"Dressing" lines and vertices in calculations of matrix elements with the coupled-cluster method and determination of Cs atomic properties

We consider evaluation of matrix elements with the coupled-cluster method. Such calculations formally involve infinite number of terms and we devise a method of partial summation (dressing) of the resulting series. Our formalism is built upon an expansion of the product $C^\dagger C$ of cluster amplitudes $C$ into a sum of $n$-body insertions. We consider two types of insertions: particle/hole line insertion and two-particle/two-hole random-phase-approximation-like insertion. We demonstrate how to ``dress'' these insertions and formulate iterative equations. We illustrate the dressing equations in the case when the cluster operator is truncated at single and double excitations. Using univalent systems as an example, we upgrade coupled-cluster diagrams for matrix elements with the dressed insertions and highlight a relation to pertinent fourth-order diagrams. We illustrate our formalism with relativistic calculations of hyperfine constant $A(6s)$ and $6s_{1/2}-6p_{1/2}$ electric-dipole transition amplitude for Cs atom. Finally, we augment the truncated coupled-cluster calculations with otherwise omitted fourth-order diagrams. The resulting analysis for Cs is complete through the fourth-order of many-body perturbation theory and reveals an important role of triple and disconnected quadruple excitations.Comment: 16 pages, 7 figures; submitted to Phys. Rev.

Precision measurement noise asymmetry and its annual modulation as a dark matter signature

Dark matter may be composed of ultralight quantum fields that form macroscopic objects. As the Earth moves through the galaxy, interactions with such objects may leave transient signatures in terrestrial experiments. These signatures may be sought by analyzing correlations between multiple devices in a distributed network. However, if the objects are small (<~10^3 km) it becomes unlikely that more than one device will be affected in a given event. Such models may, however, induce an observable asymmetry in the noise distributions of precision measurement devices, such as atomic clocks. Further, an annual modulation in this asymmetry is expected. Such an analysis may be performed very simply using existing data, and would be sensitive to models with a high event rate, even if individual events cannot be resolved. For certain models, our technique extends the discovery reach beyond that of existing experiments by many orders of magnitude

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