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Physical Review A

Collision-induced spin depolarization of alkali-metal atoms in cold He3 gas

Timur V. Tscherbul, P. Zhang, H. R. Sadeghpour, A. Dalgarno, Nathan Brahms, Yat Shan Au, John M. Doyle

Published Dec 31, 2008• 16 citations
Publisher

Abstract

We present a joint experimental and theoretical study of spin depolarization in collisions of alkali-metal atoms with $^{3}\mathrm{He}$ in a magnetic field. A rigorous quantum theory for spin-changing transitions is developed and applied to calculate the spin exchange and spin relaxation rates of Li and K atoms in cryogenic $^{3}\mathrm{He}$ gas. Magnetic trapping experiments provide upper bounds to the spin exchange rates for $\mathrm{Li}\text{\ensuremath{-}}^{3}\mathrm{He}$ and $\mathrm{K}\text{\ensuremath{-}}^{3}\mathrm{He}$, which are in agreement with the present theory. Our calculations demonstrate that the alkali-metal atoms have extremely slow spin depolarization rates, suggesting a number of potential applications in precision spectroscopy and quantum optics.

DOI
10.1103/physreva.78.060703

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We present a joint experimental and theoretical study of spin depolarization in collisions of alkali-metal atoms with 3He^{3}\mathrm{He}3He in a magnetic field. A rigorous quantum theory for spin-changing transitions is developed and applied to calculate the spin exchange and spin relaxation rates of Li and K atoms in cryogenic 3He^{3}\mathrm{He}3He gas. Magnetic trapping experiments provide upper bounds to the spin exchange rates for Li\ensuremath-3He\mathrm{Li}\text{\ensuremath{-}}^{3}\mathrm{He}Li\ensuremath-3He and K\ensuremath-3He\mathrm{K}\text{\ensuremath{-}}^{3}\mathrm{He}K\ensuremath-3He, which are in agreement with the present theory. Our calculations demonstrate that the alkali-metal atoms have extremely slow spin depolarization rates, suggesting a number of potential applications in precision spectroscopy and quantum optics.
We present a rigorous quantum study of spin-exchange transitions in collisions of the alkali-metal atoms with 3He^{3}\text{H}\text{e}3He in the presence of an external magnetic field. Using accurate ab initio interaction potentials, we obtain refined estimates for the Fermi contact interaction constants for complexes of Na, K, and Rb atoms with 3He^{3}\text{H}\text{e}3He. Ab initio calculations show that the Fermi contact interaction in Li-3He\text{Li-}^{3}\text{H}\text{e}Li-3He varies more slowly with internuclear distance than predicted by the atomic model [R. M. Herman, Phys. Rev. 37, A1062 (1965)]. The calculated spin-exchange rate constants for Na, K, and Rb atoms in a gas of 3He^{3}\text{H}\text{e}3He are in good agreement with experimental data. Our calculations demonstrate that at a temperature of 0.5 K, collision-induced spin exchange of the alkali-metal atoms occurs at a very slow rate of $\ensuremath{\sim}{10}^{\ensuremath{-}22}\text{ }{\text{cm}}^{3}/\text{s}$, suggesting potential applications in cryogenic cooling, precision spectroscopy, and quantum optics.
Collisions of atoms and molecules in external electromagnetic fields can depolarize electronic and nuclear spins, leading to decoherence of quantum superposition states. The fundamental microscopic processes giving rise to spin depolarization are spin exchange and spin relaxation. In this work, we present an analysis of spin exchange transitions in collision of alkali metal atoms with 3He. We use accurate ab initio calculations to evaluate the electron spin density of Li-He and the interaction energy of Rb-He. The Fermi contact interaction constants for the complexes of Na, K, and Rb atoms with 3He are extracted from the measured frequency shift enhancement factors using the ab initio interaction potentials. The spin density calculations also yield the hyperfine pressure shift of Li-He.
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 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 report a combined experimental and theoretical study of collision-induced dipolar relaxation in a cold spin-polarized gas of atomic nitrogen (N). We use buffer gas cooling to create trapped samples of 14N^{14}\mathrm{N}14N and 15N^{15}\mathrm{N}15N atoms with densities $(5\ifmmode\pm\else\textpm\fi{}2)\ifmmode\times\else\texttimes\fi{}{10}^{12} {\mathrm{cm}}^{\ensuremath{-}3}$ and measure their magnetic relaxation rates at milli-Kelvin temperatures. These measurements, together with rigorous quantum scattering calculations based on accurate ab initio interaction potentials for the ${}^{7}{\ensuremath{\Sigma}}_{u}^{+}$ electronic state of N2{\mathrm{N}}_{2}N2​ demonstrate that dipolar relaxation in N+N\mathrm{N}+\mathrm{N}N+N collisions occurs at a slow rate of $~{10}^{\ensuremath{-}13} {\mathrm{cm}}^{3}$/s over a wide range of temperatures (1 mK to 1 K) and magnetic fields (10 mT to 2 T). The calculated dipolar relaxation rates are insensitive to small variations of the interaction potential and to the magnitude of the spin-exchange interaction, enabling the accurate calibration of the measured N atom density. We find consistency between the calculated and experimentally determined rates. Our results suggest that N atoms are promising candidates for future experiments on sympathetic cooling of molecules.
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.