Search

We examine the effect of a parasitic rf magnetic field, attributed to ion trapping, on the highly anticipated nuclear clock based on $^{229}$Th$^{3+}$ [C. J. Campbell et al., Phys. Rev. Lett. 108, 120802 (2012)]. The rf magnetic field induces an ac Zeeman shift to the clock frequency. As we demonstrate, this shift threatens to be the dominant systematic frequency shift for the clock, exceeding other systematic frequency shifts and the projected systematic uncertainty of the clock by orders of magnitude. We propose practical means to suppress or eliminate this shift., Comment: 6 pages

We identify laser-accessible transitions in group 16-like highly charged ions as candidates for high-accuracy optical clocks, including S-, Se-, and Te-like systems. For this class of ions, the ground $^{3}P_{J}$ fine structure manifold exhibits irregular (nonmonotonic in $J$) energy ordering for large enough ionization degree. We consider the $|^3P_2\rangle \longleftrightarrow |^3P_0\rangle$ (ground to first-excited state) electric quadrupole transition, performing relativistic many-body calculations of several atomic properties important for optical clock development. All ions discussed are suitable for production in small-scale ion sources and lend themselves to sympathetic cooling and quantum-logic readout with singly charged ions., Comment: 9 pages, 1 figure

Laser cooling is a key ingredient for quantum control of atomic systems in a variety of settings. In divalent atoms, two-stage Doppler cooling is typically used to bring atoms to the uK regime. Here, we implement a pulsed radial cooling scheme using the ultranarrow 1S0-3P0 clock transition in ytterbium to realize sub-recoil temperatures, down to tens of nK. Together with sideband cooling along the one-dimensional lattice axis, we efficiently prepare atoms in shallow lattices at an energy of 6 lattice recoils. Under these conditions key limits on lattice clock accuracy and instability are reduced, opening the door to dramatic improvements. Furthermore, tunneling shifts in the shallow lattice do not compromise clock accuracy at the 10-19 level.

We propose a high-performance atomic clock based on the 1.81 PHz transition between the ground and first-excited state of doubly ionized lead. Utilizing an even isotope of lead, both clock states have $I=J=F=0$, where $I$, $J$, and $F$ are the conventional quantum numbers specifying nuclear, electronic, and total angular momentum, respectively. The clock states are nondegenerate and completely immune to nonscalar perturbations, including first order Zeeman and electric quadrupole shifts. Additionally, the proposed clock is relatively insusceptible to other frequency shifts (blackbody radiation, second order Zeeman, Doppler), accommodates "magic" rf trapping, and is robust against decoherence mechanisms that can otherwise limit clock stability. By driving the transition as a two-photon $E1$+$M1$ process, the accompanying probe Stark shift is appreciable yet manageable for practical Rabi frequencies.

We develop a model to describe the motional (i.e., external degree of freedom) energy spectra of atoms trapped in a one-dimensional optical lattice, taking into account both axial and radial confinement relative to the lattice axis. Our model respects the coupling between axial and radial degrees of freedom, as well as other anharmonicities inherent in the confining potential. We further demonstrate how our model can be used to characterize lattice light shifts in optical lattice clocks, including shifts due to higher multipolar (magnetic dipole and electric quadrupole) and higher order (hyperpolarizability) coupling to the lattice field. We compare results for our model with results from other lattice light shift models in the literature under similar conditions., Comment: 19 pages; accepted to PRA

