Physical Review Letters

Magnetic Slowing Down of Spin Relaxation due to Binary Collisions of Alkali-Metal Atoms with Buffer-Gas Atoms

D. K. Walter, W. M. Griffith, W. Happer

Published Feb 15, 2002• 37 citations

Abstract

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 $S$-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.

DOI: 10.1103/physrevlett.88.093004

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Magnetic decoupling of 129Xe−Rb and 129Xe−Cs binary spin exchange

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Measurement of Xe129−Cs binary spin-exchange rate coefficient

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Physical Review Letters

Magnetic Slowing Down of Spin Relaxation due to Binary Collisions of Alkali-Metal Atoms with Buffer-Gas Atoms

D. K. Walter, W. M. Griffith, W. Happer

Published Feb 15, 2002• 37 citations

Publisher

Abstract

S

-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.

DOI: 10.1103/physrevlett.88.093004

Related papers

Magnetic decoupling of Rb spin relaxation in H2 buffer gas

P. I. Borel, Christopher Erickson, D. K. Walter

We report studies of the magnetic decoupling of Rb spin relaxation in the presence of ${\mathrm{H}}_{2}$ buffer gas at high pressures $(>~1.5\mathrm{atm}).$ At low Rb number densities $(<~5\ifmmode\times\else\texttimes\fi{}{10}^{13}{\mathrm{cm}}^{\ensuremath{-}3}),$ we find that the observed magnetic-field dependence of the spin relaxation is almost solely due to binary collisions between Rb atoms and hydrogen molecules, and that it is very well described by three rates: the Rb-Rb spin-exchange rate, the S-damping rate, and the Carver rate associated with the hyperfine pressure-shift interaction in collisions of Rb with ${\mathrm{H}}_{2}$ molecules. At higher Rb densities, the contribution to the relaxation from Rb triplet dimers becomes significant.We report studies of the magnetic decoupling of Rb spin relaxation in the presence of ${\mathrm{H}}_{2}$ buffer gas at high pressures $(>~1.5\mathrm{atm}).$ At low Rb number densities $(<~5\ifmmode\times\else\texttimes\fi{}{10}^{13}{\mathrm{cm}}^{\ensuremath{-}3}),$ we find that the observed magnetic-field dependence of the spin relaxation is almost solely due to binary collisions between Rb atoms and hydrogen molecules, and that it is very well described by three rates: the Rb-Rb spin-exchange rate, the S-damping rate, and the Carver rate associated with the hyperfine pressure-shift interaction in collisions of Rb with ${\mathrm{H}}_{2}$ molecules. At higher Rb densities, the contribution to the relaxation from Rb triplet dimers becomes significant.

Physical Review ADec 20, 20021 citation

Spin-axis relaxation in spin-exchange collisions of alkali-metal atoms

Stephen J. Kadlecek, Thad G Walker, D. K. Walter +2 more

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.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.

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Magnetic decoupling of 129Xe−Rb and 129Xe−Cs binary spin exchange

Yuan‐Yu Jau, Nicholas N. Kuzma, W. Happer

We report calculations of the magnetic decoupling of the nuclear spin relaxation rate of ${}^{129}\mathrm{Xe}$ atoms caused by binary collisions with Rb or Cs atoms in a gas. A semiclassical approximation, using a classical path for the collision and treating the spin interactions quantum mechanically, gives results that differ by no more than 2% from calculations with the distorted-wave Born approximation. Both computational methods show that the relaxation rate decreases substantially for magnetic fields of a few tens of teslas. For ${}^{129}\mathrm{Xe}\ensuremath{-}\mathrm{Rb},$ where recent experimental measurements are available, the calculated rate coefficients at the experimental field of 9.4 T are about 80% of the calculated values at zero field. At 9.4 T, the calculated rate coefficient for ${}^{129}\mathrm{Xe}\ensuremath{-}\mathrm{Rb}$ is about one-half of the experimentally observed value. This discrepancy is probably due to inaccuracies in the van der Waals and spin-dependent potentials used in the calculations.We report calculations of the magnetic decoupling of the nuclear spin relaxation rate of ${}^{129}\mathrm{Xe}$ atoms caused by binary collisions with Rb or Cs atoms in a gas. A semiclassical approximation, using a classical path for the collision and treating the spin interactions quantum mechanically, gives results that differ by no more than 2% from calculations with the distorted-wave Born approximation. Both computational methods show that the relaxation rate decreases substantially for magnetic fields of a few tens of teslas. For ${}^{129}\mathrm{Xe}\ensuremath{-}\mathrm{Rb},$ where recent experimental measurements are available, the calculated rate coefficients at the experimental field of 9.4 T are about 80% of the calculated values at zero field. At 9.4 T, the calculated rate coefficient for ${}^{129}\mathrm{Xe}\ensuremath{-}\mathrm{Rb}$ is about one-half of the experimentally observed value. This discrepancy is probably due to inaccuracies in the van der Waals and spin-dependent potentials used in the calculations.

