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Physical Review A

Estimates of the relative magnitudes of the isotropic and anisotropic magnetic-dipole hyperfine interactions in alkali-metal–noble-gas systems

D. K. Walter, W. Happer, Thad G Walker

Published Nov 1, 1998• 34 citations
Publisher

Abstract

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-${}^{3}\mathrm{He}$ system; however, our confidence in the helium results is limited by a lack of knowledge of the interatomic potentials necessary for the calculation.

DOI
10.1103/physreva.58.3642

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A theory for calculating the spin–rotation coupling coefficient in alkali-metal–noble-gas van der Waals molecules was recently presented.1 It assumes the spin–rotation interaction in alkali-metal–noble-gas molecules to be mainly due to the spin–orbit interaction of the alkali-metal valence electron within the core of the noble gas, and predicts that the spin–rotation constant γ should depend on the spin–orbit interaction in the noble gas and be almost independent of the spin–orbit interaction of the alkali-metal atom. Experimentally, only a few of the possible pairs of the different alkali-metal atoms with different noble-gas atoms have been investigated. By measuring the sodium spin relaxation rate as a function of the helium buffer-gas pressure and the width of the sodium magnetic slowing-down curve, we report in this paper our experimentally determined value of the spin–rotation interaction constant in Na–Xe molecules γ = (1.1 ± 0.3)MHz. The measured value is nearly the same as was measured in K–Xe, Rb–Xe, and Cs–Xe.1 This result shows a reasonable agreement with the theoretical prediction.

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Frequency shifts of the magnetic-resonance spectrum of mixtures of nuclear spin-polarized noble gases and vapors of spin-polarized alkali-metal atoms

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Analytical model for polarization transfer during gas-phase collision events in spin-exchange optical pumping: Spin-$\frac{1}{2}$ $^{129}$Xe versus spin-$\frac{3}{2}$ $^{131}$Xe

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Spin-exchange optical pumping (SEOP) is a method for producing spin-hyperpolarized noble gas nuclei, such as 129Xe and 131Xe, which are used in various magnetic resonance applications from fundamental physics to quantum sensing and medical imaging. In SEOP, optically polarized alkali-metal atoms transfer their spin polarization to the noble gas nuclei in gas-phase collision events via the hyperfine coupling (HFC) between the alkali valence electron and the noble gas nucleus. While the polarization transfer physics of spin $I = 1/2$ nuclei, such as 129Xe, is relatively well understood, that of spin $I > 1/2$ nuclei, such as 131Xe ($I = 3/2$), has been far less studied, and no rigorous theoretical model has been presented to date. To this end, we derive a simple analytical model for the upper limit, neglecting relaxation, of the SEOP polarization transfer, applicable to noble gases with arbitrary nuclear spin. Analytical evaluation of the Baker-Campbell-Hausdorff expansion for the time evolution of the spin density operator $\hatρ(t)$ reveals that only even-order terms in the HFC contribute to the polarization transfer, with the leading-order quadratic term being the most significant. We obtain a result similar to that derived for the spin-exchange cross section by Herman [Phys. Rev. 137, A 1062 (1965)], but in a more general framework for the time evolution of $\hatρ(t)$ that is also more familiar to magnetic resonance researchers. The model is applied to understand the difference in the polarization transfer efficiency between 129Xe and 131Xe, yielding results in agreement with previous experiments. We also validate the model by comparison to detailed numerical multiscale simulations of the SEOP process, where full quantum-chemically computed spin Hamiltonians sampled from molecular dynamics simulations of the gas-phase collision events are used to propagate the spin dynamics.

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Impact of Heavy Noble Gases on the Magnetic Resonance Linewidth of Alkali-Metal Atoms: A Theoretical Study

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Nuclear magnetic resonance gyroscopes (NMRGs) employ noble-gas nuclear spins as inertial sensors and alkali-metal atoms as in-situ magnetometers. Heavy noble gases, particularly xenon, are widely used due to their large nuclear spin and strong spin-exchange coupling with alkali-metal atoms. However, their presence introduces additional collisional mechanisms that affect the alkali-metal magnetic resonance linewidth, thereby influencing magnetometer sensitivity and overall gyro performance. In this work, we develop a theoretical framework based on the density matrix formalism and master equation approach to quantitatively study how xenon-induced two-body and three-body interactions modify the linewidth of alkali-metal atoms under realistic NMRG conditions. Our analysis reveals that Xe atoms primarily broaden the linewidth via binary spindestruction collisions and van der Waals (vdW)-mediated F-damping processes, while the effect of Xe nuclear polarization is negligible at the ~1% level. We further demonstrate that nitrogen buffer gas plays a dual role: it directly contributes to alkali-metal spin relaxation through binary collisions and indirectly modulates vdW collision rates by altering molecular lifetimes. The interplay between these processes leads to an optimal nitrogen density that minimizes the linewidth. Additionally, we identify a temperature threshold above which light-narrowing emerges, with this threshold increasing alongside Xe density. These findings provide theoretical insight for optimizing spin relaxation control in alkali-metal magnetometers and improving NMRG performance.

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

Stephan Appelt, Andrei Ben-Amar Baranga, Christopher Erickson +3 more

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.