We have measured the quadratic Zeeman coefficient for the ${^{1}S_{0} \leftrightarrow {^{3}P_{0}}}$ optical clock transition in $^{27}$Al$^{+}$, $C_{2}=-71.944(24)$~MHz/T$^{2}$, and the unperturbed hyperfine splitting of the $^{25}$Mg$^{+}$ $^{2}S_{1/2}$ ground electronic state, $\Delta W / h = 1~788~762~752.85(13)$~Hz, with improved uncertainties. Both constants are relevant to the evaluation of the $^{27}$Al$^{+}$ quantum-logic clock systematic uncertainty. The measurement of $C_{2}$ is in agreement with a previous measurement and a new calculation at the $1~\sigma$ level. The measurement of $\Delta W$ is in good agreement with a recent measurement and differs from a previously published result by approximately $2\sigma$. With the improved value for $\Delta W$, we deduce an improved value for the nuclear-to-electronic g-factor ratio $g_{I}/g_{J} = 9.299 ~308 ~313(60) \times 10^{-5}$ and the nuclear g-factor for the $^{25}$Mg nucleus $g_{I} = 1.861 ~957 ~82(28) \times 10^{-4}$. Using the values of $C_{2}$ and $\Delta W$ presented here, we derive a quadratic Zeeman shift of the $^{27}$Al$^{+}$ quantum-logic clock of $\Delta \nu / \nu = -(9241.8 \pm 3.7) \times 10^{-19}$, for a bias magnetic field of $B \approx 0.12$~mT., Comment: 7 pages, 5 figures, updated

The pursuit of ever more precise measures of time and frequency is likely to lead to the eventual redefinition of the second in terms of an optical atomic transition. To ensure continuity with the current definition, based on a microwave transition between hyperfine levels in ground-state $^{133}$Cs, it is necessary to measure the absolute frequency of candidate standards, which is done by comparing against a primary cesium reference. A key verification of this process can be achieved by performing a loop closure$-$comparing frequency ratios derived from absolute frequency measurements against ratios determined from direct optical comparisons. We measure the $^1$S$_0\!\rightarrow^3$P$_0$ transition of $^{171}$Yb by comparing the clock frequency to an international frequency standard with the aid of a maser ensemble serving as a flywheel oscillator. Our measurements consist of 79 separate runs spanning eight months, and we determine the absolute frequency to be 518 295 836 590 863.71(11) Hz, the uncertainty of which is equivalent to a fractional frequency of $2.1\times10^{-16}$. This absolute frequency measurement, the most accurate reported for any transition, allows us to close the Cs-Yb-Sr-Cs frequency measurement loop at an uncertainty of $<$3$\times10^{-16}$, limited by the current realization of the SI second. We use these measurements to tighten the constraints on variation of the electron-to-proton mass ratio, $\mu=m_e/m_p$. Incorporating our measurements with the entire record of Yb and Sr absolute frequency measurements, we infer a coupling coefficient to gravitational potential of $k_\mathrm{\mu}=(-1.9\pm 9.4)\times10^{-7}$ and a drift with respect to time of $\frac{\dot\mu}{\mu}=(5.3 \pm 6.5)\times10^{-17}/$yr.

An optical reference based on a two-photon optical transition with ac Stark shift cancellation is proposed. The reference uses two interrogating laser fields at different frequencies. Compared to conventional optical two-photon references, the new approach offers the possibility for improved short-term stability resulting from a higher signal-to-noise and improved long-term stability due to active ac Stark shift cancellation. We demonstrate the ac Stark shift cancellation method on the $5s\,{^2S}_{1/2} \rightarrow 5d\,{^2D}_{5/2}$ two-photon transition in $^{87}$Rb., Comment: 7 pages

