Magic wavelengths for the np-ns transitions in alkali-metal atoms

Extensive calculations of the electric-dipole matrix elements in alkali-metal atoms are conducted using the relativistic all-order method. This approach is a linearized version of the coupled-cluster method, which sums infinite sets of many-body perturbation theory terms. All allowed transitions between the lowest ns, np_1∕2, np_3∕2 states and a large number of excited states are considered in these calculations and their accuracy is evaluated. The resulting electric-dipole matrix elements are used for the high-precision calculation of frequency-dependent polarizabilities of the excited states of alkali-metal atoms. We find “magic” wavelengths in alkali-metal atoms for which the ns and np_1∕2 and np_3∕2 atomic levels have the same ac Stark shifts, which facilitates state-insensitive optical cooling and trapping.