The five longest tune-out wavelengths for the potassium atom are determined using a relativistic structure model which treats the atom as consisting of a single valence electron moving outside a closed shell core. The importance of various terms in the dynamic polarizability in the vicinity of the $4{p}_{J}$, $5{p}_{J}$, and $6{p}_{J}$ transitions are discussed.
The five longest tune-out wavelengths for the potassium atom are determined using a relativistic structure model which treats the atom as consisting of a single valence electron moving outside a closed shell core. The importance of various terms in the dynamic polarizability in the vicinity of the 4pJ, 5pJ, and 6pJ transitions are discussed.
The five longest tune-out wavelengths for the rubidium atom are predicted from existing experimental and theoretical information by using an approximation formula. The formula is derived from the analysis of a non-relativistic configuration-interaction plus core polarization (CICP) calculation of the tune-out wavelengths for rubidium. The differences between the wavelengths predicted from the approximation formula and the exact CICP calculation are at the 10 −3 nm level. The predicted five longest tune-out wavelengths are 790.115 nm, 423.155 nm, 421.111 nm, 359.429 nm, and 359.022 nm, respectively.
The lowest three tune-out wavelengths of the four alkaline-earth-metal atoms Be, Mg, Ca, and Sr are determined from tabulations of matrix elements produced from large first-principles calculations. The tune-out wavelengths are located near the wavelengths for the 3P1o and 1P1o excitations. The measurement of the tune-out wavelengths could be used to establish a quantitative relationship between the oscillator strength of the transition leading to existence of the tune-out wavelength and the dynamic polarizability of the atom at the tune-out frequency. The longest tune-out wavelengths for Be, Mg, Ca, Sr, Ba, and Yb are 454.9813, 457.2372, 657.446, 689.200, 788.875, and 553.00 nm, respectively.
The influence of hyperfine interactions on the tune-out wavelengths of the 39K, 40K, and 41K isotopes of the potassium atom was investigated. The hyperfine interaction of the 4s1/2 ground state results in a shift and splitting of the primary tune-out wavelength near 769 nm. The 4s1/2 state hyperfine splittings of the primary tune-out wavelength were almost equal to the hyperfine splittings of the ground states. The splittings in the wavelengths were 0.0009, 0.0026, and 0.0005 nm for 39K, 40K, and 41K, respectively. The hyperfine splitting of the npJ levels leads to the creation of additional tune-out wavelengths. The additional tune-out wavelengths could be difficult to detect due to very small differences from the transition wavelengths to the 4pJ,F states. The hyperfine Stark shift for the ground states of all three isotopes was also computed, and the value for 39K was found to be compatible with the previous experiments and the most recent calculation using relativistic many-body perturbation theory.
We report here oscillator strengths, transition rates, branching ratios, and lifetimes due to the allowed transitions in the potassium (K) atom. We evaluate electric dipole (E1) amplitudes using an all-order relativistic many-body perturbation method. The obtained results are compared with previously available experimental and theoretical studies. Using the E1 matrix elements mentioned above and estimated from the lifetimes of the 4p2P1/2,3/2 states, we determine precise values of static and dynamic polarizabilities for the first five low-lying states in the considered atom. The static polarizabilities of the ground and 4p2P1/2,3/2 states in the present work are more precise than the available measurements in these states. Only the present work employs relativistic theory to evaluate the polarizabilities in the 3d2D3/2,5/2 states for which no experimental results are known with which to compare. We also reexamine ``magic wavelengths'' for the $4p{\phantom{\rule{4pt}{0ex}}}^{2}\phantom{\rule{-0.16em}{0ex}}{P}_{1/2}\ensuremath{\rightarrow}4s{\phantom{\rule{4pt}{0ex}}}^{2}\phantom{\rule{-0.16em}{0ex}}{S}_{1/2}$ and $4p{\phantom{\rule{4pt}{0ex}}}^{2}\phantom{\rule{-0.16em}{0ex}}{P}_{3/2}\ensuremath{\rightarrow}4s{\phantom{\rule{4pt}{0ex}}}^{2}\phantom{\rule{-0.16em}{0ex}}{S}_{1/2}$ transitions due to the linearly polarized light, which are useful to perform the state-insensitive trapping of K atoms.
We carry out a systematic study of the static and dynamic polarizabilities of the potassium atom using a first-principles 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. Recommended values and uncertainties are provided for the relevant electric-dipole matrix elements. Polarizabilities of the 4s, 4pj, 5s, 5pj, and 3dj states are compared with other theoretical and experimental values when possible. We identify magic wavelengths for the $4s\ensuremath{-}np$ transitions for n=4,5, i.e., those wavelengths for which the two levels have the same ac Stark shifts. The magic wavelengths for the $4s\ensuremath{-}5p$ transitions are of particular interest for attaining a quantum gas of potassium at high phase-space density. We find 20 such wavelengths in the technically interesting region of 1050−−1130 nm.
Using the relativistic coupled-cluster method, we calculate the static dipole polarizabilities of the 6p, 7s, 7p, 8s, 8p, and 6d states and the dynamic dipole polarizabilities of the 6p and 7s states of the thallium atom. The trivalent thallium atom is computationally treated as a monovalent system, together with all linear and nonlinear terms of single- and double-cluster operators included in the correlation calculations. We observe that the dominating contributions to the static scalar polarizabilities of the 7s1/2, 7p1/2, 8p1/2, and 8p3/2 states are from one or two specific transitions. The matrix elements of these specific transitions can be determined by combining the experimental values of relevant static scalar polarizabilities. A number of magic wavelengths for the 6p1/2--7s and 6p3/2--7s transitions in the range of 488--1300 nm and the longest tune-out wavelength of the ground state are determined. These magic wavelengths and tune-out wavelength may be useful for further thallium experiments. Experimental measurements of the magic wavelengths near 1245 nm would give estimates of the 7s1/2--7p1/2 and 7s1/2--7p3/2 transition matrix elements and their ratio. Furthermore, lifetimes of many excited states, as well as the Stark-induced scalar and vector dipole polarizabilities for the 6p1/2--7p1/2 transition, are also evaluated and compared with available theoretical and experimental values.