Precision Calculation of Hyperfine Constants for Extracting Nuclear Moments of ^{229}Th

Determination of nuclear moments for many nuclei relies on the computation of hyperfine constants, with theoretical uncertainties directly affecting the resulting uncertainties of the nuclear moments. In this work, we improve the precision of such a method by including for the first time an iterative solution of equations for the core triple cluster amplitudes into the relativistic coupled-cluster method, with large-scale complete basis sets. We carried out calculations of the energies and magnetic dipole and electric quadrupole hyperfine structure constants for the low-lying states of ^{229}Th^{3+} in the framework of such a relativistic coupled-cluster single double triple method. We present a detailed study of various corrections to all calculated properties. Using the theory results and experimental data, we found the nuclear magnetic dipole and electric quadrupole moments to be μ=0.366(6)μ_{N} and Q=3.11(2)  eb, respectively, and reduce the uncertainty of the quadrupole moment by a factor of 3. The Bohr-Weisskopf effect of the finite nuclear magnetization is investigated, with bounds placed on the deviation of the magnetization distribution from the uniform one.

Observation of an Electric Quadrupole Transition in a Negative Ion: Experiment and Theory

The first direct experimental observation of an electric quadrupole (E2) absorption transition between bound states of an atomic negative ion has been made. The transition was observed in the negative ion of bismuth by resonant (1+1) photon detachment from Bi^{-} via ^{3}P_{2}→^{3}P_{0} excitation. The E2 transition properties were completely independently calculated using a hybrid theoretical approach to account for the strong multilevel electron interactions and relativistic effects. The experimental and ab initio theoretical results are in excellent agreement, providing valuable new insight into this complex system and forbidden transitions in negative ions more generally.

State-Dependent Optical Lattices for the Strontium Optical Qubit

We demonstrate state-dependent optical lattices for the Sr optical qubit at the tune-out wavelength for its ground state. We tightly trap excited state atoms while suppressing the effect of the lattice on ground state atoms by more than 4 orders of magnitude. This highly independent control over the qubit states removes inelastic excited state collisions as the main obstacle for quantum simulation and computation schemes based on the Sr optical qubit. Our results also reveal large discrepancies in the atomic data used to calibrate the largest systematic effect of Sr optical lattice clocks.

Accurate Prediction of Clock Transitions in a Highly Charged Ion with Complex Electronic Structure

We develop a broadly applicable approach that drastically increases the ability to predict the properties of complex atoms accurately. We apply it to the case of Ir^{17+}, which is of particular interest for the development of novel atomic clocks with a high sensitivity to the variation of the fine-structure constant and to dark matter searches. In general, clock transitions are weak and very difficult to identify without accurate theoretical predictions. In the case of Ir^{17+}, even stronger electric-dipole (E1) transitions have eluded observation despite years of effort, raising the possibility that the theoretical predictions are grossly wrong. In this work, we provide accurate predictions of the transition wavelengths and E1 transition rates for Ir^{17+}. Our results explain the lack of observations of the E1 transitions and provide a pathway toward the detection of clock transitions. The computational advances we demonstrate in this work are widely applicable to most elements in the periodic table and will allow us to solve numerous problems in atomic physics, astrophysics, and plasma physics.

Narrow-line Cooling and Determination of the Magic Wavelength of Cd

We experimentally and theoretically determine the magic wavelength of the (5s^{2})^{1}S_{0}-(5s5p)^{3}P_{0} clock transition of ^{111}Cd to be 419.88(14) and 420.1(7) nm. To perform Lamb-Dicke spectroscopy of the clock transition, we use narrow-line laser cooling on the ^{1}S_{0}-^{3}P_{1} transition to cool the atoms to 6  μK and load them into an optical lattice. Cadmium is an attractive candidate for optical lattice clocks because it has a small sensitivity to blackbody radiation and its efficient narrow-line cooling mitigates higher order light shifts. We calculate the blackbody shift, including the dynamic correction, to be fractionally 2.83(8)×10^{-16} at 300 K, an order of magnitude smaller than that of Sr and Yb. We also report calculations of the Cd ^{1}P_{1} lifetime and the ground state C_{6} coefficient.

