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We propose a protocol for creating a fully entangled Greenberger-Horne-Zeilinger-type state of neutral atoms in spatially separated optical atomic clocks. In our scheme, local operations make use of the strong dipole-dipole interaction between Rydberg excitations, which give rise to fast and reliable quantum operations involving all atoms in the ensemble. The necessary entanglement between distant ensembles is mediated by single-photon quantum channels and collectively enhanced light-matter couplings. These techniques can be used to create the recently proposed quantum clock network based on neutral atom optical clocks. We specifically analyze a possible realization of this scheme using neutral Yb ensembles.

Recently invented and demonstrated, optical lattice clocks hold great promise for improving the precision of modern timekeeping. These clocks aim at the 10^-18 fractional accuracy, which translates into a clock that would neither lose or gain a fraction of a second over an estimated age of the Universe. In these clocks, millions of atoms are trapped and interrogated simultaneously, dramatically improving clock stability. Here we discuss the principles of operation of these clocks and, in particular, a novel concept of "magic" trapping of atoms in optical lattices. We also highlight recently proposed microwave lattice clocks and several applications that employ the optical lattice clocks as a platform for precision measurements and quantum information processing., 18 pages, 15 figures

The electric dipole polarizabilities evaluated at imaginary frequencies for hydrogen, the alkali-metal atoms, the alkaline earth atoms, and the inert gases are tabulated along with the resulting values of the atomic static polarizabilities, the atom-surface interaction constants, and the dispersion (or van der Waals) constants for the homonuclear and the heteronuclear diatomic combinations of the atoms.

We predict the possibility of "triply-magic" optical lattice trapping of neutral divalent atoms. In such a lattice, the ${^1}\!S_{0}$ and ${^3}\!P_{0}$ clock states and an additional Rydberg state experience identical optical potentials, fully mitigating detrimental effects of the motional decoherence. In particular, we show that this triply magic trapping condition can be satisfied for Yb atom at optical wavelengths and for various other divalent systems (Ca, Mg, Hg and Sr) in the UV region. We assess the quality of triple magic trapping conditions by estimating the probability of excitation out of the motional ground state as a result of the excitations between the clock and the Rydberg states. We also calculate trapping laser-induced photoionization rates of divalent Rydberg atoms at magic frequencies. We find that such rates are below the radiative spontaneous-emission rates, due to the presence of Cooper minima in photoionization cross-sections.

We study the effect of resonances associated with complex molecular interaction of Rydberg atoms on Rydberg blockade. We show that densely-spaced molecular potentials between doubly-excited atomic pairs become unavoidably resonant with the optical excitation at short interatomic separations. Such molecular resonances limit the coherent control of individual excitations in Rydberg blockade. As an illustration, we compute the molecular interaction potentials of Rb atoms near the $100s$ states asymptote to characterize such detrimental molecular resonances, determine the resonant loss rate to molecules and inhomogeneous light shifts. Techniques to avoid the undesired effect of molecular resonances are discussed., Comment: 5 pages + supplementary materials

The static and dynamic electric dipole, quadrupole, and octupole polarizabilities of the alkaline-earth atoms (beryllium, magnesium, calcium, strontium, and barium) in the ground state were calculated. The dynamic polarizabilities obtained were used to calculate the van der Waals coefficients C 6, C 8, and C 10 of alkaline-earth metal dimers for the interaction of two like atoms in the ground state. The results are compared with other theoretical and experimental data.

We consider long-range interactions between two alkali-metal atoms in their respective ground states. We extend the previous relativistic many-body calculations of C_6 dispersion coefficients [Phys.Rev. Lett. {\bf 82}, 3589 (1999)] to higher-multipole coefficients C_8 and C_10. A special attention is paid to usually omitted contribution of core-excited states. We calculate this contribution within relativistic random-phase approximation and demonstrate that for heavy atoms core excitations contribute as much as 10% to the dispersion coefficients. We tabulate results for both homonuclear and heteronuclear dimers and estimate theoretical uncertainties. The estimated uncertainties for C_8 coefficients range from 0.5% for Li_2 to 4% for Cs_2., Comment: 12 pages, submitted to Journal of Chemical Physics

