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Physical Review A

Measurements of 3He spin-exchange rates

Bien Chann, Earl Babcock, L. W. Anderson, Thad G Walker

Published Sep 13, 2002• 67 citations
Publisher

Abstract

Spin-exchange rate coefficients for Rb-${}^{3}\mathrm{He}$ are measured using three different methods. Two methods, using Rb repolarization and rate balance, require no assumption about the nature of the ${}^{3}\mathrm{He}$ wall relaxation and agree well; we find spin-exchange rate coefficients of $6.7\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}20}{\mathrm{cm}}^{3}/\mathrm{s}$ and $6.8\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}20}{\mathrm{cm}}^{3}/\mathrm{s}.$ These results agree with a recent repolarization measurement of Baranga and co-workers [Phys. Rev. Lett. 80, 2801 (1998)]. The third method uses the temperature dependence of the ${}^{3}\mathrm{He}$ relaxation and is 30% larger than the other two, implying a temperature-dependent wall or an unreasonably large value of the anisotropic spin-exchange interaction for $\mathrm{Rb}{\ensuremath{-}}^{3}\mathrm{He}.$ In the course of these measurements we developed and tested a new method for Rb density measurements under high power pumping conditions, and a new variant of Rb EPR polarimetry, both of which are described here.

DOI
10.1103/physreva.66.032703

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Hyatt M. Gibbs, Robert J. Hull

In a hyperfine-optical-pumping experiment we employed the Franzen transient method to determine the total spin-exchange cross sections for ${\mathrm{Rb}}^{87}$-${\mathrm{Rb}}^{87}$ and ${\mathrm{Rb}}^{87}$-${\mathrm{Cs}}^{133}$ collisions at 78\ifmmode^\circ\else\textdegree\fi{}C. Values determined in this way were: $\ensuremath{\sigma}({\mathrm{Rb}}^{87}\ensuremath{-}{\mathrm{Rb}}^{87})=(1.9\ifmmode\pm\else\textpm\fi{}0.2)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}14}$ ${\mathrm{cm}}^{2}$ and $\ensuremath{\sigma}({\mathrm{Rb}}^{87}\ensuremath{-}{\mathrm{Cs}}^{133})=(2.3\ifmmode\pm\else\textpm\fi{}0.2)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}14}$ ${\mathrm{cm}}^{2}$. A large difference between the ground-state hyperfine populations was established by pumping with light absorbable by atoms in only one hyperfine level. In the presence of a second unpumped species, the resulting polarization relaxed with a characteristic rate of $\frac{1}{\ensuremath{\tau}}=\frac{1}{T}+\frac{1}{{T}_{S1}}+\frac{1}{{T}_{E1}}$, where $T$ is the non-spin-exchange relaxation time and ${T}_{S1}$ and ${T}_{E1}$ are the self- and cross-exchange times. Then $\ensuremath{\tau}$ was obtained by fitting the signal to a single exponential and applying a small correction ($\ensuremath{\approx}10%$) to account for the fact that the signal is only approximately proportional to the polarization (and hence to a single exponential). The relaxation measurement utilized rapid data accumulation with a Kerr-cell shutter and pulse-height analyzer. The cross section can be easily deduced from the relaxation times if the corresponding densities are known. Each density was measured by determining the integral over all frequencies of the absorption coefficient by means of a scanning Fabry-Perot interferometer. We describe how to remove the effect of the Fabry-Perot on the true emission and absorption profiles.