Physical Review A•Aug 1, 1998•443 citations
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∼95\ensuremath{\sim}95%\ensuremath∼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.
A theory for calculating the spin–rotation coupling coefficient in alkali-metal–noble-gas van der Waals molecules was recently presented.1 It assumes the spin–rotation interaction in alkali-metal–noble-gas molecules to be mainly due to the spin–orbit interaction of the alkali-metal valence electron within the core of the noble gas, and predicts that the spin–rotation constant γ should depend on the spin–orbit interaction in the noble gas and be almost independent of the spin–orbit interaction of the alkali-metal atom. Experimentally, only a few of the possible pairs of the different alkali-metal atoms with different noble-gas atoms have been investigated. By measuring the sodium spin relaxation rate as a function of the helium buffer-gas pressure and the width of the sodium magnetic slowing-down curve, we report in this paper our experimentally determined value of the spin–rotation interaction constant in Na–Xe molecules γ = (1.1 ± 0.3)MHz. The measured value is nearly the same as was measured in K–Xe, Rb–Xe, and Cs–Xe.1 This result shows a reasonable agreement with the theoretical prediction.
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.
We report the first quantitative theoretical and experimental studies of frequency shifts of nuclear-magnetic-resonance (NMR) lines of noble-gas atoms and the corresponding frequency shifts of electron-paramagnetic-resonance (EPR) lines of alkali-metal atoms in mixtures of nuclear spin-polarized noble gases and vapors of spin-polarized alkali-metal atoms. The shifts are primarily due to the Fermi-contact hyperfine interaction. For the heavier noble gases there can be relatively large (\ensuremath{\approxeq}10%) contributions to the shifts from van der Waals molecules. The NMR frequencies of polarized 83Kr^{83}\mathrm{Kr}83Kr and 129Xe^{129}\mathrm{Xe}129Xe were measured in a vapor of spin-polarized alkali-metal atoms oriented parallel and antiparallel to the external magnetic field. The shift in the EPR frequency of the alkali-metal vapor due to the polarized noble-gas nuclei was measured simultaneously, thus providing a measurement of the absolute noble-gas nuclear polarization. The frequency shifts can be used as a convenient way to measure the absolute nuclear spin polarization of noble gases.
Analytical model for polarization transfer during gas-phase collision events in spin-exchange optical pumping: Spin-12\frac{1}{2}21​ 129^{129}129Xe versus spin-32\frac{3}{2}23​ 131^{131}131Xe
Spin-exchange optical pumping (SEOP) is a method for producing spin-hyperpolarized noble gas nuclei, such as 129Xe and 131Xe, which are used in various magnetic resonance applications from fundamental physics to quantum sensing and medical imaging. In SEOP, optically polarized alkali-metal atoms transfer their spin polarization to the noble gas nuclei in gas-phase collision events via the hyperfine coupling (HFC) between the alkali valence electron and the noble gas nucleus. While the polarization transfer physics of spin I=1/2I = 1/2I=1/2 nuclei, such as 129Xe, is relatively well understood, that of spin I>1/2I > 1/2I>1/2 nuclei, such as 131Xe (I=3/2I = 3/2I=3/2), has been far less studied, and no rigorous theoretical model has been presented to date. To this end, we derive a simple analytical model for the upper limit, neglecting relaxation, of the SEOP polarization transfer, applicable to noble gases with arbitrary nuclear spin. Analytical evaluation of the Baker-Campbell-Hausdorff expansion for the time evolution of the spin density operator ρ^(t)\hatρ(t)ρ^​(t) reveals that only even-order terms in the HFC contribute to the polarization transfer, with the leading-order quadratic term being the most significant. We obtain a result similar to that derived for the spin-exchange cross section by Herman [Phys. Rev. 137, A 1062 (1965)], but in a more general framework for the time evolution of ρ^(t)\hatρ(t)ρ^​(t) that is also more familiar to magnetic resonance researchers. The model is applied to understand the difference in the polarization transfer efficiency between 129Xe and 131Xe, yielding results in agreement with previous experiments. We also validate the model by comparison to detailed numerical multiscale simulations of the SEOP process, where full quantum-chemically computed spin Hamiltonians sampled from molecular dynamics simulations of the gas-phase collision events are used to propagate the spin dynamics.
Nuclear magnetic resonance gyroscopes (NMRGs) employ noble-gas nuclear spins as inertial sensors and alkali-metal atoms as in-situ magnetometers. Heavy noble gases, particularly xenon, are widely used due to their large nuclear spin and strong spin-exchange coupling with alkali-metal atoms. However, their presence introduces additional collisional mechanisms that affect the alkali-metal magnetic resonance linewidth, thereby influencing magnetometer sensitivity and overall gyro performance. In this work, we develop a theoretical framework based on the density matrix formalism and master equation approach to quantitatively study how xenon-induced two-body and three-body interactions modify the linewidth of alkali-metal atoms under realistic NMRG conditions. Our analysis reveals that Xe atoms primarily broaden the linewidth via binary spindestruction collisions and van der Waals (vdW)-mediated F-damping processes, while the effect of Xe nuclear polarization is negligible at the ~1% level. We further demonstrate that nitrogen buffer gas plays a dual role: it directly contributes to alkali-metal spin relaxation through binary collisions and indirectly modulates vdW collision rates by altering molecular lifetimes. The interplay between these processes leads to an optimal nitrogen density that minimizes the linewidth. Additionally, we identify a temperature threshold above which light-narrowing emerges, with this threshold increasing alongside Xe density. These findings provide theoretical insight for optimizing spin relaxation control in alkali-metal magnetometers and improving NMRG performance.
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.