Nonlinear collision shifts of the 0–0 hyperfine transition due to van der Waals molecule formation

Abstract

We consider the origin of nonlinear collision shifts for the 0–0 hyperfine transition in alkali/noble-gas systems due to van der Waals molecule formation. Developing a semi-empirical model, we describe the shift as arising from three fundamental interactions: (1) a fractional change in the alkali’s valence electron density at the alkali nucleus, η, which affects the hyperfine contact term; (2) a mixing of p-wavefunction character into the alkali ground state (characterized by the probability for p-state character appearing in the perturbed wavefunction ξ12), which gives rise to an electric quadrupole term in the ground-state hyperfine splitting; and (3) an interaction of the alkali’s valence electron with the magnetic field produced by molecular rotation, characterized by a magnetic field strength BvdW. In addition to these molecular parameters, the model also depends on the formation rate of van der Waals molecules, kfP2, and the breakup rate of the molecules, kbP, where P is the noble-gas pressure. Fitting the model to the 85Rb/Xe and 87Rb/Xe experimental data of McGuyer and co-workers (and taking previously measured values for kf and BvdW), we find that η = 9 × 10−3, ξ12 = 5 × 10−3, and kb = 2.9×107 s−1/Torr.

Isotope study of the nonlinear pressure shifts of $^{85}$Rb and $^{87}$Rb hyperfine resonances in Ar, Kr, and Xe buffer gases

“…To determine the bound-atom eigenstates |µ , we must choose how to treat molecular rotation. Previous work [33][34][35]43,44 approximated rotation semi-classically in the interactions and thus separately from quantum spins. However, the derivation of ( 11) with an S-matrix requires the bound-atom |µ to be energy eigenstates.…”

“…or equivalently G and G , play the role of m for rotated, bound-atom spin eigenstates, as in previous work. 34,35,43,44…”

“…This Article is organized as follows: Section II provides a theoretical model for the linear and nonlinear pressure shifts of all hyperfine transitions in an alkali-metal atom from X 2 Σ + van der Waals molecules, reproducing all previous models except for the modifications of Camparo 43,44 discussed in Section V. The derivation includes the hyperfine-shift and spinrotation interactions of previous work, but predicts an important correction to the spin-rotation contribution. Additionally, it includes the Zeeman interaction and the dipolar-and quadrupolar-hyperfine interactions.…”

“…Section V discusses these results as well as a recent analysis of the Xe data by Camparo. 43,44 Section VI concludes the article, and the Supplementary Materials provide additional details, figures, and fitting parameters.…”

Kr-Based Buffer Gas for Rb Vapor-Cell Clocks

“…This is verified for light noble gases such as Ne and Ar. For heavier noble gases, 3-bodies interactions, and in particular the creation of Van der Waals molecules, introduce a departure from the strictly linear behavior [13][14][15]. Nevertheless, the non-linear shift contribution for Kr is limited to a few tens of Hz for typical pressures (P Kr ≤ 20 Torr), whereas the absolute shift induced by an Ar-N 2 mixture usually is of a few kHz [12].…”