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arXiv:1411.2750 · Physical Review A

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, F. Gahbauer, U. Kalnins, L. Kalvāns, R. Rundans, David G. Sarkisyan

Published Feb 10, 2015• 7 citations
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Abstract

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.

DOI
10.1103/physreva.91.023410

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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\ensuremathμm1\ensuremath{\mu}\text{m}1\ensuremathμm, 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.
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 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.
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.
Saturation effects affecting absorption and fluorescence spectra of an atomic vapor confined in an extremely thin cell (cell thickness $L<1\phantom{\rule{0.3em}{0ex}}\ensuremath{\mu}\mathrm{m}$) are investigated experimentally and theoretically. The study is performed on the D2{D}_{2}D2​ line $(\ensuremath{\lambda}=852\phantom{\rule{0.3em}{0ex}}\mathrm{nm})$ of Cs and concentrates on the two situations $L=\ensuremath{\lambda}∕2$ and $L=\ensuremath{\lambda}$, the most contrasted ones with respect to the length dependence of the coherent Dicke narrowing. For $L=\ensuremath{\lambda}∕2$, the Dicke-narrowed absorption profile simply broadens and saturates in amplitude when increasing the light intensity, while for $L=\ensuremath{\lambda}$, sub-Doppler dips of reduced absorption at the line-center appear on the broad absorption profile. For a fluorescence detection at $L=\ensuremath{\lambda}$, saturation induces narrow dips, but only for hyperfine components undergoing a population loss through optical pumping. These experimental results are interpreted with the help of the various existing models and are compared with numerical calculations based upon a two-level modeling that considers both a closed and an open system.
The intensity dependent absorption was measured on the line (6 transition) in atomic cesium. The magnetic field applied to the vapour and the spatial cross section of the laser beam were controlled and varied during data collection. A three-level rate equation model is presented in an attempt to explain the results. We show that this well known approach does not sucessfully model the data obtained in the absence of a magnetic field. Hence, a more complex and complete model that explicitly includes all of the hyperfine magnetic sublevels (a multilevel model) is presented. This approach accurately models all of the data collected. The good agreement betweeen this model and the data allows the determination of the transit relaxation rate (due to atomic time of flight through the laser beam), , where is the two-dimensional root-mean-squared speed of the atom and D is the FWHM of the Gaussian laser beam spatial profile.