Variation of the Quadrupole Hyperfine Structure and Nuclear Radius due to an Interaction with Scalar and Axion Dark Matter.

Atomic spectroscopy is used to search for the space-time variation of fundamental constants which may be due to an interaction with scalar and pseudoscalar (axion) dark matter. In this Letter, we study the effects that are produced by the variation of the nuclear radius and electric quadrupole moment. The sensitivity of the electric quadrupole hyperfine structure to both the variation of the quark mass and the effects of dark matter exceeds that of the magnetic hyperfine structure by 1-2 orders of magnitude. Therefore, the measurement of the variation of the ratio of the electric quadrupole and magnetic dipole hyperfine constants is proposed. The sensitivity of the optical clock transitions in the Yb^{+} ion to the variation of the nuclear radius allows us to extract, from experimental data, limits on the variation of the hadron and quark masses, the QCD parameter θ and the interaction with axion dark matter.

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.

Search for CP-violating nuclear magnetic quadrupole moment using the LuOH+ cation.

The time-reversal and spatial parity violating interaction of the nuclear magnetic quadrupole moment (MQM) of the 175Lu and 176Lu nuclei with electrons in the molecular cation LuOH+ is studied. The resulting effect is expressed in terms of fundamental parameters, such as quantum chromodynamics angle θ¯, quark electric dipole moment (EDM), and chromo-EDM. For this, we have estimated the magnetic quadrupole moments of 175Lu and 176Lu nuclei and calculated the molecular constant that characterizes the interaction of the MQM with electrons in the considered molecules. Additionally, we predict the hyperfine structure constants for the ground electronic state of LuOH+. In the molecular calculations, both the correlation and relativistic effects including the Gaunt interaction have been considered. According to the calculated expressions in terms of the fundamental constants, we conclude that LuOH+ can be a promising system to measure the nuclear MQM.

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.

Limits on Lorentz Invariance Violation from Coulomb Interactions in Nuclei and Atoms.

Anisotropy in the speed of light that has been constrained by Michelson-Morley-type experiments also generates anisotropy in the Coulomb interactions. This anisotropy can manifest itself as an energy anisotropy in nuclear and atomic experiments. Here the experimental limits on Lorentz violation in _{10}^{21}Ne are used to improve the limits on Lorentz symmetry violations in the photon sector, namely, the anisotropy of the speed of light and the Coulomb interactions, by 7 orders of magnitude in comparison with previous experiments: the speed of light is isotropic to a part in 10^{28}.

Publisher's Note: Limits on Lorentz Invariance Violation from Coulomb Interactions in Nuclei and Atoms [Phys. Rev. Lett. 118, 142501 (2017)].

This corrects the article DOI: 10.1103/PhysRevLett.118.142501.

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.

Enhancing the Effect of Lorentz Invariance and Einstein's Equivalence Principle Violation in Nuclei and Atoms.

Local Lorentz invariance violating (LLIV) and Einstein equivalence principle violating (EEPV) effects in atomic experiments are discussed. The EEPV effects are strongly enhanced in the narrow 7.8 eV transition in the _{90}^{229}Th nucleus. The nuclear LLIV tensors describing the anisotropy in the maximal attainable speed for massive particles (analog of the Michelson-Morley experiment for light) are expressed in terms of the experimental values of the nuclear quadrupole moments. Calculations for nuclei of experimental interest _{55}^{133}Cs, _{37}^{85}Rb, _{37}^{87}Rb, _{80}^{201}Hg, _{54}^{131}Xe, and _{10}^{21}Ne are performed. The results for _{10}^{21}Ne are used to improve the limits on the proton LLIV interaction constants by 4 orders of magnitude.

Ionization of Atoms by Slow Heavy Particles, Including Dark Matter.

Atoms and molecules can become ionized during the scattering of a slow, heavy particle off a bound electron. Such an interaction involving leptophilic weakly interacting massive particles (WIMPs) is a promising possible explanation for the anomalous 9σ annual modulation in the DAMA dark matter direct detection experiment [R. Bernabei et al., Eur. Phys. J. C 73, 2648 (2013)]. We demonstrate the applicability of the Born approximation for such an interaction by showing its equivalence to the semiclassical adiabatic treatment of atomic ionization by slow-moving WIMPs. Conventional wisdom has it that the ionization probability for such a process should be exponentially small. We show, however, that due to nonanalytic, cusplike behavior of Coulomb functions close to the nucleus this suppression is removed, leading to an effective atomic structure enhancement. We also show that electron relativistic effects actually give the dominant contribution to such a process, enhancing the differential cross section by up to 1000 times.

