Effects of Electrons on Nuclear Clock Transition Frequency in

We perform calculations of the energy shift of the nuclear clock transition frequency ^{229}Th as a function of the number of electrons in Th ion. We demonstrate that the dependence of the nuclear frequency on electron configuration is significant, for example, removing one electron from the atom leads to relative shift of the nuclear frequency ∼10^{-7}, which is 12 orders of magnitude larger than the expected relative uncertainty of the nuclear clock transition frequency (∼10^{-19}). This leads to the difference of the nuclear clock frequencies in Th IV, Th III, Th II, and Th I. The relative change of the nuclear frequency between neutral Th and its bare nucleus is 1%. We also calculate the field shift constants for isotopic and isomeric shifts of atomic electron transitions in Th ions.

Erratum: Probing Long-Range Neutrino-Mediated Forces with Atomic and Nuclear Spectroscopy [Phys. Rev. Lett. 120, 223202 (2018)].

This corrects the article DOI: 10.1103/PhysRevLett.120.223202.

Precision Determination of Isotope Shifts in Ytterbium and Implications for New Physics.

We report measurements of isotope shifts for the five spinless Yb isotopes on the 6s^{2} ^{1}S_{0}→5d6s ^{1}D_{2} transition using Doppler-free two-photon spectroscopy. We combine these data with existing measurements on two transitions in Yb^{+} [Counts et al. Phys. Rev. Lett. 125, 123002 (2020)PRLTAO0031-900710.1103/PhysRevLett.125.123002], where deviation from King-plot linearity showed hints of a new bosonic force carrier at the 3σ level. The combined data strongly reduce the significance of the new-physics signal. We show that the observed nonlinearity in the joint Yb/Yb^{+} King-plot analysis can be accounted for by the deformation of the Yb nuclei.

Atomic Ionization by Scalar Dark Matter and Solar Scalars.

We calculate the cross sections of atomic ionization by absorption of scalar particles in the energy range from a few eV to 100 keV. We consider both nonrelativistic particles (dark matter candidates) and relativistic particles that may be produced inside the Sun. We provide numerical results for atoms relevant for direct dark matter searches (O, Na, Ar, Ca, Ge, I, Xe, W and Tl). We identify a crucial flaw in previous calculations and show that they overestimated the ionization cross sections by several orders of magnitude due to violation of the orthogonality of the bound and continuum electron wave functions. Using our computed cross sections, we interpret the recent data from the Xenon1T experiment, establishing the first direct bounds on coupling of scalars to electrons. We argue that the Xenon1T excess can be explained by the emission of scalars from the Sun. Although our finding is in a similar tension with astrophysical bounds as the solar axion hypothesis, we establish direct limits on scalar DM for the ∼1-10 keV mass range. We also update axio-ionization cross sections. Numerical data files are provided.

Quadruply Ionized Barium as a Candidate for a High-Accuracy Optical Clock.

We identify Ba^{4+} (Te-like) as a promising candidate for a high-accuracy optical clock. The lowest-lying electronic states are part of a ^{3}P_{J} fine structure manifold with anomalous energy ordering, being nonmonotonic in J. We propose a clock based on the 338.8 THz electric quadrupole transition between the ground (^{3}P_{2}) and first-excited (^{3}P_{0}) electronic states. We perform relativistic many-body calculations to determine relevant properties of this ion. The lifetime of the excited clock state is found to be several seconds, accommodating low statistical uncertainty with a single ion for practical averaging times. The differential static scalar polarizability is found to be small and negative, providing suppressed sensitivity to blackbody radiation while simultaneously allowing cancellation of Stark and excess micromotion shifts. With the exception of Hg^{+} and Yb^{+}, sensitivity to variation of the fine structure constant is greater than other optical clocks thus far demonstrated.

Improved Limits on Axionlike-Particle-Mediated P, T-Violating Interactions between Electrons and Nucleons from Electric Dipole Moments of Atoms and Molecules.

In the presence of P, T-violating interactions, the exchange of axionlike particles between electrons and nucleons in atoms and molecules induces electric dipole moments (EDMs) of atoms and molecules. We perform calculations of such axion-exchange-induced atomic EDMs using the relativistic Hartree-Fock-Dirac method including electron core polarization corrections. We present analytical estimates to explain the dependence of these induced atomic EDMs on the axion mass and atomic parameters. From the experimental bounds on the EDMs of atoms and molecules, including ^{133}Cs, ^{205}Tl, ^{129}Xe, ^{199}Hg, ^{171}Yb^{19}F, ^{180}Hf^{19}F^{+}, and ^{232}Th^{16}O, we constrain the P, T-violating scalar-pseudoscalar nucleon-electron and electron-electron interactions mediated by a generic axionlike particle of arbitrary mass. Our limits improve on existing laboratory bounds from other experiments by many orders of magnitude for m_{a}≳10^{-2} eV. We also place constraints on CP violation in certain types of relaxion models.

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.

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.

Probing Low-Mass Vector Bosons with Parity Nonconservation and Nuclear Anapole Moment Measurements in Atoms and Molecules.

In the presence of P-violating interactions, the exchange of vector bosons between electrons and nucleons induces parity-nonconserving (PNC) effects in atoms and molecules, while the exchange of vector bosons between nucleons induces anapole moments of nuclei. We perform calculations of such vector-mediated PNC effects in Cs, Ba^{+}, Yb, Tl, Fr, and Ra^{+} using the same relativistic many-body approaches as in earlier calculations of standard-model PNC effects, but with the long-range operator of the weak interaction. We calculate nuclear anapole moments due to vector-boson exchange using a simple nuclear model. From measured and predicted (within the standard model) values for the PNC amplitudes in Cs, Yb, and Tl, as well as the nuclear anapole moment of ^{133}Cs, we constrain the P-violating vector-pseudovector nucleon-electron and nucleon-proton interactions mediated by a generic vector boson of arbitrary mass. Our limits improve on existing bounds from other experiments by many orders of magnitude over a very large range of vector-boson masses.

