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, $^{25}$Mg, and $^{43}$Ca are also reported.
Hyperfine structures of $^{211}$Fr due to the interactions of magnetic dipole ($μ$), electric quadrupole ($Q$) and magnetic octupole ($Ω$) moments with the electrons are investigated using the relativistic coupled-cluster (RCC) theory with an approximation of singles, doubles and important valence triples excitations in the perturbative approach. Validity of our calculations are substantiated by comparing the results with their available experimental values. Its $Q$ value has also been elevated by combining the measured hyperfine structure constant of the $7p \ ^2P_{3/2}$ state with our improv…
Hyperfine structure (HFS) of atomic energy levels arises due to interactions of atomic electrons with a hierarchy of nuclear multipole moments, including magnetic dipole, electric quadrupole and higher rank moments. Recently, a determination of the magnetic octupole moment of the $^{173}\mathrm{Yb}$ nucleus was reported from HFS measurements in neutral ${}^{173}\mathrm{Yb}$ [PRA 87, 012512 (2013)], and is four orders of magnitude larger than the nuclear theory prediction. Considering this substantial discrepancy between the spectroscopically extracted value and nuclear theory, here we propose …
The magnetic octupole moment of 87Rb is determined from hyperfine intervals in the 5p 2P[3/2] state measured by Ye et al. [Opt. Lett. 21, 1280 (1996)]. Hyperfine constants A = 84.7189(22) MHz, B = 12.4942(43) MHz, and C = -0.12(09) kHz are obtained from the published measurements. The existence of a significant value for C indicates the presence of a nuclear magnetic octupole moment Omega. Combining the hyperfine constants with atomic structure calculations, we obtain Omega = -0.58(39) (b muN). Second-order corrections arising from interaction with the nearby 5p 2P[1/2] state are found to be i…
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…
Hyperfine-induced electric dipole contributions may significantly increase probabilities of otherwise very weak electric octupole and magnetic quadrupole atomic clock transitions (e.g. transitions between $s$ and $f$ electron orbitals). These transitions can be used for exceptionally accurate atomic clocks, quantum information processing and search for dark matter. They are very sensitive to new physics beyond the Standard Model, such as temporal variation of the fine structure constant, the Lorentz invariance and Einstein equivalence principle violation. We formulate conditions under which th…
We measure hyperfine structure in the metastable ${^3P}_2$ state of $^{173}$Yb and extract the nuclear magnetic octupole moment. We populate the state using dipole-allowed transitions through the ${^3P}_1$ and ${^3S}_1$ states. We measure frequencies of hyperfine transitions of the ${^3P}_2 \rightarrow {^3S}_1$ line at 770 nm using a Rb-stabilized ring cavity resonator with a precision of 200 kHz. Second-order corrections due to perturbations from the nearby ${^3P}_1$ and ${^1P}_1$ states are below 30 kHz. We obtain the hyperfine coefficients as: $A=-742.11(2)$ MHz, $B=1339.2(2)$ MHz, which re…
The hyperfine structure of the long-lived $5D_{3/2}$ and $5D_{5/2}$ levels of Ba$^+$ ion is analyzed. A procedure for extracting relatively unexplored nuclear magnetic moments $Ω$ is presented. The relevant electronic matrix elements are computed in the framework of the ab initio relativistic many-body perturbation theory. Both the first- and the second-order (in the hyperfine interaction) corrections to the energy levels are analyzed. It is shown that a simultaneous measurement of the hyperfine structure of the entire $5D_J$ fine-structure manifold allows one to extract $Ω$ without contaminat…
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 c…
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…
We present precision measurements of the hyperfine intervals in the 5D3/2 manifold of a single trapped Barium ion, 137 Ba+ . Measurements of the hyperfine intervals are made between mF = 0 sublevels over a range of magnetic fields allowing us to interpolate to the zero field values with an accuracy below a few Hz, an improvement on previous measurements by three orders of magnitude. Our results, in conjunction with theoretical calculations, provide a 30-fold reduction in the uncertainty of the magnetic dipole (A) and electric quadrupole (B) hyperfine constants. In addition, we obtain the magne…
We report the measurement of the hyperfine splitting in the $7D_{5/2}$ state of $^{133}$Cs using high resolution Doppler-free two-photon spectroscopy enabled by precise frequency scans using an acousto-optic modulator. All the six hyperfine levels are resolved in our spectra. We determine the hyperfine coupling constants A = -1.70867(62) MHz and B = 0.050(14) MHz which represent over 20-times improvement in the precision of both A and B. Moreover, our measurement is sufficiently precise to put bounds on the value of the magnetic octupole coupling constant C = 0.4(1.4) kHz for the $7D_{5/2}$ st…
Hyperfine-structure constants of odd Ra$^{+}$ due to the interactions of nuclear magnetic dipole, electric quadrupole, and magnetic octupole moments with the electrons are investigated in the framework of relativistic coupled-cluster method within single- and double-excitation approximation. The calculated energies and magnetic dipole hyperfine-structure constants $A$ exhibit a good agreement with available experimental values. Combining with the experimental electric quadrupole hyperfine-structure constant, we also extracted the electric quadrupole moments $Q$ of $^{209,211,221,223}$Ra. Our $…
We perform precision measurements on the 5D$_{5/2}$ manifold hyperfine intervals of a single trapped ion, $^{137}$Ba$^+$. RF spectroscopy is used to measure the hyperfine intervals to an accuracy of a few Hz. Our results provide a three orders of magnitude improvement in accuracy over previous work and also provide a 10-fold improvement in the value of $g_J$ for this level. These results complement our previous work on the 5D$_{3/2}$ manifold of $^{137}$Ba$^+$, providing an independent measurement of the nuclear octupole, and a consistency check on atomic structure calculations.
