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

Abstract

Stark shifts of potassium and rubidium $D1$ lines have been measured with high precision by Miller et al. [Phys. Rev. A 49, 5128 (1994)]. In this work, we combine these measurements with our all-order calculations to determine the values of the electric-dipole matrix elements for the $4{p}_{j}\text{\ensuremath{-}}3{d}_{{j}^{\ensuremath{'}}}$ transitions in K and the $5{p}_{j}\text{\ensuremath{-}}4{d}_{{j}^{\ensuremath{'}}}$ transitions in Rb to high precision. The $4{p}_{1/2}\text{\ensuremath{-}}3{d}_{3/2}$ and $5{p}_{1/2}\text{\ensuremath{-}}4{d}_{3/2}$ transitions contribute on the order of 90% to the respective polarizabilities of the $n{p}_{1/2}$ 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 $np\text{\ensuremath{-}}(n\ensuremath{-}1)d$ matrix elements and their uncertainties. We compare these values with our all-order calculations of the $np\text{\ensuremath{-}}(n\ensuremath{-}1)d$ 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.