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 $ns$, $n{p}_{1∕2}$, $n{p}_{3∕2}$ 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 $n{p}_{1∕2}$ and $n{p}_{3∕2}$ atomic levels have the same ac Stark shifts, which facilitates state-insensitive optical cooling and trapping.

Using first-principles calculations, we identify “tune-out” optical wavelengths, ${\lambda }_{\mathrm{zero}}$, for which the ground-state frequency-dependent polarizabilities of alkali-metal atoms vanish. Our approach uses high-precision, relativistic all-order method in which all single, double, and partial triple excitations of the Dirac-Fock wave functions are included to all orders of perturbation theory. We discuss the use of tune-out wavelengths for sympathetic cooling in two-species mixtures of alkali metals with group II and other elements of interest. Special cases in which these wavelengths coincide with strong resonance transitions in a target system are identified.

We present results of first-principles calculations of the frequency-dependent polarizabilities of all alkali-metal atoms for light in the wavelength range 300–1600 nm, with particular attention to wavelengths of common infrared lasers. We parametrize our results so that they can be extended accurately to arbitrary wavelengths above 800 nm. This work is motivated by recent experiments involving simultaneous optical trapping of two different alkali-metal species. Our data can be used to predict the oscillation frequencies of optically trapped atoms, and particularly the ratios of frequencies of different species held in the same trap. We identify wavelengths at which two different alkali-metal atoms have the same oscillation frequency.

We study the cancellation of differential ac Stark shifts in the 5s and 5p states of the rubidium atom using the linearly and circularly polarized lights by calculating their dynamic polarizabilities. Matrix elements were calculated using a relativistic coupled-cluster method at the single and double excitations and at the important valence triple excitation approximation including all possible nonlinear correlation terms. Some of the important matrix elements were further optimized using the experimental results available for the lifetimes and static polarizabilities of atomic states. ``Magic wavelengths'' are determined from the differential Stark shifts and results for the linearly polarized light are compared with the previously available results. The possible scope of facilitating state-insensitive optical trapping schemes using the magic wavelengths for circularly polarized light is discussed. Using the optimized matrix elements, the lifetimes of the 4d and 6s states of this atom are ameliorated.

Motivated by the prospect of an optical frequency standard based on ${}^{43}\mathrm{Ca}^{+}$, we calculate the blackbody-radiation (BBR) shift of the $4s_{1∕2}-3d_{5∕2}$ clock transition, which is a major component of the uncertainty budget. The calculations are based on the relativistic all-order single-double method where all single and double excitations of the Dirac-Fock wave function are included to all orders of perturbation theory. Additional calculations are conducted for the dominant contributions in order to evaluate some omitted high-order corrections and estimate the uncertainties of the final results. The BBR shift obtained for this transition is $0.38\left(1\right)\mathrm{Hz}$. The tensor polarizability of the $3d_{5∕2}$ level is also calculated and its uncertainty is evaluated as well. Our results are compared with other calculations.