We evaluate the feasibility of using magnetic-dipole (M1) transitions in highly-charged ions as a basis of an optical atomic clockwork of exceptional accuracy. We consider a range of possibilities, including M1 transitions between clock levels of the same fine-structure and hyperfine-structure manifolds. In highly charged ions these transitions lie in the optical part of the spectra and can be probed with lasers. The most direct advantage of our proposal comes from the low degeneracy of clock levels and the simplicity of atomic structure in combination with negligible quadrupolar shift. We demonstrate that such clocks can have projected fractional accuracies below the $10^{-20}-10^{-21}$ level for all common systematic effects, such as black-body radiation, Zeeman, AC-Stark and quadrupolar shifts. Notice that usually-employed hyperfine clock transitions lie in the microwave spectral region. Our proposal moves such transitions to the optical domain. As the hyperfine transition frequencies depend on the fine-structure constant, electron-to-proton mass ratio, and nuclear magnetic moment, our proposal expands the range of experimental schemes for probing space and time variations of fundamental constants., 5 pages, 1 figure, accepted in PRL

Quantum-mechanical calculations of the potential energy curves of the singlet and triplet states of LiH, NaH, KH, RbH, and CsH formed by the approach of ground state alkali–metal atoms and hydrogen atoms are presented. Precise values are determined for the coefficients of the van der Waals interaction and estimates are made of the contribution of the exchange interaction at large distances. Together with empirical data, they are used to assess and improve the accuracy of the ab initio potentials.

Degenerate perturbation theory is used to study dipole susceptibilities of an excited helium atom in an external electric field. The dependence of the perturbed energy of levels in atoms on fine-structure effects and on the higher-order Stark effect is investigated. Numerical results have been obtained for the (1s3p) P0 and (1s3p) P2 states of helium. The magnitude of the electric field and the energy separation at the 0 30 anticrossing are calculated. Calculations of polarizabilities and hyperpolarizabilities are carried out using sums of oscillator strengths and, alternatively, with the excited electron Green function. An estimate is given based on the model potential method for the contribution of an infinite series over the bound states, including the integral over the continuum, for secondand higher-order matrix elements. The relativistic approach for evaluating reduced dipole matrix elements based on the relativistic no-pair Hamiltonian and including both the Coulomb and Breit interactions ~configuration-interaction method! is analyzed. @S1050-2947~99!06108-9#

Reduced matrix elements and transition rates are calculated for all magnetic dipole (M1) transitions within 2l2l' configurations and for some 2l3l' - 2l2l' transitions in Be-like ions with nuclear charges ranging from Z = 4 to 100. Many-body perturbation theory (MBPT), including the Breit interaction, is used to evaluate retarded M1 matrix elements. The calculations start with a (1s)2 Dirac-Fock potential and include all possible n = 2 configurations, leading to 4 odd-parity and 6 even-parity states, and some n = 3 configurations. First-order perturbation theory is used to obtain intermediate coupling coefficients. Second-order MBPT is used to determine the matrix elements, which are evaluated for all 11 M1 transitions within 2l2l' configurations and for 35 M1 transitions between 2l3l' and 2l2l' states. The transition energies used in the calculation of oscillator strengths and transition rates are obtained from second-order MBPT. The importance of negative-energy contributions to M1 transition amplitudes is discussed.

Reduced matrix elements, oscillator strengths, and transition rates are calculated for all allowed and forbidden 2s–2p electric dipole transitions in berylliumlike ions with nuclear charges ranging from Z = 4 to 100. Many-body perturbation theory (MBPT), including the Breit interaction, is used to evaluate retarded E1 matrix elements in length and velocity forms. The calculations start with a 1s2 Dirac–Fock potential and include all possible n = 2 configurations, leading to 4 odd-parity and 6 even-parity states. First-order perturbation theory is used to obtain intermediate coupling coefficents. Second-order MBPT is used to determine the matrix elements, which are evaluated for the 16 possible E1 transitions. The transition energies used in the calculation of oscillator strengths and transition rates are evaluated using second-order MBPT. The importance of virtual electron–positron pair (negative energy) contributions to the transition amplitudes is discussed.

elements for the resonant terms in the spectral expansion of the polarizabilities are derived using two-electron basis functions of the relativistic Hamiltonian of the atom, a Hamiltonian that incorporates the Coulomb and Breit electron‐electron interactions. We formulate a new approach to determining the parameters of the Fuss model potential. Finally, we show that the polarizability values are sensitive to the choice of the wave functions used in the calculations. © 1999 American Institute of Physics.@S1063-7761~99!00902-6#