Physical Review AFeb 28, 200323 citations

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

Timur V. Tscherbul, P. Zhang, H. R. Sadeghpour +4 more

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.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.

Physical Review ADec 31, 200816 citations

Measurement of Xe129−Cs binary spin-exchange rate coefficient

Yuan‐Yu Jau, Nicholas N. Kuzma, W. Happer

We report the first measurement of the spin-exchange rate coefficient for binary collisions between Cs and $^{129}\mathrm{Xe}$ atoms in the temperature range $110<T<150\phantom{\rule{0.2em}{0ex}}\ifmmode^\circ\else\textdegree\fi{}\mathrm{C}$ at a $9.4\text{\ensuremath{-}}\mathrm{T}$ magnetic field. Under these conditions, binary spin-exchange collisions dominate the longitudinal nuclear spin-relaxation rate $1∕{T}_{1}$ of $^{129}\mathrm{Xe}$ gas. We measured $1∕{T}_{1}$ of a thermally polarized Xe gas using the saturation-recovery of conventional nuclear magnetic resonance. We also directly measured the Cs atomic number density [Cs] by using Faraday rotation of the linear polarization of a probing laser beam passing through the sample. The measured rate coefficient is $\ensuremath{\kappa}(9.4\phantom{\rule{0.3em}{0ex}}\mathrm{T})=d(1∕{T}_{1})∕d[\mathrm{Cs}]=(2.81\ifmmode\pm\else\textpm\fi{}0.2)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}16}\phantom{\rule{0.3em}{0ex}}{\mathrm{cm}}^{3}∕\mathrm{s}$, which is about a factor of 1.6 higher than the previously measured spin-exchange rate coefficient of $^{129}\mathrm{Xe}\text{\ensuremath{-}}\mathrm{Rb}$ binary collisions. Using a calculated magnetic decoupling factor, we extrapolate our result to zero magnetic field: $\ensuremath{\kappa}(0\phantom{\rule{0.3em}{0ex}}\mathrm{T})=(4.1\ifmmode\pm\else\textpm\fi{}0.3)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}16}\phantom{\rule{0.3em}{0ex}}{\mathrm{cm}}^{3}∕\mathrm{s}$.We report the first measurement of the spin-exchange rate coefficient for binary collisions between Cs and $^{129}\mathrm{Xe}$ atoms in the temperature range $110<T<150\phantom{\rule{0.2em}{0ex}}\ifmmode^\circ\else\textdegree\fi{}\mathrm{C}$ at a $9.4\text{\ensuremath{-}}\mathrm{T}$ magnetic field. Under these conditions, binary spin-exchange collisions dominate the longitudinal nuclear spin-relaxation rate $1∕{T}_{1}$ of $^{129}\mathrm{Xe}$ gas. We measured $1∕{T}_{1}$ of a thermally polarized Xe gas using the saturation-recovery of conventional nuclear magnetic resonance. We also directly measured the Cs atomic number density [Cs] by using Faraday rotation of the linear polarization of a probing laser beam passing through the sample. The measured rate coefficient is $\ensuremath{\kappa}(9.4\phantom{\rule{0.3em}{0ex}}\mathrm{T})=d(1∕{T}_{1})∕d[\mathrm{Cs}]=(2.81\ifmmode\pm\else\textpm\fi{}0.2)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}16}\phantom{\rule{0.3em}{0ex}}{\mathrm{cm}}^{3}∕\mathrm{s}$, which is about a factor of 1.6 higher than the previously measured spin-exchange rate coefficient of $^{129}\mathrm{Xe}\text{\ensuremath{-}}\mathrm{Rb}$ binary collisions. Using a calculated magnetic decoupling factor, we extrapolate our result to zero magnetic field: $\ensuremath{\kappa}(0\phantom{\rule{0.3em}{0ex}}\mathrm{T})=(4.1\ifmmode\pm\else\textpm\fi{}0.3)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}16}\phantom{\rule{0.3em}{0ex}}{\mathrm{cm}}^{3}∕\mathrm{s}$.

Physical Review AJun 7, 200424 citations

Slowing Down of Rubidium-Induced Nuclear Spin Relaxation of Xe129 Gas in a Magnetic Field

Natarajan D. Bhaskar, W. Happer, Marcus Larsson +1 more

The longitudinal relaxation rate of $^{129}\mathrm{Xe}$ nuclear spins slows down substantially in an external magnetic field of about 100 G. From an analysis of the magnetic slowing down and of the dependence of the zero-field relaxation rates on the third-body pressure, the authors have deduced the magnitudes of the spin-rotation and spin-exchange interactions in the ${\mathrm{Rb}}^{129}$ Xe molecule, as well as the formation and breakup rates of RbXe in ${\mathrm{N}}_{2}$ gas and the dissociation constant of RbXe. The magnetic slowing down shows directly that binary collisions contribute no more than a few percent to the relaxation rates.The longitudinal relaxation rate of $^{129}\mathrm{Xe}$ nuclear spins slows down substantially in an external magnetic field of about 100 G. From an analysis of the magnetic slowing down and of the dependence of the zero-field relaxation rates on the third-body pressure, the authors have deduced the magnitudes of the spin-rotation and spin-exchange interactions in the ${\mathrm{Rb}}^{129}$Xe molecule, as well as the formation and breakup rates of RbXe in ${\mathrm{N}}_{2}$ gas and the dissociation constant of RbXe. The magnetic slowing down shows directly that binary collisions contribute no more than a few percent to the relaxation rates.