The passage of time is tracked by counting oscillations of a frequency reference, such as Earth's revolutions or swings of a pendulum. By referencing atomic transitions, frequency (and thus time) can be measured more precisely than any other physical quantity, with the current generation of optical atomic clocks reporting fractional performance below the $10^{-17}$ level. However, the theory of relativity prescribes that the passage of time is not absolute, but impacted by an observer's reference frame. Consequently, clock measurements exhibit sensitivity to relative velocity, acceleration and gravity potential. Here we demonstrate optical clock measurements surpassing the present-day ability to account for the gravitational distortion of space-time across the surface of Earth. In two independent ytterbium optical lattice clocks, we demonstrate unprecedented levels in three fundamental benchmarks of clock performance. In units of the clock frequency, we report systematic uncertainty of $1.4 \times 10^{-18}$, measurement instability of $3.2 \times 10^{-19}$ and reproducibility characterised by ten blinded frequency comparisons, yielding a frequency difference of $[-7 \pm (5)_{stat} \pm (8)_{sys}] \times 10^{-19}$. While differential sensitivity to gravity could degrade the performance of these optical clocks as terrestrial standards of time, this same sensitivity can be used as an exquisite probe of geopotential. Near the surface of Earth, clock comparisons at the $1 \times 10^{-18}$ level provide 1 cm resolution along gravity, outperforming state-of-the-art geodetic techniques. These optical clocks can further be used to explore geophysical phenomena, detect gravitational waves, test general relativity and search for dark matter., Comment: 32 pages, 5 figures

We report on the first earth-scale quantum sensor network based on optical atomic clocks aimed at dark matter (DM) detection. Exploiting differences in the susceptibilities to the fine-structure constant of essential parts of an optical atomic clock, i.e. the cold atoms and the optical reference cavity, we can perform sensitive searches for dark matter signatures without the need of real-time comparisons of the clocks. We report a two orders of magnitude improvement in constraints on transient variations of the fine-structure constant, which considerably improves the detection limit for the standard model (SM) - DM coupling. We use Yb and Sr optical atomic clocks at four laboratories on three continents to search for both topological defect (TD) and massive scalar field candidates. No signal consistent with a dark-matter coupling is identified, leading to significantly improved constraints on the DM-SM couplings.

We demonstrate the absence of a DC Stark shift in an ytterbium optical lattice clock. Stray electric fields are suppressed through the introduction of an in-vacuum Faraday shield. Still, the effectiveness of the shielding must be experimentally assessed. Such diagnostics are accomplished by applying high voltage to six electrodes, which are grounded in normal operation to form part of the Faraday shield. Our measurements place a constraint on the DC Stark shift at the $10^{-20}$ level, in units of the clock frequency. Moreover, we discuss a potential source of error in strategies to precisely measure or cancel non-zero DC Stark shifts, attributed to field gradients coupled with the finite spatial extent of the lattice-trapped atoms. With this consideration, we find that Faraday shielding, complemented with experimental validation, provides both a practically appealing and effective solution to the problem of DC Stark shifts in optical lattice clocks., Comment: 5 pages + supplemental material; accepted to PRL

We examine the influence of probe laser intensity fluctuations on hyper-Ramsey spectroscopy. We assume, as is appropriate for relevant cases of interest, that the probe laser intensity $I$ determines both the Rabi frequency $(\propto\sqrt{I})$ and the frequency shift to the atomic transition $(\propto I)$ during probe laser interactions with the atom. The spectroscopic signal depends on these two quantities that co-vary with fluctuations in the probe laser intensity. Introducing a simple model for the fluctuations, we find that the signature robustness of the hyper-Ramsey method can be compromised. Taking the Yb$^+$ electric octupole clock transition as an example, we quantify the clock error under different levels of probe laser intensity fluctuations., Comment: 5 pages, accepted to PRA Rapid Communication

Optical clocks benefit from tight atomic confinement enabling extended interrogation times as well as Doppler- and recoil-free operation. However, these benefits come at the cost of frequency shifts that, if not properly controlled, may degrade clock accuracy. Numerous theoretical studies have predicted optical lattice clock frequency shifts that scale nonlinearly with trap depth. To experimentally observe and constrain these shifts in an $^{171}$Yb optical lattice clock, we construct a lattice enhancement cavity that exaggerates the light shifts. We observe an atomic temperature that is proportional to the optical trap depth, fundamentally altering the scaling of trap-induced light shifts and simplifying their parametrization. We identify an "operational" magic wavelength where frequency shifts are insensitive to changes in trap depth. These measurements and scaling analysis constitute an essential systematic characterization for clock operation at the $10^{-18}$ level and beyond., Comment: 5 + 2 pages, 3 figures, added supplemental