Suppressing Inhomogeneous Broadening in a Lutetium Multi-ion Optical Clock

We demonstrate precision measurement and control of inhomogeneous broadening in a multi-ion clock consisting of three ^{176}Lu^{+} ions. Microwave spectroscopy between hyperfine states in the ^{3}D_{1} level is used to characterize differential systematic shifts between ions, most notably those associated with the electric quadrupole moment. By appropriate alignment of the magnetic field, we demonstrate suppression of these effects to the ∼10^{-17} level relative to the ^{1}S_{0}↔^{3}D_{1} optical transition frequency. Correlation spectroscopy on the optical transition demonstrates the feasibility of a 10-s Ramsey interrogation in the three ion configuration with a corresponding projection noise limited stability of σ(τ)=8.2×10^{-17}/sqrt[τ].

Nuclear Charge Radii of ^{229}Th from Isotope and Isomer Shifts

The isotope ^{229}Th is unique in that it possesses an isomeric state of only a few electron volts above the ground state, suitable for nuclear laser excitation. An optical clock based on this transition is expected to be a very sensitive probe for variations of fundamental constants, but the nuclear properties of both states have to be determined precisely to derive the actual sensitivity. We carry out isotope shift calculations in Th^{+} and Th^{2+} including the specific mass shift, using a combination of configuration interaction and all-order linearized coupled-cluster methods and estimate the uncertainty of this approach. We perform experimental measurements of the hyperfine structure of Th^{2+} and isotopic shift between ^{229}Th^{2+} and ^{232}Th^{2+} to extract the difference in root-mean-square radii as δ⟨r^{2}⟩^{232,229}=0.299(15)  fm^{2}. Using the recently measured values of the isomer shift of lines of ^{229m}Th, we derive the value for the mean-square radius change between ^{229}Th and its low-lying isomer ^{229m}Th to be δ⟨r^{2}⟩^{229m,229}=0.0105(13)  fm^{2}.

Probing Sizes and Shapes of Nobelium Isotopes by Laser Spectroscopy

Until recently, ground-state nuclear moments of the heaviest nuclei could only be inferred from nuclear spectroscopy, where model assumptions are required. Laser spectroscopy in combination with modern atomic structure calculations is now able to probe these moments directly, in a comprehensive and nuclear-model-independent way. Here we report on unique access to the differential mean-square charge radii of ^{252,253,254}No, and therefore to changes in nuclear size and shape. State-of-the-art nuclear density functional calculations describe well the changes in nuclear charge radii in the region of the heavy actinides, indicating an appreciable central depression in the deformed proton density distribution in ^{252,254}No isotopes. Finally, the hyperfine splitting of ^{253}No was evaluated, enabling a complementary measure of its (quadrupole) deformation, as well as an insight into the neutron single-particle wave function via the nuclear spin and magnetic moment.

Ultracold Anions for High-Precision Antihydrogen Experiments

Experiments with antihydrogen (H[over ¯]) for a study of matter-antimatter symmetry and antimatter gravity require ultracold H[over ¯] to reach ultimate precision. A promising path towards antiatoms much colder than a few kelvin involves the precooling of antiprotons by laser-cooled anions. Because of the weak binding of the valence electron in anions-dominated by polarization and correlation effects-only few candidate systems with suitable transitions exist. We report on a combination of experimental and theoretical studies to fully determine the relevant binding energies, transition rates, and branching ratios of the most promising candidate La^{-}. Using combined transverse and collinear laser spectroscopy, we determined the resonant frequency of the laser cooling transition to be ν=96.592 713(91)  THz and its transition rate to be A=4.90(50)×10^{4}  s^{-1}. Using a novel high-precision theoretical treatment of La^{-} we calculated yet unmeasured energy levels, transition rates, branching ratios, and lifetimes to complement experimental information on the laser cooling cycle of La^{-}. The new data establish the suitability of La^{-} for laser cooling and show that the cooling transition is significantly stronger than suggested by a previous theoretical study.