We derive the leading term in an aZ expansion for the negative-energy ~virtual electron-positron pair! contributions to the transition amplitudes of heliumlike ions. The resulting expressions allow us to perform a general analysis of the negative-energy contributions to electric- and magnetic-multipole transition amplitudes. We observe a strong dependence on the choice of the zeroth-order Hamiltonian, which defines the negativeenergy spectrum. We show that for transitions between states with different values of total spin, the negativeenergy contributions calculated in a Coulomb basis vanish in the leading order while they remain finite in a Hartree basis. The ratio of negative-energy contributions to the total transition amplitudes for some of nonrelativistically forbidden transitions is shown to be of order 1/ Z. In the particular case of the magnetic-dipole transition 3 3 S1!2 3 S1 , we demonstrate that the neglect of negative-energy contributions, in an otherwise exact no-pair calculation, would lead one to underestimate the decay rate in helium by a factor of 1.5 in calculations using a Hartree basis and by a factor of 2.9 using a Coulomb basis. Finally, we tabulate revised values of the line strength S for the magnetic-quadrupole ( M 2) transition 2 3 P2!1 1 S0 . These values include negative-energy contributions from higher partial waves, which were neglected in our previous calculations. @S1050-2947~98!03512-4#

We derive the relativistic formulas for the van der Waals coefficients of Yb-alkali dimers that correlate to ground and excited separated-atom limits. We calculate $C_6$ and $C_8$ coefficients of particular experimental interest. We also derive a semi-empirical formula that expresses the $C_8$ coefficient of heteronuclear $A+B$ dimers in terms of the $C_6$ and $C_8$ coefficients of homonuclear dimers and the static dipole and quadrupole polarizabilities of the atomic states $A$ and $B$. We report results of calculation of the $C_6$ coefficients for the Yb-Rb $^3/!P_1^o+5s\, ^2/!S_{1/2}$ and $^1/!S_0+5p\, ^2/!P^o_{1/2}$ dimers, and the $C_8$ coefficients for the Yb-Li $^1/!S_0+2s\, ^2/!S_{1/2}$ and Yb-Rb $^1/!S_0+5s\, ^2/!S_{1/2}$ dimers. Uncertainties are estimated for all predicted properties., Comment: 9 pages

Ponderomotive energy shifts experienced by Rydberg atoms in optical fields are known to be well approximated by the classical quiver energy of a free electron. We examine such energy shifts quantum mechanically and elucidate how they relate to the ponderomotive shift of a free electron in off-resonant fields. We derive and evaluate corrections to the ponderomotive free electron polarizability in the length and velocity (transverse or Coulomb) gauges, which agree exactly as mandated by the gauge invariance. We also show how the free electron value emerges from the Dirac equation through summation over the Dirac sea states. We find that the free-electron AC Stark shift comes as an expectation value of a term proportional to the square of the vector potential in the velocity gauge. On the other hand, the same dominant contribution can be obtained to first order via a series expansion of the exact energy shift from the second order perturbation theory in the length gauge. Finally, we numerically examine the validity of the free-electron approximation. The correction to the free-electron value becomes smaller with increasing principal quantum number, and it is well below a per cent for 60s states of Rb and Sr away from the resonances.

We develop a theoretical understanding of the trapping of divalent Rydberg atoms in optical lattices. Because the size of the Rydberg electron cloud can be comparable to the scale of spatial variations of laser intensity, we pay special attention to averaging optical fields over the atomic wave functions. The optical potential is proportional to the ac Stark polarizability. We find that in the independent-particle approximation for the valence electrons, this polarizability breaks into two contributions: the singly ionized core polarizability and the contribution from the Rydberg electron. Unlike the usually employed free-electron polarizability, the Rydberg contribution depends both on the laser intensity profile and on the rotational symmetry of the total electronic wave function. We focus on the $J=0$ Rydberg states of Sr and evaluate the dynamic polarizabilities of the $5sns$(${}^{1}{S}_{0}$) and $5snp$(${}^{3}{P}_{0}$) Rydberg states. We specifically chose the Sr atom for its optical-lattice clock applications. We find that there are several magic wavelengths in the infrared region of the spectrum at which the differential Stark shift between the clock states [$5{s}^{2}$(${}^{1}{S}_{0}$) and $5s5p$(${}^{3}{P}_{0}$)] and the $J=0$ Rydberg states [$5sns$(${}^{1}{S}_{0}$) and $5snp$(${}^{3}{P}_{0}$)] vanishes. We tabulate these wavelengths as a function of the principal quantum number $n$ of the Rydberg electron. We find that because the contribution to the total polarizability from the Rydberg electron vanishes at short wavelengths, magic wavelengths below $\ensuremath{\sim}$1000 nm are ``universal'' as they do not depend on the principal quantum number $n$.

