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Physical Review A

Antirelaxation coatings in coherent spectroscopy: Theoretical investigation and experimental test

K. A. Nasyrov, Silvia Gozzini, A. Lucchesini, C. Marinelli, S. Gateva, S. Cartaleva, Luca Marmugi

Published Oct 2, 2015• 31 citations
Publisher

Abstract

We describe a theoretical model, based on a density matrix and the Liouville equation, for the investigation of magneto-optical resonances in alkali-metal atomic vapor, in particular in the case of the electromagnetically induced transparency (EIT) in the presence of antirelaxation coatings. The influence of the coating is parametrized with an empirical coefficient describing its efficiency; the calculations are extended to a broad range of coating quality, contrary to previous works, and to uncoated cells. The model takes into account also different configurations for the EIT formation and different efficiency of optical pumping, as determined by the coating characteristics and the atomic energy structure. The model is validated by investigating the EIT with degenerate Zeeman levels in $^{39}\text{K} {D}_{1}$ and Cs ${D}_{2}$ lines, which exhibit respectively an almost negligible and a relevant impact of hyperfine optical pumping. The results are compared to experimental data, exhibiting good agreement; in particular, for the $^{39}\text{K} {D}_{1}$ line, recent findings are shown here in the case of degenerate and nondegenerate EIT with amplitude-modulated light. Our results demonstrate an effective approach for the investigation of antirelaxation coatings and their contribution in the formation of magneto-optical resonances in alkali-metal atoms, in different regimes and with largely different efficiencies. This sheds new light on well-known but not yet entirely clarified phenomena and their behavior as a function of experimental parameters.

