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 [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.