Nuclear-spin-dependent corrections to the transition polarizability in cesium

TL;DR

This paper reveals that nuclear spin influences transition polarizabilities in cesium due to hyperfine mixing, introducing tensor contributions previously neglected, which affects interpretations of atomic parity violation experiments.

Contribution

It demonstrates the nuclear spin dependence of transition polarizabilities in cesium, including tensor contributions, using third-order perturbation theory, a novel insight in atomic physics.

Findings

Nuclear spin dependence arises from hyperfine mixing.

Tensor contributions to transition polarizability are significant.

Corrections are minor for current experiments but important for future precision.

Abstract

The Stark-interference technique is commonly used to amplify the feeble parity-violating signal in atomic experiments. As a result, interpretation of these experiments in terms of electroweak observables requires knowledge of the Stark-induced $E1$ transition amplitudes or, equivalently, transition polarizabilities. While the literature assumes that these transition polarizabilities do not depend on the nuclear spin, here we prove the contrary. The nuclear spin dependence arises due to hyperfine mixing of atomic states and requires a third-order perturbation theory (one hyperfine interaction and two electric-dipole interactions) treatment. We demonstrate that the so far neglected {\em tensor} contribution appears in the transition polarizability and present numerical results for the nuclear-spin-dependent corrections to the $6S_{1/2}\rightarrow{7S_{1/2}}$ transition polarizability in $^{133}$Cs. We investigate the effect of these corrections to transition polarizabilities on the extraction of the $^{133}$Cs anapole moment from the Boulder experiment [Science 275, 1759 (1997)]. We also consider their effect on the extraction of the ratio between the scalar and vector transition polarizabilities from the measurements [Phys. Rev. A 55, 2 (1997)]. While the corrections are minor at the current level of experimental accuracy, our analysis provides a framework for future experiments.