We evaluate the electric quadrupole moments of the ${^1}\!S_0$ and ${^3}\!P_0$ clock states of $^{27}$Al$^+$ and $^{115}$In$^+$. To capture all dominant contributions, our analysis extends through third order of perturbation theory and includes hyperfine coupling of the electrons to both the magnetic dipole and electric quadrupole moments of the nucleus. For $^{27}$Al$^+$, a fortuitous cancellation leads to a suppressed frequency shift. This should allow for continued improvement of the clock without special techniques to control or cancel the shift, such as the averaging schemes that are critical to other optical ion clocks., Comment: 7 pages

Atomic clocks based on optical transitions are the most stable, and therefore precise, timekeepers available. These clocks operate by alternating intervals of atomic interrogation with dead time required for quantum state preparation and readout. This non-continuous interrogation of the atom system results in the Dick effect, an aliasing of frequency noise of the laser interrogating the atomic transition. Despite recent advances in optical clock stability achieved by improving laser coherence, the Dick effect has continually limited optical clock performance. Here we implement a robust solution to overcome this limitation: a zero-dead-time optical clock based on the interleaved interrogation of two cold-atom ensembles. This clock exhibits vanishingly small Dick noise, thereby achieving an unprecedented fractional frequency instability of $6 \times 10^{-17} / \sqrt{\tau}$ for an averaging time $\tau$ in seconds. We also consider alternate dual-atom-ensemble schemes to extend laser coherence and reduce the standard quantum limit of clock stability, achieving a spectroscopy line quality factor $Q> 4 \times 10^{15}$.

The Stark shift due to blackbody radiation (BBR) is the key factor limiting the performance of many atomic frequency standards, with the BBR environment inside the clock apparatus being difficult to characterize at a high level of precision. Here we demonstrate an in-vacuum radiation shield that furnishes a uniform, well-characterized BBR environment for the atoms in an ytterbium optical lattice clock. Operated at room temperature, this shield enables specification of the BBR environment to a corresponding fractional clock uncertainty contribution of $5.5 \times 10^{-19}$. Combined with uncertainty in the atomic response, the total uncertainty of the BBR Stark shift is now $1\times10^{-18}$. Further operation of the shield at elevated temperatures enables a direct measure of the BBR shift temperature dependence and demonstrates consistency between our evaluated BBR environment and the expected atomic response., Comment: 5 pages, 3 figures, accepted to PRL

We identify a potential means to extract the $^{229g}$Th $\rightarrow$ $^{229m}$Th nuclear excitation energy from precision microwave spectroscopy of the $5F_{5/2,7/2}$ hyperfine manifolds in the ion $^{229g}$Th$^{3+}$. The hyperfine interaction mixes this ground fine structure doublet with states of the nuclear isomer, introducing small but observable shifts to the hyperfine sub-levels. We demonstrate how accurate atomic structure calculations may be combined with measurement of the hyperfine intervals to quantify the effects of this mixing. Further knowledge of the magnetic dipole decay rate of the isomer, as recently reported, allows an indirect determination of the nuclear excitation energy., Comment: 5 pages

Atomic clocks have been transformational in science and technology, leading to innovations such as global positioning, advanced communications, and tests of fundamental constant variation. Next-generation optical atomic clocks can extend the capability of these timekeepers, where researchers have long aspired toward measurement precision at 1 part in $\bm{10^{18}}$. This milestone will enable a second revolution of new timing applications such as relativistic geodesy, enhanced Earth- and space-based navigation and telescopy, and new tests on physics beyond the Standard Model. Here, we describe the development and operation of two optical lattice clocks, both utilizing spin-polarized, ultracold atomic ytterbium. A measurement comparing these systems demonstrates an unprecedented atomic clock instability of $\bm{1.6\times 10^{-18}}$ after only $\bm{7}$ hours of averaging.

