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Bulletin of the American Physical Society

Nonlinear pressure shifts of alkali-metal atoms in xenon

B. H. McGuyer, Tian Xia, Yuan‐Yu Jau, W. Happer

Published Jun 17, 2011• 0 citations
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Abstract

We demonstrate that the microwave resonant frequencies of ground-state 87Rb and 133Cs atoms have a nonlinear dependence on the pressure of the buffer gas Xe. Surprisingly, though the frequency shifts of Rb and Cs in the heavy noble gases Ar, Kr, and Xe are all negative, the nonlinearity in Xe is of the opposite sign to the nonlinearities in Ar and Kr. This discrepancy suggests that the frequency shifts due to alkali-noble van der Waals molecules in Xe are opposite in sign to the those in Ar and Kr. The nonlinearity in Xe shows a reproducible deviation from a simple model used to describe the shifts in Ar and Kr, which suggests that the spin-rotation interaction plays a significant role in the frequency shifts due to molecules. No nonlinearities were observed with the gases He and N 2 , as expected, and also Ne to within experimental error, which suggests that molecules do not form in Ne. Additionally, we present improved measurements of the shifts of Rb in Ar and Kr and of Rb and Cs in He and N 2 .

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Nonlinear pressure shifts of alkali-metal atoms in Xenon

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We demonstrate that the microwave resonant frequencies of ground-state87Rb and133Csatoms have a nonlinear dependence on the pressure of the buffer gas Xe. Surprisingly, though the frequency shifts of Rb and Cs in the heavy noble gases Ar, Kr, and Xe are all negative, the nonlinearity in Xe is of the opposite sign to the nonlinearities in Ar and Kr. This discrepancy suggests that the frequency shifts due to alkali-noble van der Waals molecules in Xe are opposite in sign to the those in Ar and Kr. The nonlinearity in Xe shows a reproducible deviation from a simple model used to describe the shifts in Ar and Kr, which suggests that the spin-rotation interaction plays a significant role in the frequency shifts due to molecules. No nonlinearities were observed with the gases He and N2, as expected, and also Ne to within experimental error, which suggests that molecules do not form in Ne. Additionally, we present improved measurements of the shifts of Rb in Ar and Kr and of Rb and Cs in He and N2.

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We demonstrate that the microwave resonant frequencies of ground-state 87Rb and 133Cs atoms have a nonlinear dependence on the pressure of the buffer gas Xe. Surprisingly, though the frequency shifts of Rb and Cs in the heavy noble gases Ar, Kr, and Xe are all negative, the nonlinearity in Xe is of the opposite sign to the nonlinearities in Ar and Kr. This discrepancy suggests that the frequency shifts due to alkali-noble van der Waals molecules in Xe are opposite in sign to the those in Ar and Kr. The nonlinearity in Xe shows a reproducible deviation from a simple model used to describe the shifts in Ar and Kr, which suggests that the spin-rotation interaction plays a significant role in the frequency shifts due to molecules. No nonlinearities were observed with the gases He and N 2 , as expected, and also Ne to within experimental error, which suggests that molecules do not form in Ne. Additionally, we present improved measurements of the shifts of Rb in Ar and Kr and of Rb and Cs in He and N 2 .
We demonstrate that the microwave resonant frequencies of ground-state87Rb and133Csatoms have a nonlinear dependence on the pressure of the buffer gas Xe. Surprisingly, though the frequency shifts of Rb and Cs in the heavy noble gases Ar, Kr, and Xe are all negative, the nonlinearity in Xe is of the opposite sign to the nonlinearities in Ar and Kr. This discrepancy suggests that the frequency shifts due to alkali-noble van der Waals molecules in Xe are opposite in sign to the those in Ar and Kr. The nonlinearity in Xe shows a reproducible deviation from a simple model used to describe the shifts in Ar and Kr, which suggests that the spin-rotation interaction plays a significant role in the frequency shifts due to molecules. No nonlinearities were observed with the gases He and N2, as expected, and also Ne to within experimental error, which suggests that molecules do not form in Ne. Additionally, we present improved measurements of the shifts of Rb in Ar and Kr and of Rb and Cs in He and N2.
We demonstrated the nonlinear dependence of the microwave resonance frequencies of ground-state Rb or Cs atoms on the pressure of the buffer gases Ar and Kr. No nonlinearities were observed in the gases He or N2. These observations strongly suggest that the nonlinearities are due to the van der Waals molecules that form in Ar and Kr, but not in He or N2. We developed a simple model, parameterized by the effective three-body formation rate of molecules and by the effective product of the collisionally-limited lifetime times the shift of the hyperfine coupling coefficient in the molecule, and it explained the data very well.
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.
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.
Collisions with chemically inert atoms or molecules change the hyperfine coupling $A\phantom{\rule{0.16em}{0ex}}\mathbf{I}\ifmmode\cdot\else\textperiodcentered\fi{}\mathbf{S}$ of an alkali-metal atom through the hyperfine-shift interaction $\ensuremath{\delta}A\phantom{\rule{0.16em}{0ex}}\mathbf{I}\ifmmode\cdot\else\textperiodcentered\fi{}\mathbf{S}$. This interaction is responsible for the pressure shifts of the microwave resonances of alkali-metal atoms in buffer gases, is an important spin interaction in alkali-metal--noble-gas van der Waals molecules, and is anticipated to enable the magnetoassociation of ultracold molecules such as RbSr. An improved estimate is presented for the long-range asymptote of this interaction for Na, K, Rb, and Cs. To test the results, the change in hyperfine coupling due to a static electric field is estimated and reasonable agreement is found.
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.