New Methods for Testing Lorentz Invariance with Atomic Systems

We describe a broadly applicable experimental proposal to search for the violation of local Lorentz invariance (LLI) with atomic systems. The new scheme uses dynamic decoupling and can be implemented in current atomic clock experiments, with both single ions and arrays of neutral atoms. Moreover, the scheme can be performed on systems with no optical transitions, and therefore it is also applicable to highly charged ions which exhibit a particularly high sensitivity to Lorentz invariance violation. We show the results of an experiment measuring the expected signal of this proposal using a two-ion crystal of ^{88}Sr^{+} ions. We also carry out a systematic study of the sensitivity of highly charged ions to LLI to identify the best candidates for the LLI tests.

Multipolar Polarizabilities and Hyperpolarizabilities in the Sr Optical Lattice Clock

We address the problem of the lattice Stark shifts in the Sr clock caused by the multipolar M1 and E2 atom-field interactions and by the term nonlinear in lattice intensity and determined by the hyperpolarizability. We develop an approach to calculate hyperpolarizabilities for atoms and ions based on a solution of the inhomogeneous equation which allows us to effectively and accurately carry out complete summations over intermediate states. We apply our method to the calculation of the hyperpolarizabilities for the clock states in Sr. We also carry out an accurate calculation of the multipolar polarizabilities for these states at the magic frequency. Understanding these Stark shifts in optical lattice clocks is crucial for further improvement of the clock accuracy.

Relativistic all-order many-body calculation of energies, wavelengths, and M1 and E2 transition rates for the 3d n configurations in tungsten ions

Energy levels, wavelengths, magnetic-dipole and electric-quadrupole transition rates between the low-lying states are evaluated for W51+ to W54+ ions with 3d n (n = 2 to 5) electronic configurations by using an approach combining configuration interaction with the linearized coupled-cluster single-double method. The QED corrections are directly incorporated into the calculations and their effect is studied in detail. Uncertainties of the calculations are discussed. This study of such highly charged ions with the present method opens the way for future applications allowing an accurate prediction of properties for a very wide range of highly charged ions aimed at providing precision benchmarks for various applications.

Quantum Electrodynamical Shifts in Multivalent Heavy Ions

The quantum electrodynamics (QED) corrections are directly incorporated into the most accurate treatment of the correlation corrections for ions with complex electronic structure of interest to metrology and tests of fundamental physics. We compared the performance of four different QED potentials for various systems to access the accuracy of QED calculations and to make a prediction of highly charged ion properties urgently needed for planning future experiments. We find that all four potentials give consistent and reliable results for ions of interest. For the strongly bound electrons, the nonlocal potentials are more accurate than the local potential.

Ionization potentials of superheavy elements No, Lr, and Rf and their ions

We predict ionization potentials of superheavy elements No, Lr, and Rf and their ions using a relativistic hybrid method that combines configuration interaction (CI) with the linearized coupled-cluster approach. Extensive study of the completeness of the four-electron CI calculations for Hf and Rf was carried out. As a test of theoretical accuracy, we also calculated ionization potential of Yb, Lu, Hf, and their ions, which are homologues of the superheavy elements of this study.

Towards a Mg Lattice Clock: Observation of the ^{1}S_{0}-^{3}P_{0} Transition and Determination of the Magic Wavelength

We optically excite the electronic state 3s3p ^{3}P_{0} in ^{24}Mg   atoms, laser cooled and trapped in a magic-wavelength lattice. An applied magnetic field enhances the coupling of the light to the otherwise strictly forbidden transition. We determine the magic wavelength, the quadratic magnetic Zeeman shift, and the transition frequency to be 468.46(21) nm, -206.6(2.0)  MHz/T^{2}, and 655 058 646 691(101) kHz, respectively. These are compared with theoretical predictions and results from complementary experiments. We also develop a high-precision relativistic structure model for magnesium, give an improved theoretical value for the blackbody radiation shift, and discuss a clock based on bosonic magnesium.

