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Measuring the spin polarization of alkali-metal atoms using nuclear magnetic resonance frequency shifts of noble gases

Xiaohu Liu, Hui Luo, Tianliang Qu, Kun Yang, Zhichao Ding

Published Oct 1, 2015• 21 citations
Publisher

Abstract

We report a novel method of measuring the spin polarization of alkali-metal atoms by detecting the NMR frequency shifts of noble gases. We calculated the profile of 87Rb D1 line absorption cross sections. We then measured the absorption profile of the sample cell, from which we calculated the 87Rb number densities at different temperatures. Then we measured the frequency shifts resulted from the spin polarization of the 87Rb atoms and calculated its polarization degrees at different temperatures. The behavior of frequency shifts versus temperature in experiment was consistent with theoretical calculation, which may be used as compensative signal for the NMRG closed-loop control system.

DOI
10.1063/1.4932131

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We report a novel method of measuring the spin polarization of alkali-metal atoms by detecting the NMR frequency shifts of noble gases. We calculated the profile of 87Rb D1 line absorption cross sections. We then measured the absorption profile of the sample cell, from which we calculated the 87Rb number densities at different temperatures. Then we measured the frequency shifts resulted from the spin polarization of the 87Rb atoms and calculated its polarization degrees at different temperatures. The behavior of frequency shifts versus temperature in experiment was consistent with theoretical calculation, which may be used as compensative signal for the NMRG closed-loop control system.
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.
We demonstrate a method for simultaneously measuring the spin polarizations of noble-gas and alkali-metal atoms. Under a low magnetic field, the polarized alkali-metal and noble-gas spin ensembles exhibit novel dynamics in the self-compensation and resonance regimes, which can be used to measure the polarizations. We perform this method on a K\mathrm{K}K-Rb\mathrm{Rb}Rb-21{}^{21}21Ne\mathrm{Ne}Ne comagnetometer with various operation temperatures and pump-light intensities. The polarization of alkali-metal electrons from 0.245 to 0.964 and the polarization of noble-gas nuclear spins from 0.01 to 0.065 are measured with relative uncertainties less than $12.4\mathrm{%}$. The measured polarizations are consistent with the theoretical model and are also verified by the traditional polarization-measurement method.
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.
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.
Self-compensated comagnetometers, employing overlapping samples of spin-polarized alkali and noble gases (for example K-3He{}^{3}\mathrm{He}3He) are promising sensors for exotic beyond-the-standard-model fields and high-precision metrology such as rotation sensing. When the comagnetometer operates in the so-called self-compensated regime, the effective field, originating from contact interactions between the alkali valence electrons and the noble-gas nuclei, is compensated with an applied magnetic field. When the comagnetometer begins operation in a given magnetic field, spin-exchange optical pumping establishes an equilibrium between the alkali electron-spin polarization and the nuclear-spin polarization. Subsequently, when the magnetic field is tuned to the compensation point, the spin polarization is brought out of the equilibrium conditions. This causes a practical issue for long measurement times. We report on a method for closed-loop control of the compensation field. This method allows optimization of the operating parameters, especially magnetic field gradients, in spite of the inherently slow (hours to days) dynamics of the system. With the optimization, higher stable nuclear polarization, longer relaxation times, and stronger electron-nuclear coupling are achieved which is useful for nuclear-spin-based quantum memory, spin amplifiers, and gyroscopes. The optimized sensor demonstrates a sensitivity comparable to the best previous comagnetometer but with four times lower noble-gas density. This paves the way for applications in both fundamental and applied science.
Theoretical pseudopotentials and dispersion potentials are used to study ground-state hyperfine splitting frequencies of alkali-metal atoms (Li, Na, K, Rb, and Cs) in noble gases (He, Ne, Ar, Kr, and Xe) in all combinations. With a single fitting parameter, calculations based on first-order perturbation theory qualitatively present each temperature dependence of the measured frequency shift. With this parameter and excitation energies of alkali-metal and noble-gas atoms, the hyperfine splitting frequency of alkali-metal atoms is suitable for investigating the properties of noble-gas atoms, such as the s-wave scattering length of electrons, the electric-dipole polarizability, and the van der Waals radius. This study suggests the possibility of improving excitation energies and van der Waals potentials of colliding pairs.