Intensity-modulated optical lattice potentials can change sign for an alkali-metal Rydberg atom, and the atoms are not always attracted to intensity minima in optical lattices with wavelengths near the CO${}_{2}$ laser band. Here we demonstrate that such IR lattices can be tuned so that the trapping potential experienced by the Rydberg atom can be made to vanish for atoms in ``targeted'' Rydberg states. Such state-selective trapping of Rydberg atoms can be useful in controlled cold Rydberg collisions, cooling Rydberg states, and species-selective trapping and transport of Rydberg atoms in optical lattices. We tabulate wavelengths at which the trapping potential vanishes for the $ns$, $np$, and $nd$ Rydberg states of Na and Rb atoms and discuss advantages of using such optical lattices for state-selective trapping of Rydberg atoms. We also develop exact analytical expressions for the lattice-induced polarizability for the ${m}_{z}=0$ Rydberg states and derive an accurate formula predicting tune-out wavelengths at which the optical trapping potential becomes invisible to Rydberg atoms in targeted $l=0$ states.

Motivated by compelling advances in manipulating cold Rydberg (Ry) atoms in optical traps, we consider the effect of the large extent of a Ry electron wave function on trapping potentials. We find that, when the Ry orbit lies outside inflection points in the laser intensity landscape, the atom can stably reside in laser intensity maxima. Effectively, the free-electron ac polarizability of the Ry electron is modulated by the intensity landscape and can accept both positive and negative values. We apply these insights to determining the magic wavelengths for Ry-ground-state transitions for alkali-metal atoms trapped in infrared optical lattices. We find magic wavelengths to be around $10\phantom{\rule{0.28em}{0ex}}\ensuremath{\mu}\mathrm{m}$ with exact values that depend on Ry-state quantum numbers.

We explore the possibility of decelerating and Doppler cooling an ensemble of tree-level $\Lambda$-type atoms by a coherent train of short, non-overlapping laser pulses. We show that $\Lambda$-atoms can be Doppler cooled without additional repumping of the population from the intermediate ground state. We derive analytical expression for the scattering force in the quasi-steady-state regime and analyze its dependence on pulse train parameters. Based on this analysis we propose a method of choosing pulse train parameters to optimize the cooling process., Comment: 22 pages, 6 figures

Violation of fundamental symmetries in atoms is the subject of intense experimental and theoretical interest. $P$-odd, $T$-even transitions have been observed and are in excellent agreement with electroweak theory. Searches for permanent electric dipole moments have placed bounds on $T$-odd, $P$-odd interactions, constraining proposed extensions to the standard model of elementary particles. Here we propose a search for $T$-odd, $P$-even (TOPE) interactions in atoms. We consider open-shell atoms, such as rare-earth-metal atoms, which have dense, chaotic excitation spectra with strong level repulsion. The strength of the level repulsion depends on the underlying symmetries of the atomic Hamiltonian. TOPE interactions lead to enhanced level repulsion. We demonstrate how a statistical analysis of many chaotic spectra can determine the strength of level repulsion; in particular, the variance of the number of levels in an energy range has been shown to be a useful measure. We estimate that, using frequency comb spectroscopy, a sufficient number of chaotic levels could be measured to match or exceed the current experimental bounds on TOPE interactions.

We show that optical spectroscopy of Rydberg states can provide accurate {\em in situ} thermometry at room-temperature. Transitions from a metastable state to Rydberg states with principal quantum numbers of 25 to 30 have 200 times larger fractional frequency sensitivities to blackbody radiation than the Strontium clock transition. We demonstrate that magic wavelength lattices exist for both Strontium and Ytterbium transitions between the metastable and Rydberg states. Frequency measurements of Rydberg transitions with $10^{-16}$ accuracy provide $10 \, \mathrm{mK}$ resolution and yield a blackbody uncertainty for the clock transition of $10^{-18}$.

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 nonscalar state atoms have the necessary characteristics to achieve such Stark shift cancellation. We then present numerical results on ''magic'' trapping conditions for {sup 27}Al paired with {sup 87}Sr, as well as several other divalent atoms.