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Physical Review•Jan 6, 1964•36 citations
Spin-exchange rate coefficients for Rb-3He{}^{3}\mathrm{He}3He are measured using three different methods. Two methods, using Rb repolarization and rate balance, require no assumption about the nature of the 3He{}^{3}\mathrm{He}3He wall relaxation and agree well; we find spin-exchange rate coefficients of 6.7\ifmmode×\else\texttimes\fi10\ensuremath−20cm3/s6.7\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}20}{\mathrm{cm}}^{3}/\mathrm{s}6.7\ifmmode×\else\texttimes\fi10\ensuremath−20cm3/s and 6.8\ifmmode×\else\texttimes\fi10\ensuremath−20cm3/s.6.8\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}20}{\mathrm{cm}}^{3}/\mathrm{s}.6.8\ifmmode×\else\texttimes\fi10\ensuremath−20cm3/s. These results agree with a recent repolarization measurement of Baranga and co-workers [Phys. Rev. Lett. 80, 2801 (1998)]. The third method uses the temperature dependence of the 3He{}^{3}\mathrm{He}3He relaxation and is 30% larger than the other two, implying a temperature-dependent wall or an unreasonably large value of the anisotropic spin-exchange interaction for Rb\ensuremath−3He.\mathrm{Rb}{\ensuremath{-}}^{3}\mathrm{He}.Rb\ensuremath−3He. In the course of these measurements we developed and tested a new method for Rb density measurements under high power pumping conditions, and a new variant of Rb EPR polarimetry, both of which are described here.
We describe a method of 3He{}^{3}\mathrm{He}3He polarimetry relying on the polarization-dependent frequency shift of the Rb Zeeman resonance. Our method is ideally suited for on-line measurements of the 3He{}^{3}\mathrm{He}3He polarization produced by spin-exchange optical pumping. To calibrate the frequency shift we performed an accurate measurement of the imaginary part of the $\mathrm{Rb}{\ensuremath{-}}^{3}\mathrm{He}$ spin-exchange cross section in the temperature range typical for spin-exchange optical pumping of 3He.{}^{3}\mathrm{He}.3He. We also present a detailed study of possible systematic errors in the frequency shift polarimetry.
We report on extensive experimental measurements of the key rates that determine the efficiency for polarizing the nuclei of 3He{}^{3}\mathrm{He}3He by spin exchange with optically pumped Rb vapor. In agreement with recent theoretical predictions, we find a strong temperature dependence of the electron-spin loss rates due to 3HeRb{}^{3}\mathrm{HeRb}3HeRb collisions. We also find that the maximum possible efficiency for spin-exchange polarization of 3He{}^{3}\mathrm{He}3He by K is 10 times greater than for Rb.
Estimates of the Rb-131Xe^{131}\mathrm{Xe}131Xe spin-exchange cross section have been obtained by observing the nuclear spin relaxation of 131Xe^{131}\mathrm{Xe}131Xe in the presence of a Rb vapor. Nuclear spin relaxation of 131Xe^{131}\mathrm{Xe}131Xe due to the presence of a foreign buffer gas and the relaxation rate on the glass walls of the cell have also been observed.
In a hyperfine-optical-pumping experiment we employed the Franzen transient method to determine the total spin-exchange cross sections for Rb87{\mathrm{Rb}}^{87}Rb87-Rb87{\mathrm{Rb}}^{87}Rb87 and Rb87{\mathrm{Rb}}^{87}Rb87-Cs133{\mathrm{Cs}}^{133}Cs133 collisions at 78\ifmmode^\circ\else\textdegree\fi{}C. Values determined in this way were: $\ensuremath{\sigma}({\mathrm{Rb}}^{87}\ensuremath{-}{\mathrm{Rb}}^{87})=(1.9\ifmmode\pm\else\textpm\fi{}0.2)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}14}$ cm2{\mathrm{cm}}^{2}cm2 and $\ensuremath{\sigma}({\mathrm{Rb}}^{87}\ensuremath{-}{\mathrm{Cs}}^{133})=(2.3\ifmmode\pm\else\textpm\fi{}0.2)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}14}$ cm2{\mathrm{cm}}^{2}cm2. A large difference between the ground-state hyperfine populations was established by pumping with light absorbable by atoms in only one hyperfine level. In the presence of a second unpumped species, the resulting polarization relaxed with a characteristic rate of $\frac{1}{\ensuremath{\tau}}=\frac{1}{T}+\frac{1}{{T}_{S1}}+\frac{1}{{T}_{E1}}$, where TTT is the non-spin-exchange relaxation time and TS1{T}_{S1}TS1​ and TE1{T}_{E1}TE1​ are the self- and cross-exchange times. Then $\ensuremath{\tau}$ was obtained by fitting the signal to a single exponential and applying a small correction ($\ensuremath{\approx}10%$) to account for the fact that the signal is only approximately proportional to the polarization (and hence to a single exponential). The relaxation measurement utilized rapid data accumulation with a Kerr-cell shutter and pulse-height analyzer. The cross section can be easily deduced from the relaxation times if the corresponding densities are known. Each density was measured by determining the integral over all frequencies of the absorption coefficient by means of a scanning Fabry-Perot interferometer. We describe how to remove the effect of the Fabry-Perot on the true emission and absorption profiles.
The spin-exchange cross section for Rb85{\mathrm{Rb}}^{85}Rb85-Rb87{\mathrm{Rb}}^{87}Rb87 collisions has been measured to be (1.70\ifmmode\pm\else\textpm\fi{}0.21)\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}14}$ cm2{\mathrm{cm}}^{2}cm2 using the techniques of optical pumping and an interferometric method for measuring the Rb vapor density. The Rb87{\mathrm{Rb}}^{87}Rb87 constituent in a vapor of natural Rb was polarized through absorption of circularly polarized resonance radiation, and the Rb87{\mathrm{Rb}}^{87}Rb87 polarization was partially transferred to the Rb85{\mathrm{Rb}}^{85}Rb85 constituent through spin-exchange collisions. A phenomenological theory of the optical pumping plus the exchange polarization process which neglects nuclear spin was used to relate the cross section to the ratio of the signal strengths for the Rb87{\mathrm{Rb}}^{87}Rb87 and Rb85{\mathrm{Rb}}^{85}Rb85 Zeeman resonances, the relaxation time, and the Rb87{\mathrm{Rb}}^{87}Rb87 vapor density. The density was measured by comparing spectral profiles of the resonance radiation transmitted through the optical pumping cell at room temperature with the resonance radiation transmitted at the temperature at which the signal strengths were measured. These spectral profiles were obtained through use of a scanning Fabry-Perot interferometer.