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Physical Review A

Spin relaxation in alkali-metal 1Σg+ dimers

Stephen J. Kadlecek, L. W. Anderson, Christopher Erickson, Thad G Walker

Published Oct 15, 2001• 11 citations
Publisher

Abstract

We discuss the relaxation of a spin-polarized alkali-metal vapor due to the electric-quadrupole interaction in ${}^{1}{\ensuremath{\Sigma}}_{g}^{+}$ dimers, and present a model that accurately describes the measured relaxation rates under a wide variety of conditions. We use the model along with experimental results to deduce the quadrupole interaction strength, atom-dimer chemical-exchange reaction rate, and the rate of reorientation of singlet dimers due to collisions with the buffer gas.

DOI
10.1103/physreva.64.052717

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We discuss the relaxation of a spin-polarized alkali-metal vapor due to the electric-quadrupole interaction in 1\ensuremathΣg+{}^{1}{\ensuremath{\Sigma}}_{g}^{+}1\ensuremathΣg+​ dimers, and present a model that accurately describes the measured relaxation rates under a wide variety of conditions. We use the model along with experimental results to deduce the quadrupole interaction strength, atom-dimer chemical-exchange reaction rate, and the rate of reorientation of singlet dimers due to collisions with the buffer gas.
Relaxation constants T1{T}_{1}T1​ and T2{T}_{2}T2​ have been computed for experiments involving optical pumping and optical detection in alkali metal vapor. The calculations have been performed for several possible spin relaxation mechanisms; namely, magnetic dipole, electric quadrupole, spin exchange, and the optical pumping process itself. For all of these mechanisms a reorientation experiment will approximately predict a spin resonance line width (equivalent to the statement ${T}_{1}\ensuremath{\approx}{T}_{2}$ for spin-\textonehalf{} particles.) However, a spin reorientation experiment of the type originally performed by Dehmelt, employing circularly polarized light, gives approximate results because of the nonexponential character of the reorientation. A more suitable experiment is one employing hyperfine population differences and unpolarized light.
We report the first studies of magnetic decoupling of the spin relaxation of alkali-metal atoms due to binary collisions with buffer gases. When binary collisions are the dominant relaxation mechanism, the relaxation and its magnetic decoupling are well described by the SSS-damping rate ${\ensuremath{\Gamma}}_{\mathrm{SD}}$ due to the spin-rotation interaction $\ensuremath{\gamma}\mathbf{N}\ifmmode \dot{}\else \.{}\fi{}\mathbf{S}$, the spin exchange rate ${\ensuremath{\Gamma}}_{\mathrm{EX}}$ for collisions between alkali atoms, and a new ``Carver rate'' ${\ensuremath{\Gamma}}_{\mathrm{C}}$, due to the pressure-shift interaction $\ensuremath{\delta}A\mathbf{I}\ifmmode \dot{}\else \.{}\fi{}\mathbf{S}$, which can substantially broaden the magnetic decoupling curve while having no influence on the zero-field rates.
We present calculations of spin-relaxation rates of alkali-metal atoms due to the spin-axis interaction acting in binary collisions between the atoms. We show that for the high-temperature conditions of interest here, the spin-relaxation rates calculated with classical-path trajectories are nearly the same as those calculated with the distorted-wave Born approximation. We compare these calculations to recent experiments that used magnetic decoupling to isolate spin relaxation due to binary collisions from that due to the formation of triplet van der Waals molecules. The values of the spin-axis coupling coefficients deduced from measurements of binary collision rates are consistent with those deduced from molecular decoupling experiments, and follow a physically plausible scaling law for the spin-axis coupling coefficients.
By measuring the relaxation rates of the nuclear spin polarization of 129Xe^{129}\mathrm{Xe}129Xe in the presence of alkali-metal vapor at different densities, we have extracted the spin-exchange rates between 129Xe^{129}\mathrm{Xe}129Xe and the three alkali metals K, Rb, and Cs. By studying the alkali-metal--129Xe^{129}\mathrm{Xe}129Xe spin-exchange rates as functions of the cell number density from 0.2 to 0.7 amagat, the binary collision and van der Waals molecular terms are separated, and constants governing both mechanisms are determined. The results from our work can be used to optimize the parameter space for polarizing 129Xe^{129}\mathrm{Xe}129Xe, a promising agent for magnetic resonance imaging and other applications.
We present a comprehensive theory of nuclear spin polarization of 3He{}^{3}\mathrm{He}3He and 129Xe{}^{129}\mathrm{Xe}129Xe 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 3He{}^{3}\mathrm{He}3He or 129Xe{}^{129}\mathrm{Xe}129Xe 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 3He{}^{3}\mathrm{He}3He or 129Xe{}^{129}\mathrm{Xe}129Xe gas are assumed, namely, atmospheres of gas pressure and nearly complete quenching of the optically excited alkali-metal atoms by collisions with N2{\mathrm{N}}_{2}N2​ or H2{\mathrm{H}}_{2}H2​ 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.
We present a detailed theoretical analysis of the noble-gas nuclear-spin relaxation due to the anisotropic magnetic-dipole hyperfine interaction between the noble-gas nucleus and alkali-metal valence electron vis \`a vis the already well-understood (spin-conserving) isotropic magnetic-dipole hyperfine interaction in alkali-metal--noble-gas systems. We find that, for all pairs in which the noble gas is not helium, the predicted spin-relaxation rate from the anisotropic interaction does not exceed 2.5% of the rate from the isotropic interaction, thereby not appreciably limiting the maximum noble-gas nuclear polarization attainable via spin-exchange collisions with polarized alkali-metal atoms. For alkali-metal--helium pairs, we predict that the anisotropic interaction has a slightly larger relative effect, perhaps limiting the nuclear polarization to $\ensuremath{\sim}95%$ of the electronic polarization in the Rb-3He{}^{3}\mathrm{He}3He system; however, our confidence in the helium results is limited by a lack of knowledge of the interatomic potentials necessary for the calculation.