Ion clock and search for the variation of the fine structure constant using optical transitions in Nd13+^{13+} and Sm15+^{15+}

We study ultranarrow $5s_{1/2}$ - $4f_{5/2}$ transitions in Nd$^{13+}$ and Sm$^{15+}$ and demonstrate that they lie in the optical region. The transitions are insensitive to external perturbations. At the same time they are sensitive to the variation of the fine structure constant $\alpha$. The fractional accuracy of the frequency of the transitions can be smaller than $10^{-19}$, which may provide a basis for atomic clocks of superb accuracy. Sensitivity to the variation of $\alpha$ approaches $10^{-20}$ per year.Comment: 4 pages, 2 tables, no figure

Magic frequencies for cesium primary frequency standard

We consider microwave hyperfine transitions in the ground state of cesium and rubidium atoms which are presently used as the primary and the secondary frequency standards. The atoms are confined in an optical lattice generated by a circularly polarized laser field. We demonstrate that applying an external magnetic field with appropriately chosen direction may cancel dynamic Stark frequency shift making the frequency of the clock transition insensitive to the strengths of both the laser and the magnetic fields. This can be attained for practically any laser frequency which is sufficiently distant from a resonance.Comment: 4 pages, 2 figure

Possibility of "magic" co-trapping of two atomic species in optical lattices

Much effort has been devoted to removing differential Stark shifts for atoms trapped in specially tailored "magic" optical lattices, but thus far work has focused on a single trapped atomic species. In this work, we extend these ideas to include two atomic species sharing the same optical lattice. We show qualitatively that, in particular, scalar J = 0 divalent atoms paired with non-scalar state atoms have the necessary characteristics to achieve such Stark shift cancellation. We then present numerical results on "magic" trapping conditions for 27Al paired with 87Sr, as well as several other divalent atoms.Comment: 5 pages, 2 figures, 1 tabl

Core-valence correlations for atoms with open shells

We present an efficient method of inclusion of the core-valence correlations into the configuration interaction (CI) calculations. These correlations take place in the core area where the potential of external electrons is approximately constant. A constant potential does not change the core electron wave functions and Green's functions. Therefore, all operators describing interaction of $M$ valence electrons and $N-M$ core electrons (the core part of the Hartree-Fock Hamiltonian $V^{N-M}$, the correlation potential $\hat\Sigma_1({\bf r},{\bf r'},E)$ and the screening of interaction between valence electrons by the core electrons $\hat\Sigma_2$) may be calculated with all $M$ valence electrons removed. This allows one to avoid subtraction diagrams which make accurate inclusion of the core-valence correlations for $M>2$ prohibitively complicated. Then the CI Hamiltonian for $M$ valence electrons is calculated using orbitals in complete $V^{N}$ potential (the mean field produced by all electrons); $\hat\Sigma_1$ + $\hat\Sigma_2$ are added to the CI Hamiltonian to account for the core-valence correlations. We calculate $\hat\Sigma_1$ and $\hat\Sigma_2$ using many-body perturbation theory in which dominating classes of diagrams are included in all orders. We use neutral Xe I and all positive ions up to Xe VIII as a testing ground. We found that the core electron density for all these systems is practically the same. Therefore, we use the same $\hat\Sigma_1$ and $\hat\Sigma_2$ to build the CI Hamiltonian in all these systems ($M=1,2,3,4,5,6,7,8$). Good agreement with experiment for energy levels and Land\'{e} factors is demonstrated for all cases from Xe I to Xe VIII.Comment: 13 pages, 5 figure

Micromagic clock: microwave clock based on atoms in an engineered optical lattice

We propose a new class of atomic microwave clocks based on the hyperfine transitions in the ground state of aluminum or gallium atoms trapped in optical lattices. For these elements magic wavelengths exist at which both levels of the hyperfine doublet are shifted at the same rate by the lattice laser field, cancelling its effect on the clock transition. Our analysis of various systematic effects shows that, while offering an improved control over systematic errors, the accuracy of the proposed microwave clock is competitive to that of the state-of-the-art primary frequency standard.Comment: 4pgs+3fig

AC Stark shift of the Cs microwave atomic clock transitions

We analyze the AC Stark shift of the Cs microwave atomic clock transition theoretically and experimentally. Theoretical and experimental data are in a good agreement with each other. Results indicate the absence of a magic wavelength at which there would be no differential shift of the clock states having zero projections of the total angular momentum