Dynamic polarizability measurements in $^{176}$Lu$^+$

TL;DR

This paper presents experimental measurements of the differential polarizability of the $^{176}$Lu$^+$ clock transition across multiple wavelengths, and compares these with advanced theoretical calculations to improve understanding of blackbody radiation shifts.

Contribution

It introduces precise experimental measurements of differential polarizability in $^{176}$Lu$^+$ and develops a hybrid theoretical model including quadratic and triple excitations.

Findings

Experimental differential polarizability data up to 372 THz.

Verification of measurement methods through independent approaches.

High-precision benchmarks for matrix elements supporting the theoretical model.

Abstract

We measure the differential polarizability of the $^{176}$Lu$^+$ $^1S_0$ -to- ${^3}D_1$ clock transition at multiple wavelengths. This experimentally characterizes the differential dynamic polarizability for frequencies up to 372 THz and allows an experimental determination of the dynamic correction to the blackbody radiation shift for the clock transition. In addition, measurements at the near resonant wavelengths of 598 and 646 nm determine the two dominant contributions to the differential dynamic polarizability below 372 THz. These additional measurements are carried out by two independent methods to verify the validity of our methodology. We also carry out a theoretical calculation of the polarizabilities using the hybrid method that combines the configuration interaction (CI) and the coupled-cluster approaches, incorporating for the first time quadratic non-linear terms and partial triple excitations in the coupled-cluster calculations. The experimental measurements of the $|\langle ^3D_1|| r || ^3P_J\rangle|$ matrix elements provide high-precision benchmarks for this theoretical approach.