exciting laser radiation, and the mixing of magnetic sublevels in an external magnetic field and also included averaging over the Doppler profile. The experimental signals were reproduced very well at each hyperfine transition and over a wide range of laser power densities, beam diameters, and laser detunings from the exact transition frequency. The bright resonance expected at the ${F}_{g}=1\ensuremath{\rightarrow}{F}_{e}=2$ transition of 87Rb^{87}\text{R}\text{b}87Rb has been observed. A bright resonance was observed at the ${F}_{g}=2\ensuremath{\rightarrow}{F}_{e}=3$ transition of 85Rb^{85}\text{R}\text{b}85Rb, but displaced from the exact position of the transition due to the influence of the nearby ${F}_{g}=2\ensuremath{\rightarrow}{F}_{e}=2$ transition, which is a dark resonance whose contrast is almost 2 orders of magnitude larger than the contrast of the bright resonance at the ${F}_{g}=2\ensuremath{\rightarrow}{F}_{e}=3$ transition. Even in this very delicate situation, the theoretical model described in detail the experimental signals at different laser detunings.
Nonlinear magneto-optical resonances on the hyperfine transitions belonging to the D2{D}_{2}D2​ line of rubidium were changed from bright to dark resonances by changing the laser power density of the single exciting laser field or by changing the vapor temperature in the cell. In one set of experiments atoms were excited by linearly polarized light from an extended cavity diode laser with polarization vector perpendicular to the light's propagation direction and magnetic field, and laser-induced fluorescence was observed along the direction of the magnetic field, which was scanned. A low-contrast bright resonance was observed at low laser power densities when the laser was tuned to the ${F}_{g}=2\ensuremath{\rightarrow}{F}_{e}=3$ transition of 87{}^{87}87Rb and near to the ${F}_{g}=3\ensuremath{\rightarrow}{F}_{e}=4$ transition of 85{}^{85}85Rb. The bright resonance became dark as the laser power density was increased above 0.6 mW/cm2{}^{2}2 or 0.8 mW/cm2{}^{2}2, respectively. When the ${F}_{g}=2\ensuremath{\rightarrow}{F}_{e}=3$ transition of 87{}^{87}87Rb was excited with circularly polarized light in a second set of experiments, a bright resonance was observed, which became dark when the temperature was increased to around 50${}^{\phantom{\rule{0.16em}{0ex}}\ensuremath{\circ}}$C. The experimental observations at room temperature could be reproduced with good agreement by calculations based on a theoretical model, although the theoretical model was not able to describe measurements at elevated temperatures, where reabsorption was thought to play a decisive role. The model was derived from the optical Bloch equations and included all nearby hyperfine components, averaging over the Doppler profile, mixing of magnetic sublevels in the external magnetic field, and a treatment of the coherence properties of the exciting radiation field.
We have measured magneto-optical signals obtained by exciting the D1{D}_{1}D1​ line of cesium atoms confined to an extremely thin cell (ETC), whose walls are separated by less than $1\ensuremath{\mu}\text{m}$, and developed an improved theoretical model to describe these signals with experimental precision. The theoretical model was based on the optical Bloch equations and included all neighboring hyperfine transitions, the mixing of the magnetic sublevels in an external magnetic field, and the Doppler effect, as in previous studies. However, in order to model the extreme conditions in the ETC more realistically, the model was extended to include a unified treatment of transit relaxation and wall collisions with relaxation rates that were obtained directly from the thermal velocities of the atoms and the length scales involved. Furthermore, the interactions of the atoms with different regions of the laser beam were modeled separately to account for the varying laser beam intensity over the beam profile as well as saturation effects that become important near the center of the beam at the relatively high laser intensities used during the experiments in order to obtain measurable signals. The model described the experimentally measured signals for laser intensities for magnetic fields up to 55 G and laser intensities up to 1W/cm21{\text{W/cm}}^{2}1W/cm2 with excellent agreement.
Bright and dark nonlinear magneto-optical resonances associated with the ground state Hanle effect have been studied experimentally and theoretically for D1{D}_{1}D1​ excitation of atomic cesium. This system offers the advantage that the separation between the different hyperfine levels exceeds the Doppler width, and hence transitions between individual levels can be studied separately. At the same time, the system retains the advantages offered by ordinary glass cells, including simplicity and subnatural width Hanle resonances. Experimental measurements for various laser power densities and transit relaxation times are compared with a model based on the optical Bloch equations, which averages over the Doppler contour of the absorption line and simultaneously takes into account all hyperfine levels, as well as mixing of magnetic sublevels in an external magnetic field. In contrast to previous studies, which could not resolve the hyperfine transitions because of Doppler broadening, in this study there is excellent agreement between experiment and theory regarding the sign (bright or dark), contrast and width of the resonance. The results support the traditional theoretical interpretation, according to which these effects are related to the relative strengths of transition probabilities between different magnetic sublevels in a given hyperfine transition.
Experimental and theoretical studies are presented related to the ground-state magneto-optical resonance observed in cesium vapor confined in an extremely thin cell (ETC), with thickness equal to the wavelength of the irradiating light. It is shown that utilization of the ETC allows one to examine the formation of a magneto-optical resonance on the individual hyperfine transitions, thus distinguishing processes resulting in dark (reduced absorption) or bright (enhanced absorption) resonance formation. We report experimental evidence of bright magneto-optical resonance sign reversal in Cs atoms confined in an ETC. A theoretical model is proposed based on the optical Bloch equations that involves the elastic interaction processes of atoms in the ETC with its walls, resulting in depolarization of the Cs excited state, which is polarized by the exciting radiation. This depolarization leads to the sign reversal of the bright resonance. Using the proposed model, the magneto-optical resonance amplitude and width as a function of laser power are calculated and compared with the experimental ones. The numerical results are in good agreement with those of experiment.
We studied magneto-optical resonances caused by excited-state level crossings in a nonzero magnetic field. Experimental measurements were performed on the transitions of the D2{D}_{2}D2​ line of rubidium. These measured signals were described by a theoretical model that takes into account all neighboring hyperfine transitions, the mixing of magnetic sublevels in an external magnetic field, the coherence properties of the exciting laser radiation, and the Doppler effect. Good agreement between the experimental measurements and the theoretical model could be achieved over a wide range of laser power densities. We further showed that the contrasts of the level-crossing peaks can be sensitive to changes in the frequency of the exciting laser radiation as small as several tens of megahertz when the hyperfine splitting of the exciting state is larger than the Doppler broadening.