Nuclear-spin-dependent (NSD) parity violating (PV) effects can be strongly enhanced in diatomic molecules containing heavy atoms. Future measurements are anticipated to provide nuclear anapole moments and strength constants for PV nuclear forces. In light molecules, the NSD electroweak electron-nucleus interaction may also be detected. Here we calculate NSD PV effects for molecular ions. Our calculations are motivated by rapid developments in trapping techniques for such systems at low temperatures., Comment: arXiv admin note: substantial text overlap with arXiv:1201.0582

The Stark shift of the ytterbium optical clock transition due to room temperature blackbody radiation is dominated by a static Stark effect, which was recently measured to high accuracy [J. A. Sherman et al., Phys. Rev. Lett. 108, 153002 (2012)]. However, room temperature operation of the clock at 10^{-18} inaccuracy requires a dynamic correction to this static approximation. This dynamic correction largely depends on a single electric dipole matrix element for which theoretically and experimentally derived values disagree significantly. We determine this important matrix element by two independent methods, which yield consistent values. Along with precise radiative lifetimes of 6s6p 3P1 and 5d6s 3D1, we report the clock's blackbody radiation shift to 0.05% precision.

We utilize accurate experimental data available in the literature to yield bounds on the polarizabilities of the ground and first excited states of atomic Yb. For the 6s^2 1S0 ground state, we find the polarizability alpha to be constrained to 134.4

We present ab initio calculations of the $W_A$ parameter of the P-odd spin-rotational Hamiltonian for a variety of diatomic molecules, including the group--2 and --12 halides. The results were obtained by relativistic Dirac--Hartree--Fock and density functional theory approaches, and corrected for core polarization effects. Strong enhancement of $W_A$ is found for the group--12 diatomic halides, which should be helpful in future determination of the nuclear anapole moment., Comment: 1 figure

We consider the effect of $\alpha$ variation on the vibrational spectrum of Sr$_2$ in the context of a planned experiment to test the stability of $\mu\equiv m_e/m_p$ using optically trapped Sr$_2$ molecules [Zelevinsky et al., Phys. Rev. Lett. {\bf 100}, 043201; Kotochigova et al., Phys. Rev. A {\bf 79}, 012504]. We find the prospective experiment to be 3 to 4 times less sensitive to fractional variation in $\alpha$ as it is to fractional variation in $\mu$. Depending on the precision ultimately achieved by the experiment, this result may give justification for the neglect of $\alpha$ variation or, alternatively, may call for its explicit consideration in the interpretation of experimental results., Comment: 5 pages, 3 figures

We consider the influence of variation in the fine structure constant alpha on a promising experiment proposed by DeMille et al. to search for variation in the electron-to-proton mass ratio mu using diatomic molecules [DeMille et al., Phys. Rev. Lett. 100, 043202 (2008)]. The proposed experiment involves spectroscopically probing the splitting between two nearly-degenerate vibrational levels supported by different electronic potentials. Here we demonstrate that this splitting may be equally or more sensitive to variation in alpha as to variation in mu. For the anticipated experimental precision, this implies that the alpha variation may not be negligible, as previously assumed, and further suggests that the method could serve as a competitive means to search for alpha variation as well.

