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

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 4p_j-3d_j^′ transitions in K and 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.