High-precision Electric Dipole Polarizabilities of the Clock States in $^{133}$Cs

TL;DR

This paper precisely calculates the electric dipole polarizabilities of $^{133}$Cs clock states, combining advanced theoretical methods and experimental data to improve the accuracy of Stark shift estimations in high-precision measurements.

Contribution

The study provides highly accurate calculations of static and dynamic polarizabilities of $^{133}$Cs clock states, integrating relativistic coupled-cluster methods with experimental data for the first time.

Findings

Good agreement with experimental static polarizability values.

Reliable dynamic polarizability estimates for Stark shift calculations.

Enhanced understanding of hyperfine level contributions.

Abstract

We have calculated static and dynamic electric dipole (E1) polarizabilities ($\alpha_F$) of the hyperfine levels of the clock transition precisely in $^{133}$Cs. The scalar, vector, and tensor components of $\alpha_F$ are estimated by expressing as sum of valence, core, core-core, core-valence, and valence-core contributions that are arising from the virtual and core intermediate states. The dominant valence contributions are estimated by combining a large number of matrix elements of the E1 and magnetic dipole hyperfine interaction operators from the relativistic coupled-cluster method and measurements. For an insightful understanding of their accurate determination, we explicitly give intermediate contributions in different forms to the above quantities. Very good agreement of the static values for the scalar and tensor components with their experimental results suggest that our estimated dynamic $\alpha_F$ values can be used reliably to estimate the Stark shifts while conducting high-precision measurements at the respective laser frequency using the clock states of $^{133}$Cs.