DOI
10.1103/physreva.92.043803

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We describe a theoretical model, based on a density matrix and the Liouville equation, for the investigation of magneto-optical resonances in alkali-metal atomic vapor, in particular in the case of the electromagnetically induced transparency (EIT) in the presence of antirelaxation coatings. The influence of the coating is parametrized with an empirical coefficient describing its efficiency; the calculations are extended to a broad range of coating quality, contrary to previous works, and to uncoated cells. The model takes into account also different configurations for the EIT formation and different efficiency of optical pumping, as determined by the coating characteristics and the atomic energy structure. The model is validated by investigating the EIT with degenerate Zeeman levels in 39KD1^{39}\text{K} {D}_{1}39KD1​ and Cs D2{D}_{2}D2​ lines, which exhibit respectively an almost negligible and a relevant impact of hyperfine optical pumping. The results are compared to experimental data, exhibiting good agreement; in particular, for the 39KD1^{39}\text{K} {D}_{1}39KD1​ line, recent findings are shown here in the case of degenerate and nondegenerate EIT with amplitude-modulated light. Our results demonstrate an effective approach for the investigation of antirelaxation coatings and their contribution in the formation of magneto-optical resonances in alkali-metal atoms, in different regimes and with largely different efficiencies. This sheds new light on well-known but not yet entirely clarified phenomena and their behavior as a function of experimental parameters.
Abstract Destruction of the laser-induced coherence in the ground state of alkali atoms manifests itself as an ultra-narrow resonance in the atomic spectrum. Depending on the geometry of irradiation and observation, the coherent spectroscopy studies CPT (coherent population trapping), EIT (electromagnetically-induced transparency) or EIA (electromagnetically-induced absorption). In the present work, we investigated EIA on the D1 87Rb line by applying a counter-propagating dual-beam scheme. The main advantage of this scheme is the high resonance contrast – an important parameter for many applications. In our previous work performed in a paraffin-coated cell we observed that, unlike the resonance in buffer gas cell detected in the same experimental scheme, the EIA signal has a complex form, because it is formed by two atomic sub-ensembles in the vapor cell with different relaxation rates determined by the laser excitation conditions. We focused on the narrow component, since it has a higher amplitude-width ratio, making it preferable for applications. We investigate the influence of the atomic vapor density and the pump laser intensity on the resonance parameters in order to optimize the amplitude ratio of the wide and narrow components and achieve the highest amplitude-width ratio value for the narrow component of the EIA resonance.
Nonlinear magneto-optical Faraday rotation (NMOR) on the potassium D1 and D2 lines was used to study Zeeman relaxation rates in an antirelaxation paraffin-coated $3\text{\ensuremath{-}}\mathrm{cm}$-diameter potassium vapor cell. Intrinsic Zeeman relaxation rates of ${\ensuremath{\gamma}}^{NMOR}∕2\ensuremath{\pi}=2.0(6)\phantom{\rule{0.3em}{0ex}}\mathrm{Hz}$ were observed. The relatively small hyperfine intervals in potassium lead to significant differences in NMOR in potassium compared to rubidium and cesium. Using laser optical pumping, widths and frequency shifts were also determined for transitions between ground-state hyperfine sublevels of 39K^{39}\mathrm{K}39K atoms contained in the same paraffin-coated cell. The intrinsic hyperfine relaxation rate of ${\ensuremath{\gamma}}_{\mathit{expt}}^{\mathit{hf}}∕2\ensuremath{\pi}=10.6(7)\phantom{\rule{0.3em}{0ex}}\mathrm{Hz}$ and a shift of $\ensuremath{-}9.1(2)\phantom{\rule{0.3em}{0ex}}\mathrm{Hz}$ were observed. These results show that adiabatic relaxation gives only a small contribution to the overall hyperfine relaxation in the case of potassium, and the relaxation is dominated by other mechanisms similar to those observed in previous studies with rubidium.
It is predicted theoretically that the combination of elliptically polarized radiation and an antirelaxation coating of the walls of a vacuum cell containing alkali metal vapor provides an asymmetric shape of the magneto-optical resonance. The cause of the asymmetry is the optical pumping of the ground-state hyperfine component which is not destroyed upon collision of the atom with the wall. The effect is most pronounced when the laser frequency is tuned to the resonance with the the F → F + 1 transition.
The specific features of absorption in a cell with an antirelaxation coating related to optical pumping and a finite rate of laser-frequency scanning are studied. The internal state of an atom in such cells is likely to remain unaltered after a collision with a wall. This results in optical pumping of an atomic ensemble over all velocities and the entire cell volume. Both the frequency corresponding to the maximum absorption in the D 2 line of 133 Cs and the absorption maximum itself depend on the sign of laser-frequency scanning. A theoretical model attributing the power dependence of asymmetry of the absorption contour of the 133 Cs D 2 line to the presence of cyclic transition levels in the system is presented.
Antirelaxation coatings in atomic vapor cells allow ground-state coherent spin states to survive many collisions with the cell walls. This reduction in the ground-state decoherence rate gives rise to ultranarrow-bandwidth features in electromagnetically induced transparency (EIT) spectra, which can form the basis of, for example, long-time scale slow and stored light, sensitive magnetometers, and precise frequency standards. Here we study, both experimentally and theoretically, how Zeeman EIT contrast and width in paraffin-coated rubidium vapor cells are determined by cell and laser-beam geometry, laser intensity, and atomic density. Using a picture of Ramsey pulse sequences, where atoms alternately spend ``bright'' and ``dark'' time intervals inside and outside the laser beam, we explain the behavior of EIT features in coated cells, highlighting their unique characteristics and potential applications.
Abstract The features of electromagnetically induced transparency (EIT) in gas cells with antirelaxation coating of the walls are considered. It is shown that the simultaneous effect of the motion of atoms, the finite size of a cell, and the nondegeneracy of the ground state of atoms leads to a number of qualitative phenomena. In particular, even for the simplest three-level lambda scheme with a nondegenerate ground state, a significant difference in the spectra of EIT is revealed and investigated in detail depending on the relation between the frequencies of the probe and control fields, i.e., depending on whether the probe radiation is scattered in the Stokes or anti-Stokes channel. A significant spatial inhomogeneity of the excited low-frequency coherence is observed, which persists for large cells even far from their boundaries. In this case, the EIT resonances formed by atoms in different regions of a cell turn out to be differently shifted in frequency, which causes an additional inhomogeneous broadening of the observed profile. The observed effects are studied as a function of the nature of the accommodation of atoms on the surface of the antirelaxation coating.