Physical Review LettersJan 10, 198342 citations

S

-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 studies of the magnetic decoupling of Rb spin relaxation in the presence of

{\mathrm{H}}_{2}

buffer gas at high pressures

(>~1.5\mathrm{atm}).

At low Rb number densities $(<~5\ifmmode\times\else\texttimes\fi{}{10}^{13}{\mathrm{cm}}^{\ensuremath{-}3}),$ we find that the observed magnetic-field dependence of the spin relaxation is almost solely due to binary collisions between Rb atoms and hydrogen molecules, and that it is very well described by three rates: the Rb-Rb spin-exchange rate, the S-damping rate, and the Carver rate associated with the hyperfine pressure-shift interaction in collisions of Rb with

{\mathrm{H}}_{2}

molecules. At higher Rb densities, the contribution to the relaxation from Rb triplet dimers becomes significant.

We report calculations of the magnetic decoupling of the nuclear spin relaxation rate of

{}^{129}\mathrm{Xe}

atoms caused by binary collisions with Rb or Cs atoms in a gas. A semiclassical approximation, using a classical path for the collision and treating the spin interactions quantum mechanically, gives results that differ by no more than 2% from calculations with the distorted-wave Born approximation. Both computational methods show that the relaxation rate decreases substantially for magnetic fields of a few tens of teslas. For ${}^{129}\mathrm{Xe}\ensuremath{-}\mathrm{Rb},$ where recent experimental measurements are available, the calculated rate coefficients at the experimental field of 9.4 T are about 80% of the calculated values at zero field. At 9.4 T, the calculated rate coefficient for ${}^{129}\mathrm{Xe}\ensuremath{-}\mathrm{Rb}$ is about one-half of the experimentally observed value. This discrepancy is probably due to inaccuracies in the van der Waals and spin-dependent potentials used in the calculations.

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.

We report the first measurement of the spin-exchange rate coefficient for binary collisions between Cs and

^{129}\mathrm{Xe}

atoms in the temperature range $110<T<150\phantom{\rule{0.2em}{0ex}}\ifmmode^\circ\else\textdegree\fi{}\mathrm{C}$ at a $9.4\text{\ensuremath{-}}\mathrm{T}$ magnetic field. Under these conditions, binary spin-exchange collisions dominate the longitudinal nuclear spin-relaxation rate

1∕{T}_{1}

^{129}\mathrm{Xe}

gas. We measured

1∕{T}_{1}

of a thermally polarized Xe gas using the saturation-recovery of conventional nuclear magnetic resonance. We also directly measured the Cs atomic number density [Cs] by using Faraday rotation of the linear polarization of a probing laser beam passing through the sample. The measured rate coefficient is $\ensuremath{\kappa}(9.4\phantom{\rule{0.3em}{0ex}}\mathrm{T})=d(1∕{T}_{1})∕d[\mathrm{Cs}]=(2.81\ifmmode\pm\else\textpm\fi{}0.2)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}16}\phantom{\rule{0.3em}{0ex}}{\mathrm{cm}}^{3}∕\mathrm{s}$, which is about a factor of 1.6 higher than the previously measured spin-exchange rate coefficient of $^{129}\mathrm{Xe}\text{\ensuremath{-}}\mathrm{Rb}$ binary collisions. Using a calculated magnetic decoupling factor, we extrapolate our result to zero magnetic field: $\ensuremath{\kappa}(0\phantom{\rule{0.3em}{0ex}}\mathrm{T})=(4.1\ifmmode\pm\else\textpm\fi{}0.3)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}16}\phantom{\rule{0.3em}{0ex}}{\mathrm{cm}}^{3}∕\mathrm{s}$.

The longitudinal relaxation rate of

^{129}\mathrm{Xe}

nuclear spins slows down substantially in an external magnetic field of about 100 G. From an analysis of the magnetic slowing down and of the dependence of the zero-field relaxation rates on the third-body pressure, the authors have deduced the magnitudes of the spin-rotation and spin-exchange interactions in the

{\mathrm{Rb}}^{129}

Xe molecule, as well as the formation and breakup rates of RbXe in

{\mathrm{N}}_{2}

gas and the dissociation constant of RbXe. The magnetic slowing down shows directly that binary collisions contribute no more than a few percent to the relaxation rates.