Accurate determination of electric-dipole matrix elements in K and Rb from Stark shift measurements

TL;DR

This study combines high-precision Stark shift measurements with all-order calculations to accurately determine electric-dipole matrix elements in potassium and rubidium, crucial for optical standards and trapping applications.

Contribution

The paper introduces a method combining experimental Stark shift data with theoretical calculations to precisely determine matrix elements in K and Rb, improving accuracy for related applications.

Findings

Determined matrix elements with high precision using combined data and theory.

Validated the all-order calculation method for transitions involving nd states.

Provided benchmark data for future theoretical and experimental studies.

Abstract

Stark shifts of potassium and rubidium D1 lines have been measured with high precision by Miller et al [1]. In this work, we combine these measurements with our all-order calculations to determine the values of the electric-dipole matrix elements for the 4p_j-3d_j' transitions in K and for the 5p_j-4d_j' transitions in Rb to high precision. The 4p_1/2-3d_3/2 and 5p_1/2-4d_3/2 transitions contribute on the order of 90% to the respective polarizabilities of the np_1/2 states in K and Rb, and the remaining 10% can be accurately calculated using the relativistic all-order method. Therefore, the combination of the experimental data and theoretical calculations allows us to determine the np-(n-1)d matrix elements and their uncertainties. We compare these values with our all-order calculations of the np-(n-1)d matrix elements in K and Rb for a benchmark test of the accuracy of the all-order method for transitions involving nd states. Such matrix elements are of special interest for many applications, such as determination of magic wavelengths in alkali-metal atoms for state-insensitive cooling and trapping and determination of blackbody radiation shifts in optical frequency standards with ions.