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Physical Review Letters

Hyperfine Polarization and Its Normal Gradient Coefficient of Rb87 Atoms in the Vicinity ( ∼10−5 cm ) of Coated and Uncoated Pyrex Glass Surfaces

Kaifeng Zhao, Z. Wu

Published Sep 10, 2003• 10 citations
Publisher

Abstract

We have made regionally specific measurement of the hyperfine polarization $⟨\mathbit{S}\ifmmode\cdot\else\textperiodcentered\fi{}\mathbit{I}⟩$ of $^{87}\mathrm{R}\mathrm{b}$ atoms in the vicinity ($\ensuremath{\sim}{10}^{\ensuremath{-}5}\text{ }\mathrm{c}\mathrm{m}$) of coated and uncoated Pyrex glass surfaces. We find that the polarization near an uncoated surface decreases rapidly with decreasing distance from the surface whereas for a silicone-coated surface the polarization is independent of the distance from the surface. We have also determined the normal gradient coefficient ${\ensuremath{\mu}}_{\mathbit{S}\ifmmode\cdot\else\textperiodcentered\fi{}\mathbit{I}}$ of the hyperfine polarization in uncoated cells. In a representative uncoated cell, at a Rb density $7.35\ifmmode\times\else\texttimes\fi{}{10}^{13}\text{ }{\mathrm{c}\mathrm{m}}^{\ensuremath{-}3}$ and a pump beam intensity $1.3\text{ }\mathrm{W}/{\mathrm{c}\mathrm{m}}^{2}$, we find ${\ensuremath{\mu}}_{\mathbit{S}\ifmmode\cdot\else\textperiodcentered\fi{}\mathbit{I}}=24\ifmmode\pm\else\textpm\fi{}7\text{ }\ensuremath{\mu}{\mathrm{m}}^{\ensuremath{-}1}$.