We identify the molecular ion NH^+ as a potential candidate for probing variations in the fine structure constant alpha and electron-to-proton mass ratio mu. NH^+ has an anomalously low-lying excited Sigma state, being only a few hundred cm^-1 above the ground Pi state. Being a light molecule, this proximity is such that rotational levels of the respective states are highly intermixed for low angular momenta. We find that several low-frequency transitions within the collective rotational spectrum experience enhanced sensitivity to alpha- and mu-variation. This is attributable to the close proximity of the Pi and Sigma states, as well as the ensuing strong spin-orbit coupling between them. Suggestions that NH^+ may exist in interstellar space and recent predictions that trapped-ion precision spectroscopy will be adaptable to molecular ions make NH^+ a promising system for future astrophysical and laboratory studies of alpha- and mu-variation., Comment: 8 pages, 1 figure

We present numerical calculations for cesium and mercury to estimate the sensitivity of the scattering length to the variation of the fine structure constant alpha. The method used follows ideas Chin and Flambaum [Phys. Rev. Lett. 96, 230801 (2006)], where the sensitivity to the variation of the electron to proton mass ratio, beta, was considered. We demonstrate that for heavy systems, the sensitivity to variation of alpha is of the same order of magnitude as to variation of beta. Near narrow Feshbach resonances the enhancement of the sensitivity may exceed nine orders of magnitude., Comment: 5 pages, 1 figure

We apply relativistic many-body methods to compute static differential polarizabilities for transitions inside the ground-state hyperfine manifolds of monovalent atoms and ions. Knowing this transition polarizability is required in a number of high-precision experiments, such as microwave atomic clocks and searches for CP-violating permanent electric dipole moments. While the traditional polarizability arises in the second-order of interaction with the externally-applied electric field, the differential polarizability involves additional contribution from the hyperfine interaction of atomic electrons with nuclear moments. We derive formulas for the scalar and tensor polarizabilities including contributions from magnetic dipole and electric quadrupole hyperfine interactions. Numerical results are presented for Al, Rb, Cs, Yb$^+$, Hg$^+$, and Fr., Comment: 13 pages, 1 figure

Recently it was pointed out that transition frequencies in certain diatomic molecules have an enhanced sensitivity to variations in the fine-structure constant $\alpha$ and the proton-to-electron mass ratio $m_p/m_e$ due to a near cancellation between the fine-structure and vibrational interval in a ground electronic multiplet [V.~V.~Flambaum and M.~G.~Kozlov, Phys. Rev. Lett.~{\bf 99}, 150801 (2007)]. One such molecule possessing this favorable quality is silicon monobromide. Here we take a closer examination of SiBr as a candidate for detecting variations in $\alpha$ and $m_p/m_e$. We analyze the rovibronic spectrum by employing the most accurate experimental data available in the literature and perform \emph{ab initio} calculations to determine the precise dependence of the spectrum on variations in $\alpha$. Furthermore, we calculate the natural linewidths of the rovibronic levels, which place a fundamental limit on the accuracy to which variations may be determined., Comment: 8 pages, 2 figures

We discuss results of the most accurate to-date test of the low-energy electroweak sector of the standard model of elementary particles. Combining previous measurements with our high-precision calculations we extracted the weak charge of the 133Cs nucleus, Q_W = -73.16(29)_exp (20)_th [S.G. Porsev, K. Beloy, and A. Derevianko, Phys. Rev. Lett. {\bf 102}, 181601 (2009)]. The result is in perfect agreement with Q_W^{SM} predicted by the standard model, Q_W^{SM} =-73.16(3), and confirms energy-dependence (or running) of the electroweak interaction and places constraints on a variety of new physics scenarios beyond the standard model. In particular, we increase the lower limit on the masses of extra Z-bosons predicted by models of grand unification and string theories. This paper provides additional details to the Letter. We discuss large-scale calculations in the framework of the coupled-cluster method, including full treatment of single, double, and valence triple excitations. To determine the accuracy of the calculations we computed energies, electric-dipole amplitudes, and hyperfine-structure constants. An extensive comparison with high-accuracy experimental data was carried out.