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.

Identification of the predicted 5s-4f level crossing optical lines with applications to metrology and searches for the variation of fundamental constants.

We measure optical spectra of Nd-like W, Re, Os, Ir, and Pt ions of particular interest for studies of a possibly varying fine-structure constant. Exploiting characteristic energy scalings we identify the strongest lines, confirm the predicted 5s-4f level crossing, and benchmark advanced calculations. We infer two possible values for optical M2/E3 and E1 transitions in Ir^{17+} that have the highest predicted sensitivity to a variation of the fine-structure constant among stable atomic systems. Furthermore, we determine the energies of proposed frequency standards in Hf^{12+} and W^{14+}.

Limiting P-odd interactions of cosmic fields with electrons, protons, and neutrons.

We propose methods for extracting limits on the strength of P-odd interactions of pseudoscalar and pseudovector cosmic fields with electrons, protons, and neutrons, by exploiting the static and dynamic parity-nonconserving amplitudes and electric dipole moments they induce in atoms. Candidates for such fields are dark matter (including axions) and dark energy, as well as several more exotic sources described by Lorentz-violating standard model extensions. Atomic calculations are performed for H, Li, Na, K, Rb, Cs, Ba(+), Tl, Dy, Fr, and Ra(+). From these calculations and existing measurements in Dy, Cs, and Tl, we constrain the interaction strengths of the parity-violating static pseudovector cosmic field to be 7 × 10(-15) GeV with an electron, and 3 × 10(-8) GeV with a proton.

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.

Limits on violations of Lorentz symmetry and the Einstein equivalence principle using radio-frequency spectroscopy of atomic dysprosium.

We report a joint test of local Lorentz invariance and the Einstein equivalence principle for electrons, using long-term measurements of the transition frequency between two nearly degenerate states of atomic dysprosium. We present many-body calculations which demonstrate that the energy splitting of these states is particularly sensitive to violations of both special and general relativity. We limit Lorentz violation for electrons at the level of 10(-17), matching or improving the best laboratory and astrophysical limits by up to a factor of 10, and improve bounds on gravitational redshift anomalies for electrons by 2 orders of magnitude, to 10(-8). With some enhancements, our experiment may be sensitive to Lorentz violation at the level of 9 × 10(-20).

Highly charged ions as a basis of optical atomic clockwork of exceptional accuracy.

We propose a novel class of atomic clocks based on highly charged ions. We consider highly forbidden laser-accessible transitions within the 4f(12) ground-state configurations of highly charged ions. Our evaluation of systematic effects demonstrates that these transitions may be used for building exceptionally accurate atomic clocks which may compete in accuracy with recently proposed nuclear clocks.

Revisiting parity nonconservation in cesium.

We apply the sum-over-states approach to calculate partial contributions to parity nonconservation (PNC) in cesium [Porsev, Beloy, and Drevianko, Phys. Rev. Lett. 102, 181601 (2009)]. We find significant corrections to two nondominating terms coming from the contribution of the core and highly excited states (n>9, the so called tail). When these differences are taken into account the result of Porsev et al., E(PNC)=0.8906(24)×10(-11)i(-Q(W)/N) changes to 0.8977 (40), coming into good agreement with our previous calculations, 0.8980 (45). The interpretation of the PNC measurements in cesium still indicates reasonable agreement with the standard model (1.5σ); however, it gives new constraints on physics beyond it.

Optical transitions in highly charged californium ions with high sensitivity to variation of the fine-structure constant.

We study electronic transitions in highly charged Cf ions that are within the frequency range of optical lasers and have very high sensitivity to potential variations in the fine-structure constant, α. The transitions are in the optical range despite the large ionization energies because they lie on the level crossing of the 5f and 6p valence orbitals in the thallium isoelectronic sequence. Cf(16+) is a particularly rich ion, having several narrow lines with properties that minimize certain systematic effects. Cf(16+) has very large nuclear charge and large ionization energy, resulting in the largest α sensitivity seen in atomic systems. The lines include positive and negative shifters.

Single-ion nuclear clock for metrology at the 19th decimal place.

The 7.6(5) eV nuclear magnetic-dipole transition in a single 229Th3+ ion may provide the foundation for an optical clock of superb accuracy. A virtual clock transition composed of stretched states within the 5F(5/2) electronic ground level of both nuclear ground and isomeric manifolds is proposed. It is shown to offer unprecedented systematic shift suppression, allowing for clock performance with a total fractional inaccuracy approaching 1×10(-19).

Electron-hole transitions in multiply charged ions for precision laser spectroscopy and searching for variations in α.

We consider transitions of electron holes (vacancies in otherwise filled shells of atomic systems) in multiply charged ions that, due to level crossing of the holes, have frequencies within the range of optical atomic clocks. Strong E1 transitions provide options for laser cooling and trapping, while narrow transitions can be used for high-precision spectroscopy and tests of fundamental physics. We show that hole transitions can have extremely high sensitivity to α variation and propose candidate transitions that have much larger α sensitivities than any previously seen in atomic systems.

Exponential increase of energy level density in atoms: Th and Th II.

We present analytical estimates and numerical calculations showing that the energy level density in open-shell atoms increases exponentially with the increase of excitation energy. As an example, we use the relativistic Hartree-Fock and configuration interaction methods to calculate the density of states of Th and Th II. The result is used to estimate the effect of electrons on the nuclear transition which is considered for the nuclear clock.