DOI
10.1103/physrevlett.91.113003

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We have made regionally specific measurement of the hyperfine polarization ⟨\mathbitS\ifmmode⋅\else\textperiodcentered\fi\mathbitI⟩⟨\mathbit{S}\ifmmode\cdot\else\textperiodcentered\fi{}\mathbit{I}⟩⟨\mathbitS\ifmmode⋅\else\textperiodcentered\fi\mathbitI⟩ of 87Rb^{87}\mathrm{R}\mathrm{b}87Rb atoms in the vicinity (\ensuremath∼10\ensuremath−5 cm\ensuremath{\sim}{10}^{\ensuremath{-}5}\text{ }\mathrm{c}\mathrm{m}\ensuremath∼10\ensuremath−5 cm) of coated and uncoated Pyrex glass surfaces. We find that the polarization near an uncoated surface decreases rapidly with decreasing distance from the surface whereas for a silicone-coated surface the polarization is independent of the distance from the surface. We have also determined the normal gradient coefficient \ensuremathμ\mathbitS\ifmmode⋅\else\textperiodcentered\fi\mathbitI{\ensuremath{\mu}}_{\mathbit{S}\ifmmode\cdot\else\textperiodcentered\fi{}\mathbit{I}}\ensuremathμ\mathbitS\ifmmode⋅\else\textperiodcentered\fi\mathbitI​ of the hyperfine polarization in uncoated cells. In a representative uncoated cell, at a Rb density 7.35\ifmmode×\else\texttimes\fi1013 cm\ensuremath−37.35\ifmmode\times\else\texttimes\fi{}{10}^{13}\text{ }{\mathrm{c}\mathrm{m}}^{\ensuremath{-}3}7.35\ifmmode×\else\texttimes\fi1013 cm\ensuremath−3 and a pump beam intensity 1.3 W/cm21.3\text{ }\mathrm{W}/{\mathrm{c}\mathrm{m}}^{2}1.3 W/cm2, we find \ensuremathμ\mathbitS\ifmmode⋅\else\textperiodcentered\fi\mathbitI=24\ifmmode±\else\textpm\fi7 \ensuremathμm\ensuremath−1{\ensuremath{\mu}}_{\mathbit{S}\ifmmode\cdot\else\textperiodcentered\fi{}\mathbit{I}}=24\ifmmode\pm\else\textpm\fi{}7\text{ }\ensuremath{\mu}{\mathrm{m}}^{\ensuremath{-}1}\ensuremathμ\mathbitS\ifmmode⋅\else\textperiodcentered\fi\mathbitI​=24\ifmmode±\else\textpm\fi7 \ensuremathμm\ensuremath−1.
We made regionally specific measurement of the hyperfine polarization $⟨\mathbit{S}∙\mathbit{I}⟩$ of Rb atoms in the vicinity $(\ensuremath{\sim}{10}^{\ensuremath{-}5}\phantom{\rule{0.3em}{0ex}}\mathrm{cm})$ of coated and uncoated Pyrex glass surfaces in optical pumping cells. This is in contrast to the previous hyperfine polarization studies, where the quantity measured is the bulk hyperfine polarization, which depends on surface interactions averaged over the entire cell surfaces. We probe the hyperfine polarization of the Rb atoms in the vicinity of cell surfaces using the evanescent wave of a weak laser beam. We find that the polarization in the vicinity of uncoated surfaces is significantly lower than that in the bulk. The polarization decreases rapidly with decreasing distance from the surface. By contrast, the polarization in the vicinity of a silicone-coated Pyrex glass surface is independent of the distance from the cell surface and is equal to the bulk polarization. Regionally specific measurement of the hyperfine polarization as a function of the penetration depth of the evanescent wave allows us to deduce the hyperfine polarization, its normal gradient, as well as the normal gradient coefficient ${\ensuremath{\mu}}_{\mathbit{S}∙\mathbit{I}}$ at the cell surface. We present the values of these quantities for three representative uncoated cells.
We present a simple method for directly measuring the average dwell time of spin-polarized Rb atoms on coated Pyrex glass surfaces. The method relies on the light shift of the Zeeman resonances of spin-polarized Rb atoms pumped and probed by evanescent waves, and does not depend on the microscopic details of surface interactions. We use a cell whose length is adjustable between 70 and $500\text{ }\text{ }\ensuremath{\mu}\mathrm{m}$. The inverse of the difference between the frequency shifts caused by ${\ensuremath{\sigma}}^{+}$ and ${\ensuremath{\sigma}}^{\ensuremath{-}}$ pump beams depends linearly on the cell length, from which we obtain the average dwell time ${\ensuremath{\tau}}_{s}$. For a Pyrex glass cell coated with octadecyltrichlorosilane we find that ${\ensuremath{\tau}}_{s}=0.53\ifmmode\pm\else\textpm\fi{}0.03\text{ }\text{ }\ensuremath{\mu}\mathrm{s}$ at a cell wall temperature of $103\text{ }\ifmmode^\circ\else\textdegree\fi{}\mathrm{C}$. The temperature dependence of ${\ensuremath{\tau}}_{s}$ is fitted to ${\ensuremath{\tau}}_{s}={\overline{\ensuremath{\tau}}}_{0}\mathrm{exp}({E}_{a}/kT)$, yielding a preexponential factor ${\overline{\ensuremath{\tau}}}_{0}={2.2}_{\ensuremath{-}1.4}^{+5.1}\text{ }\text{ }\mathrm{ns}$ and an activation energy ${E}_{a}=0.19\ifmmode\pm\else\textpm\fi{}0.03\text{ }\text{ }\mathrm{eV}$.
We present a detailed experimental and theoretical study of edge enhancement in optically pumped Rb vapor in coated cylindrical pyrex glass cells. The Zeeman polarization of Rb atoms is produced and probed in the vicinity ( ~ ${10}^{\ensuremath{-}4}$ cm) of the cell surface by evanescent pump and probe beams. Spin-polarized Rb atoms diffuse throughout the cell in the presence of magnetic field gradients. In the present experiment the edge enhanced signal from the back surface of the cell is suppressed compared to that from the front surface, due to the fact that polarization is probed by the evanescent wave at the front surface only. The observed magnetic resonance line shape is reproduced quantitatively by a theoretical model and yields information about the dwell time and relaxation probability of Rb atoms on Pyrex glass surfaces coated with antirelaxation coatings.
We present a method for measuring surface interaction parameters of spin-polarized Rb atoms on coated Pyrex glass surfaces based on edge enhancement in optically pumped Rb vapor. The best fit to the measured magnetic resonance lines using a theoretical model yields a dwell time ${\ensuremath{\tau}}_{s}=1.8\phantom{\rule{0.3em}{0ex}}\ensuremath{\mu}\mathrm{s}$ and a spin relaxation probability ${\ensuremath{\xi}}_{s}=0.015$ for a spin-polarized Rb atom on a Pyrex glass surface coated with dichlorooctamethyl-tetrasiloxane (Surfasil), and ${\ensuremath{\tau}}_{s}=0.5\phantom{\rule{0.3em}{0ex}}\ensuremath{\mu}\mathrm{s}$ and ${\ensuremath{\xi}}_{s}=0.001$ on a surface coated with octadecyltrichlorosilane (OTS).