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Joint Conference of the European Frequency and Time Forum and IEEE International Frequency Control Symposium (EFTF/IFCS)

Nonlinear Pressure Shifts of 87Rb and 133Cs in Ar and Kr

F. Gong, Yuan‐Yu Jau, W. Happer

Published May 1, 2008• 1 citation
Publisher

Abstract

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.

DOI
10.1109/freq.2008.4622969

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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.
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.
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.
Relaxation experiments performed on optically polarized Rb atoms in a rare gas have been previously reported; their detailed interpretation is given below. It is shown that the relaxation governed by the spin-orbit interaction is strongly affected by the formation of chemically unstable Rb-Kr molecules bound by van der Waals forces. Two processes of molecule formation are analyzed: binary resonant collisions leading to metastable states and three-body collisions producing actual bound states. A relaxation model valid for any disorientation probability per single Rb-Kr interaction is developed. Aside from clear evidence for the existence of alkali-rare-gas molecules, the success of the theoretical interpretation of the relaxation experiments yields the equilibrium constant $\mathcal{K}=1.7\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}22}$ cm3{\mathrm{cm}}^{3}cm3/molecule for the reaction Rb+Kr \ensuremath{\rightleftharpoons} Rb-Kr at 300\ifmmode^\circ\else\textdegree\fi{}K, the average lifetime of a Rb-Kr molecule in the gas phase, $\ensuremath{\tau}=0.65\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}7}$ sec, at a krypton pressure of one Torr, and the average spin-orbit coupling constant in a Rb-Kr molecule, $\overline{\ensuremath{\gamma}}{h}^{\ensuremath{-}1}=0.63$ MHz. It is also shown that the spin-orbit potential is predominantly short-range.
Relaxation experiments performed on alkali atoms polarized in their ground state by optical pumping in the presence of a rare gas have been previously reported and interpreted. It was shown that the relaxation governed by the spin-orbit interaction is strongly affected by the formation of chemically unstable Rb-Kr molecules bound by van der Waals forces. The previous theoretical analysis, restricted to the longitudinal relaxation, is extended here to relaxation processes involving the transverse components of the electronic polarization and hyperfine "coherences" (elements of the density matrix between different hyperfine states). The effects resulting from the action of a rf field are also examined. The main results of this work, among others, are (a) the prediction of a Zeeman transition-line pressure shift, in some circumstances larger by several orders of magnitude than the one calculated by Herman, and having a very peculiar variation with the rare-gas pressure; (b) a quantitative explanation of the anomalous pressure dependence of the hyperfine transition linewidth discovered by Bender and Cohen; (c) a proposal of a method of detection of rf transitions between states of the alkali---rare-gas molecules by their effect on the relaxation process.
The shift and broadening of the 87Rb^{87}\mathrm{Rb}87Rb 0-0 line (frequency 6.8 GHz) due to collisions with Kr atoms have been studied in the pressure range 0.2-10 Torr. The shift versus pressure has been found to be linear and equal to -542 \ifmmode\pm\else\textpm\fi{} 10 Hz/Torr. The linewidth results from the super-position of several effects which are analyzed, one of the most important being the relaxation due to the spin-orbit interaction experienced by Rb atoms while temporarily bound in van der Waals Rb-Kr molecules.