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Physical Review A

Theory of spin-exchange optical pumping of 3 He and 129 Xe

Stephan Appelt, Andrei Ben-Amar Baranga, Christopher Erickson, M. V. Romalis, Albert R. Young, W. Happer

Published Aug 1, 1998• 443 citations
Publisher

Abstract

We present a comprehensive theory of nuclear spin polarization of ${}^{3}\mathrm{He}$ and ${}^{129}\mathrm{Xe}$ gases by spin-exchange collisions with optically pumped alkali-metal vapors. The most important physical processes considered are (1) spin-conserving spin-exchange collisions between like or unlike alkali-metal atoms; (2) spin-destroying collisions of the alkali-metal atoms with each other and with buffer-gas atoms; (3) electron-nuclear spin-exchange collisions between alkali-metal atoms and ${}^{3}\mathrm{He}$ or ${}^{129}\mathrm{Xe}$ atoms; (4) spin interactions in van der Waals molecules consisting of a Xe atom bound to an alkali-metal atom; (5) optical pumping by laser photons; (6) spatial diffusion. The static magnetic field is assumed to be small enough that the nuclear spin of the alkali-metal atom is well coupled to the electron spin and the total spin is very nearly a good quantum number. Conditions appropriate for the production of large quantities of spin-polarized ${}^{3}\mathrm{He}$ or ${}^{129}\mathrm{Xe}$ gas are assumed, namely, atmospheres of gas pressure and nearly complete quenching of the optically excited alkali-metal atoms by collisions with ${\mathrm{N}}_{2}$ or ${\mathrm{H}}_{2}$ gas. Some of the more important results of this work are as follows: (1) Most of the pumping and relaxation processes are sudden with respect to the nuclear polarization. Consequently, the steady-state population distribution of alkali-metal atoms is well described by a spin temperature, whether the rate of spin-exchange collisions between alkali-metal atoms is large or small compared to the optical pumping rate or the collisional spin-relaxation rates. (2) The population distributions that characterize the response to sudden changes in the intensity of the pumping light are not described by a spin temperature, except in the limit of very rapid spin exchange. (3) Expressions given for the radio-frequency (rf) resonance linewidths and areas can be used to make reliable estimates of the local spin polarization of the alkali-metal atoms. (4) Diffusion effects for these high-pressure conditions are mainly limited to thin layers at the cell surface and at internal resonant surfaces generated by radio-frequency magnetic fields when the static magnetic field has substantial spatial inhomogeneities. The highly localized effects of diffusion at these surfaces are described with closed-form analytic functions instead of the spatial eigenmode expansions that are appropriate for lower-pressure cells.

