Hyperfine frequencies of ${}^{87}$Rb and ${}^{133}$Cs atoms in Xe gas

The microwave resonant frequencies of ground-state ${}^{87}$Rb and ${}^{133}$Cs atoms in Xe buffer gas are shown to have a relatively large nonlinear dependence on the Xe pressure, presumably because of RbXe or CsXe van der Waals molecules. The nonlinear shifts for Xe are opposite in sign to the previously measured shifts for Ar and Kr, even though all three gases have negative linear shifts. The Xe data show striking discrepancies with the previous theory for nonlinear shifts. Most of this discrepancy is eliminated by accounting for the spin-rotation interaction, $\gamma \mathbf{N}·\mathbf{S}$, in addition to the hyperfine-shift interaction, $\delta A\mathbf{I}·\mathbf{S}$, in the molecules. To the limit of our experimental accuracy, the shifts of ${}^{87}$Rb and ${}^{133}$Cs in He, Ne, and N${}_2$ were linear with pressure.

Figure 1

Measured “0-0” resonant frequencies $\nu$ of ${}^{87}$Rb in Xe at 40.0${}^{\circ }$C and $B=1$ G. (a) The shift $\delta {\nu }_1=\nu -{\nu }_0$ from the free-atom frequency ${\nu }_0\approx 6.834683$ GHz. The solid line is the linear, limiting shift $sp$ at high pressures. (b) The nonlinear shift $\delta {\nu }_2=\delta {\nu }_1-sp$. The solid curve is the nonlinear shift ${\Delta }^2\nu$ of (3). (c) The fit residuals to (2), $\delta {\nu }_3=\delta {\nu }_2-{\Delta }^2\nu =\nu -f_0$. The solid curve is the difference, $f_1-f_0$, of the best-fit theoretical curves, with and without the spin-rotation interaction (4). Three separate data sets demonstrate the repeatability of the measurements.

Figure 2

Energy shifts of the sublevels of a ${}^{87}$Rb atom in a vdW molecule due to interactions (1) and (4). Representative perturbations $1+r_1\sigma$ of the coherence frequencies are shown. The sublevels are quantized along $\mathbf{N}$.

Figure 3

Summary of the nonlinear shifts $\delta {\nu }_2$ for ${}^{87}$Rb at 40${}^{\circ }$C and $B=1$ G and for ${}^{133}$Cs at 35${}^{\circ }$C and $B=0.2$ G. (a) Rb and Cs in Xe, with Rb in Ar and Kr for comparison. (b) Rb in Ar and Kr, and Rb and Cs in He, Ne, and N${}_2$. The solid curves are the function $f_0$ of (2) with parameters in Table .