Precision Calculation of Hyperfine Constants for Extracting Nuclear Moments of

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.

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.

Nuclear Charge Radii of

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.

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.

Towards a Mg Lattice Clock: Observation of the

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.

Michelson-Morley analogue for electrons using trapped ions to test Lorentz symmetry.

All evidence so far suggests that the absolute spatial orientation of an experiment never affects its outcome. This is reflected in the standard model of particle physics by requiring all particles and fields to be invariant under Lorentz transformations. The best-known tests of this important cornerstone of physics are Michelson-Morley-type experiments verifying the isotropy of the speed of light. For matter, Hughes-Drever-type experiments test whether the kinetic energy of particles is independent of the direction of their velocity, that is, whether their dispersion relations are isotropic. To provide more guidance for physics beyond the standard model, refined experimental verifications of Lorentz symmetry are desirable. Here we search for violation of Lorentz symmetry for electrons by performing an electronic analogue of a Michelson-Morley experiment. We split an electron wave packet bound inside a calcium ion into two parts with different orientations and recombine them after a time evolution of 95 milliseconds. As the Earth rotates, the absolute spatial orientation of the two parts of the wave packet changes, and anisotropies in the electron dispersion will modify the phase of the interference signal. To remove noise, we prepare a pair of calcium ions in a superposition of two decoherence-free states, thereby rejecting magnetic field fluctuations common to both ions. After a 23-hour measurement, we find a limit of h × 11 millihertz (h is Planck's constant) on the energy variations, verifying the isotropy of the electron's dispersion relation at the level of one part in 10(18), a 100-fold improvement on previous work. Alternatively, we can interpret our result as testing the rotational invariance of the Coulomb potential. Assuming that Lorentz symmetry holds for electrons and that the photon dispersion relation governs the Coulomb force, we obtain a fivefold-improved limit on anisotropies in the speed of light. Our result probes Lorentz symmetry violation at levels comparable to the ratio between the electroweak and Planck energy scales. Our experiment demonstrates the potential of quantum information techniques in the search for physics beyond the standard model.

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.

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.

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.

Excitation of the isomeric 229mTh nuclear state via an electronic bridge process in 229Th+.

We consider the excitation of the nuclear transition 229gTh-229mTh near 7.6 eV in singly ionized thorium via an electronic bridge process. The process relies on the excitation of the electron shell by two laser photons whose sum frequency is equal to the nuclear transition frequency. This scheme allows us to determine the nuclear transition frequency with high accuracy. Based on calculations of the electronic level structure of Th+ which combine the configuration-interaction method and many-body perturbation theory, we estimate that a nuclear excitation rate in the range of 10 s⁻¹ can be obtained using conventional laser sources.

Precision determination of electroweak coupling from atomic parity violation and implications for particle physics.

We carry out high-precision calculation of parity violation in a cesium atom, reducing theoretical uncertainty by a factor of 2 compared to previous evaluations. We combine previous measurements with calculations and extract the weak charge of the 133Cs nucleus, QW=-73.16(29)expt(20)theor. 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 4 orders of magnitude (from approximately 10 MeV to approximately 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.

Proposed experimental method to determine alpha sensitivity of splitting between ground and 7.6 eV isomeric states in 229Th.

The 7.6 eV electromagnetic transition between the nearly degenerate ground state and first excited state in the 229Th nucleus may be very sensitive to potential changes in the fine-structure constant, alpha=e2/variant Planck's over 2pic. However, the sensitivity is not known, and nuclear calculations are currently unable to determine it. We propose measurements of the differences of atomic transition frequencies between thorium atoms (or ions) with the nucleus in the ground state and in the first excited (isomeric) state. This will enable extraction of the change in nuclear charge radius and electric-quadrupole moment between the isomers, and hence the alpha dependence of the isomeric transition frequency with reasonable accuracy.

Trapping of neutral mercury atoms and prospects for optical lattice clocks.

We report vapor-cell magneto-optical trapping of Hg isotopes on the (1)S(0)-(3)P(1) intercombination transition. Six abundant isotopes, including four bosons and two fermions, were trapped. Hg is the heaviest nonradioactive atom trapped so far, which enables sensitive atomic searches for "new physics" beyond the standard model. We propose an accurate optical lattice clock based on Hg and evaluate its systematic accuracy to be better than 10;{-18}. Highly accurate and stable Hg-based clocks will provide a new avenue for the research of optical lattice clocks and the time variation of the fine-structure constant.

High-accuracy calculation of 6s --> 7s parity-nonconserving amplitude in Cs.

We calculated the parity-nonconserving (PNC) 6s-->7s amplitude in Cs. In the Dirac-Coulomb approximation our result is in good agreement with other calculations. Breit corrections to the PNC amplitude and to the Stark-induced amplitude beta are found to be -0.4% and -1%, respectively. The weak charge of 133Cs is Q(W) = -72.5+/-0.7 in agreement with the standard model.