The low-lying n(=3,4,5)d $^2D_{5/2}$ states alkaline earth ions are of vital importance in a number of different physical applications. The hyperfine structure constants of these states are characterized by unusually strong electron correlation effects. Relativistic coupled-cluster theory has been employed to carry out {\it ab initio} calculations of these constants. The role of the all order core-polarization effects was found to be decisive in obtaining good agreement of the results of our calculations with accurate measurements. The present work is an apt demonstration of the power of the coupled-cluster method to cope with strongly interacting configurations.
The Z-vector method in the relativistic coupled-cluster framework is used to calculate magnetic hyperfine structure constant ($A_J$) of alkali metals and singly charged alkaline earth metals in their ground state electronic configuration. The Z-vector results are in very good agreement with the experiment. The $A_J$ values of Li, Na, K, Rb, Cs, Be$^{+}$, Mg$^{+}$, Ca$^{+}$, and Sr$^{+}$ obtained in the Z-vector method are compared with the extended coupled-cluster results taken from Phys. Rev. A 91, 022512 (2015). The same basis and cutoff are used for the comparison purpose. The comparison sh…
Ultracold molecules with both electron spin and an electric dipole moment offer new possibilities in quantum science. We use density-functional theory to calculate hyperfine coupling constants for a selection of molecules important in this area, including RbSr, LiYb, RbYb, CaF and SrF. We find substantial hyperfine coupling constants for the fermionic isotopes of the alkaline-earth and Yb atoms. We discuss the hyperfine level patterns and Zeeman splittings expected for these molecules. The results will be important both to experiments aimed at forming ultracold open-shell molecules and to thei…
Measuring the hyperfine structure (HFS) of long-lived $^3P_2$ states of divalent atoms may offer the opportunity of extracting relatively unexplored nuclear magnetic octupole and electric hexadecapole moments. Here, using relativistic many-body methods of atomic structure and the nuclear shell model, we evaluate the effect of these higher nuclear moments on the hyperfine structure. We find that the sensitivity of HFS interval measurements in $^{87}$Sr needed to reveal the perturbation caused by the nuclear octupole moment is on the order of kHz. Results of similar analyses for $^{9}$Be, $^{25}…
The Z-vector method in the relativistic coupled-cluster framework is employed to calculate the parallel and perpendicular components of the magnetic hyperfine structure constant of a few small alkaline earth hydrides (BeH, MgH, and CaH) and fluorides (MgF and CaF). We have compared our Z-vector results with the values calculated by the extended coupled-cluster (ECC) method reported in Phys. Rev. A 91 022512 (2015). All these results are compared with the available experimental values. The Z-vector results are found to be in better agreement with the experimental values than those of the ECC va…
This article deals with the general implementation of 4-component spinor relativistic extended coupled cluster (ECC) method to calculate first order property of atoms and molecules in their open-shell ground state configuration. The implemented relativistic ECC is employed to calculate hyperfine structure (HFS) constant of alkali metals (Li, Na, K, Rb and Cs), singly charged alkaline earth metal atoms (Be+, Mg+, Ca+ and Sr+) and molecules (BeH, MgF and CaH). We have compared our ECC results with the calculations based on restricted active space configuration interaction (RAS-CI) method. Our re…
The theory is developed for one and two atom interactions when the atom has a Rydberg electron attached to a hyperfine split core state. This situation is relevant for some of the rare earth and alkaline earth atoms that have been proposed for experiments on Rydberg-Rydberg interactions. For the rare earth atoms, the core electrons can have a very substantial total angular momentum, $J$, and a non-zero nuclear spin, $I$. In the alkaline earth atoms there is a single, $s$, core electron whose spin can couple to a non-zero nuclear spin for odd isotopes. The resulting hyperfine splitting of the c…
We present additional magic wavelengths ($λ_{\rm{magic}}$) for the clock transitions in the alkaline-earth metal ions considering circular polarized light aside from our previously reported values in [J. Kaur et al., Phys. Rev. A {\bf 92}, 031402(R) (2015)] for the linearly polarized light. Contributions from the vector component to the dynamic dipole polarizabilities ($α_d(ω)$) of the atomic states associated with the clock transitions play major roles in the evaluation of these $λ_{\rm{magic}}$, hence facilitating in choosing circular polarization of lasers in the experiments. Moreover, the …