We explore the possibility of decelerating and Doppler cooling an ensemble of two-level atoms by a coherent train of short, nonoverlapping laser pulses. We derive analytical expressions for mechanical force exerted by the train. In frequency space the force pattern reflects the underlying frequency comb structure. The pattern depends strongly on the ratio of the atomic lifetime to the repetition time between the pulses and pulse area. For example, in the limit of short lifetimes, the frequency-space peaks of the optical force wash out. We propose to tune the carrier-envelope offset frequency to follow the Doppler-shifted detuning as atoms decelerate; this leads to compression of atomic velocity distribution about comb teeth and results in a ``velocity comb''---a series of narrow equidistant peaks in the velocity space.

The Rydberg blockade mechanism has shown noteworthy promise for scalable quantum computation with neutral atoms. Both qubit states and gate-mediating Rydberg state belong to the same optically-trapped atom. The trapping fields, while being essential, induce detrimental decoherence. Here we theoretically demonstrate that this Stark-induced decoherence may be completely removed using powerful concepts of "magic" optical traps. We analyze "magic" trapping of a prototype three-level system: a Rydberg state along with two qubit states: hyperfine states attached to a J=1/2 ground state. Our numerical results show that, while such a "magic" trap for alkali metals would require prohibitively large magnetic fields, the group IIIB metals such as Al are suitable candidates., Comment: 5 pages, 3 figures

Precision measurements and quantum-information processing with cold atoms may benefit from trapping atoms with specially engineered, ``magic'' optical fields. At the magic trapping conditions, the relevant atomic properties remain immune to strong perturbations by the trapping fields. Here we develop a theoretical analysis of magic trapping for especially valuable Zeeman-insensitive clock transitions in alkali-metal atoms. The involved mechanism relies on applying a magic bias $B$ field along a circularly polarized trapping laser field. We map out these $B$ fields as a function of trapping laser wavelength for all commonly used alkalis. We also highlight a common error in evaluating Stark shifts of hyperfine manifolds.

We demonstrate near-complete cancellation of the differential light shift of a two-photon magnetic-field-insensitive microwave hyperfine (clock) transition in $^{87}$Rb atoms trapped in an optical lattice. Up to $95(2)%$ of the differential light shift is canceled while maintaining magnetic-field insensitivity. This technique should have applications in quantum information and frequency metrology., Comment: 5 pages, 4 figures

We explore a feasibility of measuring atom-wall interaction using atomic clocks based on atoms trapped in engineered optical lattices. Optical lattice is normal to the wall. By monitoring the wall-induced clock shift at individual wells of the lattice, one would measure a dependence of the atom-wall interaction on the atom-wall separation. We rigorously evaluate the relevant clock shifts and show that the proposed scheme may uniquely probe the long-range atom-wall interaction in all three qualitatively-distinct regimes of the interaction: van der Waals (image-charge interaction), Casimir-Polder (QED vacuum fluctuations) and Lifshitz (thermal bath fluctuations). The analysis is carried out for atoms Mg, Ca, Sr, Cd, Zn, and Hg, with a particular emphasis on Sr clock., 4 pages, 4 figures

The present definition of the unit of time, the second, is based on the frequency of the microwave transition between two hyperfine levels of the Cs atom. Recently, it has been realized that the accuracy and stability of atomic clocks can be substantially improved by trapping atoms in optical lattices operated at a certain “magic” wavelength [1, 2]. At this magic wavelength, both clock levels experience the same AC Stark shift; the clock frequency becomes essentially independent on trapping laser intensity.

The excitation energies of ns, np, nd, and nf (n{

The long-range quadrupole-quadrupole ($\sim R^{-5}$) and leading dispersion ($\sim R^{-6}$) interactions between all pairs of excited Hg($6s6p$) $^3P_0$, $^3P_1$, $^3P_2$, and $^1P_1$ atoms are determined. The quadrupole moments are calculated using the {\it ab initio} relativistic configuration-interaction method coupled with many-body perturbation theory. The van der Waals coefficients are approximated using previously calculated static polarizabilities and expressions for the dispersion energy that are validated with similar systems. The long-range interactions are critical for associative ionization in thermal and cold collisions, and are found to be quite different for different pairs of interacting states. Based on this knowledge and the short-range parts of previously calculated potential curves, improved estimates of the chemi-ionization cross sections are obtained., Comment: accepted in Phys Rev A