DOI
10.1103/physreva.58.1412

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The theory of spin exchange between optically pumped alkali-metal atoms and noble-gas nuclei is presented. Spin exchange with heavy noble gases is dominated by interactions in long-lived van der Waals molecules. The main spin interactions are assumed to be the spin-rotation interactions $\ensuremath{\gamma}\stackrel{\ensuremath{\rightarrow}}{\mathrm{N}}\ifmmode\cdot\else\textperiodcentered\fi{}\stackrel{\ensuremath{\rightarrow}}{\mathrm{S}}$ between the rotational angular momentum $\stackrel{\ensuremath{\rightarrow}}{\mathrm{N}}$ of the alkali-metal---noble-gas pair and the electron spin $\stackrel{\ensuremath{\rightarrow}}{\mathrm{S}}$ of the alkali-metal atom, and the contact hyperfine interaction $\ensuremath{\alpha}\stackrel{\ensuremath{\rightarrow}}{\mathrm{K}}\ifmmode\cdot\else\textperiodcentered\fi{}\stackrel{\ensuremath{\rightarrow}}{\mathrm{S}}$ between the nuclear spin $\stackrel{\ensuremath{\rightarrow}}{\mathrm{K}}$ of the noble-gas atom and the electron spin $\stackrel{\ensuremath{\rightarrow}}{\mathrm{S}}$. Arbitrary values for KKK and for the nuclear spin III of the alkali-metal atom are assumed. Precise formal expressions for spin transfer coefficients are given along with convenient approximations based on a perturbation expansion in powers of ${(\frac{\ensuremath{\alpha}}{\ensuremath{\gamma}N})}^{2}$, a quantity which has been shown to be small by experiment.
By analyzing the measured spin-relaxation transients of 129Xe^{129}\mathrm{Xe}129Xe nuclear spins and alkali-metal-atomic spins in mixtures of alkali-metal-atom vapors, Xe gas, and larger amounts of N2{\mathrm{N}}_{2}N2​ gas, we have determined the three-body formation rates and the spin-transfer probabilities for alkali- metal--noble-gas van der Waals molecules. Three parameters, in addition to the spin quantum numbers of the alkali-metal and noble-gas nuclei, are needed to predict the spin-transfer rates. These parameters, which we have determined from experimental measurements, are x=\ensuremath{\gamma}N/\ensuremath{\alpha}, the ratio of the spin-rotation interaction \ensuremath{\gamma}N to the spin-exchange interaction \ensuremath{\alpha}; p0{p}_{0}p0​, the third-body pressure for which the molecular breakup rate ${\ensuremath{\tau}}^{\mathrm{\ensuremath{-}}1}$ is equal to the spin-rotation frequency \ensuremath{\gamma}N/h; and Z, the three-body rate constant for forming van der Waals molecules.
Optical pumping is fundamental to high-precision measurement using thermal alkali-metal atoms in vapor cells. In applications such as atomic magnetometry, buffer gases (e.g., N2\mathrm{N}_2N2​ or He\mathrm{He}He) at specific pressures are introduced to quench fluorescence and mitigate wall relaxation. In the high-pressure limit (e.g., the N2\mathrm{N}_2N2​ pressure pN2>1p_{\mathrm{N}_2}> 1pN2​​>1~atm), where collisional broadening exceeds hyperfine splittings of the atoms, optical pumping theory provides a clear description of the angular momentum exchange between photons and atomic spins. However, in many magnetic sensing scenarios, the high-pressure approximation becomes inadequate as its pressure conditions are not strictly satisfied. Consequently, an explicit description of optical pumping under realistic pressures is critical for selecting operating points and enhancing system performance. To address this, we develop a unified theoretical framework of optical pumping in the quasi-high-pressure regime, where collisional broadening is comparable to the ground-state hyperfine splitting. We demonstrate that light absorption, spin polarization, and magnetic-resonance linewidth in this regime differ significantly from those predicted by the high-pressure limit and offer favorable operating conditions. Our study extends conventional modeling and offers critical guidance for atomic magnetometry operating under realistic buffer gas pressures.
We present a design for a spin-exchange optical pumping system to produce large quantities of highly polarized 129Xe and 131Xe. Low xenon concentrations in the flowing gas mixture which allow the laser to maintain high Cs polarization. The large spin-exchange rate between Cs and Xe through the long-lived van der Waals molecules at low pressure, combined with a high flow rate, results in large production rates of hyperpolarized xenon. The fast rates make it possible to obtain large nuclear polarizations after several minutes of optical pumping with a laser.At high Xe pressures. According to the theory, the longitudinal spin-elaxation rate 1T1 of Xe in a high-pressure sample containing only Xe and Cs vapor has the simple form is the velocity averaged binary spin-exchange cross section, It is the relaxation rate due to wall collisions and perhaps magnetic field inhomogeneities. Our results complement earlier studies performed at 129Xe pressures of about 20 Torr and 131Xe pressures of about 20 Torr and N2 pressures of 600 Torr . This work is useful for predicting spin-exchange rates between polarized Cs atoms and Xe nuclei.
The spin-exchange rates due to binary collisions and due to the formation of van der Waals molecules between 83Kr^{83}\mathrm{Kr}83Kr nuclei and optically pumped rubidium-metal vapor have been determined using a technique that relies on the simultaneous observation of frequency shifts of nuclear magnetic resonance lines of noble-gas atoms and corresponding frequency shifts of electron paramagnetic resonance lines of alkali-metal atoms. In contrast, earlier studies have relied on the observation of the spin-relaxation rate of either the alkali-metal atoms or the noble-gas atoms.