Highly charged ions for atomic clocks, quantum information, and search for α variation

We propose 10 highly charged ions as candidates for the development of next generation atomic clocks, quantum information, and search for α variation. They have long-lived metastable states with transition wavelengths to the ground state between 170-3000 nm, relatively simple electronic structure, stable isotopes, and high sensitivity to α variation (e.g., Sm(14+), Pr(10+), Sm(13+), Nd(10+)). We predict their properties crucial for the experimental exploration and highlight particularly attractive systems for these applications.

Precision measurement of transition matrix elements via light shift cancellation

We present a method for accurate determination of atomic transition matrix elements at the 10(-3) level. Measurements of the ac Stark (light) shift around "magic-zero" wavelengths, where the light shift vanishes, provide precise constraints on the matrix elements. We make the first measurement of the 5s - 6p matrix elements in rubidium by measuring the light shift around the 421 and 423 nm zeros through diffraction of a condensate off a sequence of standing wave pulses. In conjunction with existing theoretical and experimental data, we find 0.3235(9)ea(0) and 0.5230(8)ea(0) for the 5s - 6p(1/2) and 5s - 6p(3/2) elements, respectively, an order of magnitude more accurate than the best theoretical values. This technique can provide needed, accurate matrix elements for many atoms, including those used in atomic clocks, tests of fundamental symmetries, and quantum information.

Ytterbium in quantum gases and atomic clocks: van der Waals interactions and blackbody shifts

We evaluated the C(6) coefficients of Yb-Yb, Yb-alkali, and Yb-group II van der Waals interactions with 2% uncertainty. The only existing experimental result for such quantities is for the Yb-Yb dimer. Our value, C(6)=1929(39) a.u., is in excellent agreement with the recent experimental determination of 1932(35) a.u. We have also developed a new approach for the calculation of the dynamic correction to the blackbody radiation shift. We have calculated this quantity for the Yb 6s(2) (1)S(0)-6s6p (3)P(0)(o) clock transition with 3.5% uncertainty. This reduces the fractional uncertainty due to the blackbody radiation shift in the Yb optical clock at 300 K to the 10(-18) level.

Electric dipole moment enhancement factor of thallium

The goal of this work is to resolve the present controversy in the value of the electric dipole moment (EDM) enhancement factor of Tl. We carry out several calculations by different high-precision methods, study previously omitted corrections, as well as test our methodology on other, parity conserving, quantities. We find the EDM enhancement factor of Tl to be equal to -573(20). This value is 20% larger than the recently published result of Nataraj et al. [Phys. Rev. Lett. 106, 200403 (2011)], but agrees very well with several earlier results.

Precision calculation of blackbody radiation shifts for optical frequency metrology

We show that three group IIIB divalent ions, B(+), Al(+), and In(+), have anomalously small blackbody radiation (BBR) shifts of the ns(2) (1)S(0)-nsnp (3)P(0)(o) clock transitions. The fractional BBR shifts for these ions are at least 10 times smaller than those of any other present or proposed optical frequency standards at the same temperature, and are less than 0.3% of the Sr clock shift. We have developed a hybrid configuration-interaction + coupled-cluster method that provides accurate treatment of correlation corrections in such ions and yields a rigorous upper bound on the uncertainty of the final results. We reduce the BBR contribution to the fractional frequency uncertainty of the Al(+) clock to 4×10(-19) at T=300  K. We also reduce the uncertainties due to this effect at room temperature to 10(-18) level for B(+) and In(+) to facilitate further development of these systems for metrology and quantum sensing.

Nuclear magnetic moment of 210Fr: a combined theoretical and experimental approach

We measure the hyperfine splitting of the 9S_{1/2} level of 210Fr, and find a magnetic dipole hyperfine constant A=622.25(36) MHz. The theoretical value, obtained using the relativistic all-order method from the electronic wave function at the nucleus, allows us to extract a nuclear magnetic moment of 4.38(5)micro_{N} for this isotope, which represents a factor of 2 improvement in precision over previous measurements. The same method can be applied to other rare isotopes and elements.