The dual-kinetic-balance (DKB) finite basis set method for solving the Dirac equation for hydrogen-like ions [V. M. Shabaev et al., Phys. Rev. Lett. 93, 130405 (2004)] is extended to problems with a non-local spherically-symmetric Dirac-Hartree-Fock potential. We implement the DKB method using B-spline basis sets and compare its performance with the widely-employed approach of Notre Dame (ND) group [W.R. Johnson and J. Sapirstein, Phys. Rev. Lett. 57, 1126 (1986)]. We compare the performance of the ND and DKB methods by computing various properties of Cs atom: energies, hyperfine integrals, the parity-non-conserving amplitude of the $6s_{1/2}-7s_{1/2}$ transition, and the second-order many-body correction to the removal energy of the valence electrons. We find that for a comparable size of the basis set the accuracy of both methods is similar for matrix elements accumulated far from the nuclear region. However, for atomic properties determined by small distances, the DKB method outperforms the ND approach. In addition, we present a strategy for optimizing the size of the basis sets by choosing progressively smaller number of basis functions for increasingly higher partial waves. This strategy exploits suppression of contributions of high partial waves to typical many-body correlation corrections., Comment: 10 pages

We propose a method of stimulated laser decelerating of diatomic molecules by counter-propagating π-trains of ultrashort laser pulses. The decelerating cycles occur on the rovibrational transitions inside the same ground electronic manifold, thus avoiding the common problem of radiative branching in Doppler cooling of molecules. By matching the frequency comb spectrum of the pulse trains to the spectrum of the R-branch rovibrational transitions we show that stimulated deceleration can be carried out on several rovibrational transitions simultaneously. This enables an increase in the number of cooled molecules with only a single laser source. The exerted optical force does not rely on the decay rates in a system and can be orders of magnitude larger than the typical values of scattering force obtained in conventional Doppler laser cooling schemes.

We investigate the feasibility of combining Raman optical lattices with a quantum computing architecture based on lattice-confined magnetically interacting neutral atoms. A particular advantage of the standing Raman field lattices comes from reduced interatomic separations leading to increased interatomic interactions and improved multiqubit gate performance. Specifically, we analyze a $J=3∕2$ Zeeman system placed in ${\ensuremath{\sigma}}_{+}\text{\ensuremath{-}}{\ensuremath{\sigma}}_{\ensuremath{-}}$ Raman fields which exhibit $\ensuremath{\lambda}∕4$ periodicity. We find that the resulting controlled-NOT (CNOT) gate operations times are in the order of millisecond. We also investigate motional and magnetic-field induced decoherences specific to the proposed architecture.

We propose a scalable quantum-computing architecture based on cold atoms confined to sites of a tight optical lattice. The lattice is placed in a non-uniform magnetic field and the resulting Zeeman sublevels define qubit states. Microwave pulses tuned to space-dependent resonant frequencies are used for individual addressing. The atoms interact via magnetic-dipole interactions allowing implementation of a universal controlled-NOT gate. The resulting gate operation times for alkalis are on the order of milliseconds, much faster then the anticipated decoherence times. Single qubit operations take about 10 microseconds. Analysis of motional decoherence due to NOT operations is given. We also comment on the improved feasibility of the proposed architecture with complex open-shell atoms, such as Cr, Eu and metastable alkaline-earth atoms with larger magnetic moments., Comment: fixed bibliography and eps figures

The scalar and tensor dynamic polarizabilities of the first excited P1/2,3/2 states of the alkali-metal atoms Na, K, and Rb are calculated using relativistic many-body perturbation theory. Comparison with experimental measurements of the static polarizabilities suggests that the errors in the theoretical predictions do not exceed 1%. The dynamic polarizabilities at imaginary frequencies are employed to calculate the long-range van der Waals coefficients for the interaction of ground-state helium atoms with the excited alkali-metal atoms to a probable error of less than 2%.

We illuminate the importance of a self-consistent many-body treatment in calculations of vacuum polarization corrections to the energies of atomic orbitals in many-electron atoms. Including vacuum polarization in the atomic Hamiltonian causes a substantial re-adjustment (relaxation) of the electrostatic self-consistent field. The induced change in the electrostatic energies is substantial for states with the orbital angular momentum $l &;gt; 0$. For such orbitals, the relaxation mechanism determines the sign and even the order of magnitude of the total vacuum polarization correction. This relaxation mechanism is illustrated with numerical results for the Cs atom.