We experimentally demonstrate hyperfine optical pumping of rubidium atoms probed by an evanescent electromagnetic field at a dielectric-vapor interface. This light-atom interaction at the nanoscale is investigated using a right angle prism integrated with a vapor cell and excited by evanescent wave under total internal reflection. An efficient hyperfine optical pumping, leading to a complete suppression of absorption on the probed evanescent signal, is observed when a pump laser beam is sent at normal incidence to the interface. In contrast, when the pump and probe beams are co-propagating in …
The circular polarized laser beam of the ``magic'' wavelength may be used for mixing the $^3P_1$ state into the long-living metastable state $^3P_0$, thus enabling the strictly forbidden $^1S_0$$-$$^3P_0$ ''clock'' transition in even isotopes of alkaline-earth-like atoms, without change of the transition frequency. In odd isotopes the laser beam may adjust to an optimum value the line width of the "clock" transition, originally enabled by the hyperfine mixing. We present a detailed analysis of various factors influencing resolution and uncertainty for an optical frequency standard based on ato…
We demonstrate an iterative scheme for coupled-cluster properties calculations without truncating the dressed properties operator. For validation, magnetic dipole hyperfine constants of alkaline Earth ions are calculated with relativistic coupled-cluster and role of electron correlation examined. Then, a detailed analysis of the higher order terms is carried out. Based on the results, we arrive at an optimal form of the dressed operator. Which we recommend for properties calculations with relativistic coupled-cluster theory.
We study the formation and destabilization of dark states in a single trapped 88Sr+ ion caused by the cooling and repumping laser fields required for Doppler cooling and fluorescence detection of the ion. By numerically solving the time-dependent density matrix equations for the eight-level system consisting of the sublevels of the 5s 2S1/2, 5p 2P1/2, and 4d 2D3/2 states, we analyze the different types of dark states and how to prevent them in order to maximize the scattering rate, which is crucial for both the cooling and the detection of the ion. The influence of the laser linewidths and ion…
We measure the spectrum of tellurium-130 in the vicinity of the 461~nm ${}^1\text{S}_0-{}^{1}\text{P}_1$ cycling transition in neutral strontium, a popular element for atomic clocks, quantum information, and quantum-degenerate gases. The lack of hyperfine structure in tellurium results in a spectral density of transitions nearly 50 times lower than that available in iodine, making use of tellurium as a laser-frequency reference challenging. By frequency-offset locking two lasers, we generate the large frequency shifts required to span the difference between a tellurium line and the ${}^1\text{…
We demonstrate all-optical implementation of spin-orbit coupling (SOC) in a two-electron Fermi gas of $^{173}$Yb atoms by coupling two hyperfine ground states with a narrow optical transition. Due to the SU($N$) symmetry of the $^1$S$_0$ ground-state manifold which is insensitive to external magnetic fields, an optical AC Stark effect is applied to split the ground spin states, which exhibits a high stability compared with experiments on alkali and lanthanide atoms, and separate out an effective spin-1/2 subspace from other hyperfine levels for the realization of SOC. The dephasing spin dynami…
We present a comprehensive spectroscopic study of C$_{2v}$ point-group symmetry sites in Sm$^{3+}$:CaF$_2$/SrF$_2$ codoped with either NaF or LiF. Data includes electron paramagnetic resonance measurements of Zeeman and hyperfine interactions for the ground state, as well as site-selective excitation and fluorescence spectroscopy up to the $^{4}$G$_{5/2}$ multiplet. Inclusion of the EPR data allowed us to determine unique crystal-field parameters. The parameters provide information about the geometry of the sites and the nature of the interactions between the Sm$^{3+}$ dopant and the alkaline …
Determination of nuclear quadrupole moments for $^{25}$Mg, $^{87}$Sr, and $^{135,137}$Ba via configuration-interaction combined with a coupled-cluster approach