The hyperfine constants of the $^3$P$^{\circ}_2$ state in neutral Yb have been measured using three different dipole transitions. This state was recently shown to have a comparatively large hyperfine magnetic octupole splitting, and thus a puzzlingly large magnetic octupole moment. The measurement is performed using collinear laser spectroscopy on a fast atomic beam, which provides a straightforward route to probing long-lived metastable atomic states with high resolution. From the combined analysis of all three lines we find no significant evidence for a non-zero octupole moment in $^{173}$Yb…
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 …
$^{229}$Th is a promising candidate for developing a nuclear optical clock and searching the new physics beyond the standard model. Accurate knowledge of the nuclear properties of $^{229}$Th is very important. In this work, we calculate hyperfine-structure constants for the first four states of $^{229}$Th$^{3+}$ using the relativistic coupled-cluster method based on the Gauss basis set. The no-pair Dirac-Coulomb-Breit Hamiltonian with the lowest-order quantum electrodynamics (QED) correction is the starting point, together with all linear and non-linear terms of single and double excitations a…
The long-range non-additive three-body dispersion interaction coefficients $Z_{111}$, $Z_{112}$, $Z_{113}$, and $Z_{122}$ are computed for many atomic combinations using standard expressions. The atoms considered include hydrogen, the rare gases, the alkali atoms (up to Rb) and the alkaline-earth atoms (up to Sr). The term $Z_{111}$, arising from three mutual dipole interactions is known as the Axilrod-Teller-Muto coefficient or the DDD (dipole-dipole-dipole) coefficient. Similarly, the terms $Z_{112}$, $Z_{113}$, and $Z_{122}$ arise from the mutual combinations of dipole (1), quadrupole (2), …
Effective oscillator strength distributions are systematically generated and tabulated for the alkali atoms, the alkaline-earth atoms, the alkaline-earth ions, the rare gases and some miscellaneous atoms. These effective distributions are used to compute the dipole, quadrupole and octupole static polarizabilities, and are then applied to the calculation of the dynamic polarizabilities at imaginary frequencies. These polarizabilities can be used to determine the long-range $C_6$, $C_8$ and $C_{10}$ atom-atom interactions for the dimers formed from any of these atoms and ions, and we present tab…
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…
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…
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…
High precision spectroscopy of the $^1S_0$-to-${^1}D_2$ clock transition of $^{176}$Lu is reported. Measurements are performed with Hertz level precision with the accuracy of the hyperfine-averaged frequency limited by the calibration of an active hydrogen maser to the SI definition of the second via a GPS link. The measurements also provide accurate determination of the $^1D_2$ hyperfine structure. Hyperfine structure constants associated with the magnetic octupole and electric hexadecapole moments of the nucleus are considered, which includes a derivation of correction terms from third-order…
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{…
Recently the first laser spectroscopy measurement of the radioactive RaF molecule has been reported by Ruiz \textit{et al.} [Nature \textbf{581}, 396 (2020)]. This and similar molecules are considered to search for the New Physics effects. The radium nucleus is of interest as it is octupole-deformed and has close levels of opposite parity. The preparation of such experiments can be simplified if there are reliable theoretical predictions. It is shown that the accurate prediction of the hyperfine structure of the RaF molecule requires to take into account the finite magnetization distribution i…
We perform high resolution spectroscopy on $^{176}$Lu$^+$ including the $^1S_0\leftrightarrow{^3}D_1$ and $^1S_0\leftrightarrow{^3}D_2$ clock transitions. Hyperfine structures and optical frequencies relative to the $^1S_0$ ground state of four low lying excited states are given to a few tens of kHz resolution. This covers the most relevant transitions involved in clock operation with this isotope. Additionally, measurements of the $^3D_2$ hyperfine structure may provide access to higher order nuclear moments, specifically the magnetic octupole and electric hexadecapole moments.
Determination of nuclear quadrupole moments for $^{25}$Mg, $^{87}$Sr, and $^{135,137}$Ba via configuration-interaction combined with a coupled-cluster approach
Alkaline-earth-like~(AEL) atoms with two valence electrons and a nonzero nuclear spin can be excited to Rydberg state for quantum computing. Typical AEL ground states possess no hyperfine splitting, but unfortunately a GHz-scale splitting seems necessary for Rydberg excitation. Though strong magnetic fields can induce a GHz-scale splitting, weak fields are desirable to avoid noise in experiments. Here, we provide two solutions to this outstanding challenge with realistic data of well-studied AEL isotopes. In the first theory, the two nuclear spin qubit states $|0\rangle$ and $|1\rangle$ are ex…