We carry out relativistic many-body calculations of the Stark-induced absorption coefficient on the 254-nm $6s6p ^3P_1 (F=1/2) - 6s^2 ^1S_0$ line of $^{199}$Hg atom, the effect considered before by Lamoreaux and Fortson using a simple central field estimate [Phys. Rev. A {\bf 46}, 7053 (1992)]. The Stark-induced admixing of states of opposite parity opens additional M1 and E2 transition channels. We find that the resulting M1-E1 absorption dominates over E2-E1 absorption. The value of the E2-E1 absorption coefficient depends strongly on the details of treatment of the correlation problem. As a result, our numerical values differ substantially from those of the earlier central field calculation. Reliable calculation of this effect can enable a useful experimental check on the optical technique being used to search for a permanent electric dipole moment of the $^{199}$Hg atom., Comment: 5 pages

We carry out high-precision calculation of parity violation in cesium atom, reducing theoretical uncertainty by a factor of two compared to previous evaluations. We combine previous measurements with our calculations and extract the weak charge of the 133Cs nucleus, Q_W = -73.16(29)_exp(20)_th. The result is in agreement with the Standard Model (SM) of elementary particles. This is the most accurate to-date test of the low-energy electroweak sector of the SM. In combination with the results of high-energy collider experiments, we confirm the energy-dependence (or "running") of the electroweak force over an energy range spanning four orders of magnitude (from ~10 MeV to ~100 GeV). Additionally, our result places constraints on a variety of new physics scenarios beyond the SM. In particular, we increase the lower limit on the masses of extra $Z$-bosons predicted by models of grand unification and string theories., Comment: 4 pages/3 figs /1 table

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.

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+3figs

We analyze second-order $M1$-$M1$ and $M1$-$E2$ effects to the hyperfine structure (HFS) of the lowest energy $P$ states of alkali-metal atoms arising from the coupling of the two ($J=1/2,3/2$) fine-structure levels through the hyperfine interaction. We find these effects to be especially sizable in Li, leading to a $9\sigma$ correction to the most accurate reported experimental value of the $A(P_{1/2})$ HFS constant of $^7$Li [D. Das and V. Natarajan, J. Phys. B \textbf{41}, 035001 (2008)]. For the remaining alkali-metal systems, the results tabulated within may be referenced as higher precision is sought in experimental determination of the HFS constants.

We present and analyze results of the relativistic coupled-cluster calculation of energies, hyperfine constants, and dipole matrix elements for the $2s$, $2p_{1/2}$, and $2p_{3/2}$ states of Li atom. The calculations are complete through the fourth order of many-body perturbation theory for energies and through the fifth order for matrix elements and subsume certain chains of diagrams in all orders. A nearly complete many-body calculation allows us to draw conclusions on the convergence pattern of the coupled-cluster method. Our analysis suggests that the high-order many-body contributions to energies and matrix elements scale proportionally and provides a quantitative ground for semi-empirical fits of {\em ab inito} matrix elements to experimental energies., Comment: 4 pages, 3 figures

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 $\Omega$ 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 $\Omega$ without contamination from the second-order corrections. Measurements to the required accuracy should be possible with a single trapped barium ion using sensitive techniques already demonstrated in Ba$^+$ experiments., Comment: Phys Rev A in press

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., Comment: 11 pages, Phys. Rev. A in press. In v2 added discussion of second-order magnetic-dipole electring-quadrupole correction

Black-body radiation (BBR) shift is an important systematic correction for the atomic frequency standards realizing the SI unit of time. Presently, there is a controversy over the value of the BBR shift for the primary $^{133}$Cs standard. At room temperatures the values from various groups differ at $3 \times 10^{-15}$ level, while the modern clocks are aiming at $10^{-16}$ accuracies. We carry out high-precision relativistic many-body calculations of the BBR shift. For the BBR coefficient $\beta$ at $T=300K$ we obtain $\beta=-(1.708\pm0.006) \times 10^{-14}$, implying $6 \times 10^{-17}$ fractional uncertainty. While in accord with the most accurate measurement, our 0.35%-accurate value is in a substantial, 10%, disagreement with recent semi-empirical calculations. We identify an oversight in those calculations., Comment: 4 pages