We report calculations assessing the ultimate precision of an atomic clock based on the 578 nm $6{}^{1}{S}_{0}\ensuremath{\rightarrow}6{}^{3}{P}_{0}$ transition in Yb atoms confined in an optical lattice trap. We find that this transition has a natural linewidth less than 10 mHz in the odd Yb isotopes, caused by hyperfine coupling. The shift in this transition due to the trapping light acting through the lowest order ac polarizability is found to become zero at the magic trap wavelength of about 752 nm. The effects of Rayleigh scattering, multipole polarizabilities, vector polarizability, and hyperfine induced electronic magnetic moments can all be held below 1 mHz (about one part in ${10}^{18}).$ In the case of the hyperpolarizability, however, larger shifts due to nearly resonant terms cannot be ruled out without an accurate measurement of the magic wavelength.

A method for determination of atomic lifetimes from the value of dispersion coefficient ${C}_{6}$ of molecular potentials correlating to two ground-state atoms is proposed. The method is illustrated with atomic Cs using ${C}_{6}$ deduced from high-resolution Feshbach spectroscopy. The following lifetimes are determined: ${\ensuremath{\tau}}_{{6P}_{1/2}}=34.80\ifmmode\pm\else\textpm\fi{}0.07 \mathrm{ns}$ and ${\ensuremath{\tau}}_{{6P}_{3/2}}=30.39\ifmmode\pm\else\textpm\fi{}0.06 \mathrm{ns}.$ The underlying electric-dipole matrix elements are required for a refined analysis of parity violation in ${}^{133}\mathrm{Cs}.$ We also obtain static polarizability of the Cs ground state, $\ensuremath{\alpha}(0)=400.49(81)$ atomic units. It is demonstrated that the uncertainties may be considerably reduced as the coefficient ${C}_{6}$ is constrained further.

In this paper, we have calculated the values of the ${\mathrm{C}}_{6}$ coefficients and the anisotropy parameters $\ensuremath{\gamma}$ of the leading term of the van der Waals interactions between molecular hydrogen and alkali-metal atoms from Li to Fr. The uncertainties in our results are less than $2%.$

Relativistic many-body calculations of van der Waals coefficients ${C}_{6}$ for dimers correlating to two ground-state alkaline-earth-metal atoms at large internuclear separations are reported. The following values and uncertainties were determined: ${C}_{6}=214(3)$ for Be, 627(12) for Mg, 2221(15) for Ca, 3170(196) for Sr, and 5160(74) for Ba in atomic units.

Van der Waals coefficients for the heteronuclear alkali-metal dimers of Li, Na, K, Rb, Cs, and Fr are calculated using relativistic ab initio methods augmented by high-precision experimental data. We argue that the uncertainties in the coefficients are unlikely to exceed about 1%., 11 pages, 2 figs, graphicx.sty

We present semiempirical calculations of long-range van der Waals interactions for two interacting metastable rare-gas atoms Ne through Xe. Dispersion coefficients $C_6$ are obtained for homonuclear molecular potentials asymptotically connecting to the $ns(3/2)_{2} + ns(3/2)_{2}$ atomic states. The estimated uncertainty of the calculated $C_6$ dispersion coefficients is 4%., 7 pages

The photoionization cross section $\sigma$, spin-polarization parameters $P$ and $Q$, and the angular-distribution asymmetry parameter $\beta$ are calculated for the $7s$ state of francium for photon energies below 10 eV. Two distinct calculations are presented, one based on many-body perturbation theory and another based on the model potential method. Although predictions of the two calculations are similar, the detailed energy dependence of the photoionization parameters from the two calculations differ. From the theoretical p-wave phase shifts, we infer quantum defects for $p_{1/2}$ and $p_{3/2}$ Rydberg series, permitting us to calculate positions of experimentally unknown $p$ states in francium., Comment: 8 pages, 9 figures

The van der Waals coefficients for the alkali-metal atoms from Na to Fr interacting in their ground states are calculated using relativistic ab initio methods. The accuracy of the calculations is estimated by also evaluating atomic static electric-dipole polarizabilities and coefficients for the interaction of the atoms with a perfectly conducting wall. The results are in excellent agreement with the latest data from studies of magnetic field induced Feshbach resonances in ultracold collisions of Na and of Rb atoms. For Cs we provide critically needed data for ultracold collision studies.