Search for the Effect of Massive Bodies on Atomic Spectra and Constraints on Yukawa-Type Interactions of Scalar Particles.

We propose a new method to search for hypothetical scalar particles that have feeble interactions with standard-model particles. In the presence of massive bodies, these interactions produce a nonzero Yukawa-type scalar-field magnitude. Using radio-frequency spectroscopy data of atomic dysprosium, as well as atomic clock spectroscopy data, we constrain the Yukawa-type interactions of a scalar field with the photon, electron, and nucleons for a range of scalar-particle masses corresponding to length scales >10 cm. In the limit as the scalar-particle mass m_{ϕ}→0, our derived limits on the Yukawa-type interaction parameters are Λ_{γ}≳8×10^{19} GeV, Λ_{e}≳1.3×10^{19} GeV, and Λ_{N}≳6×10^{20} GeV. Our measurements also constrain combinations of interaction parameters, which cannot otherwise be probed with traditional anomalous-force measurements. We suggest further measurements to improve on the current level of sensitivity.

Can Dark Matter Induce Cosmological Evolution of the Fundamental Constants of Nature?

We demonstrate that massive fields, such as dark matter, can directly produce a cosmological evolution of the fundamental constants of nature. We show that a scalar or pseudoscalar (axionlike) dark matter field ϕ, which forms a coherently oscillating classical field and interacts with standard model particles via quadratic couplings in ϕ, produces "slow" cosmological evolution and oscillating variations of the fundamental constants. We derive limits on the quadratic interactions of ϕ with the photon, electron, and light quarks from measurements of the primordial (4)He abundance produced during big bang nucleosynthesis and recent atomic dysprosium spectroscopy measurements. These limits improve on existing constraints by up to 15 orders of magnitude. We also derive limits on the previously unconstrained linear and quadratic interactions of ϕ with the massive vector bosons from measurements of the primordial (4)He abundance.

Searching for dark matter and variation of fundamental constants with laser and maser interferometry.

Any slight variations in the fundamental constants of nature, which may be induced by dark matter or some yet-to-be-discovered cosmic field, would characteristically alter the phase of a light beam inside an interferometer, which can be measured extremely precisely. Laser and maser interferometry may be applied to searches for the linear-in-time drift of the fundamental constants, detection of topological defect dark matter through transient-in-time effects, and for a relic, coherently oscillating condensate, which consists of scalar dark matter fields, through oscillating effects. Our proposed experiments require either minor or no modifications of existing apparatus, and offer extensive reach into important and unconstrained spaces of physical parameters.

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+}.

Searching for topological defect dark matter via nongravitational signatures.

We propose schemes for the detection of topological defect dark matter using pulsars and other luminous extraterrestrial systems via nongravitational signatures. The dark matter field, which makes up a defect, may interact with standard model particles, including quarks and the photon, resulting in the alteration of their masses. When a topological defect passes through a pulsar, its mass, radius, and internal structure may be altered, resulting in a pulsar "quake." A topological defect may also function as a cosmic dielectric material with a distinctive frequency-dependent index of refraction, which would give rise to the time delay of a periodic extraterrestrial light or radio signal, and the dispersion of a light or radio source in a manner distinct to a gravitational lens. A topological defect passing through Earth may alter Earth's period of rotation and give rise to temporary nonzero electric dipole moments for an electron, proton, neutron, nuclei and atoms.

Time-reversal symmetry violation in molecules induced by nuclear magnetic quadrupole moments.

Recent measurements in paramagnetic molecules improved the limit on the electron electric dipole moment (EDM) by an order of magnitude. Time-reversal (T) and parity (P) symmetry violation in molecules may also come from their nuclei. We point out that nuclear T, P-odd effects are amplified in paramagnetic molecules containing deformed nuclei, where the primary effects arise from the T, P-odd nuclear magnetic quadrupole moment (MQM). We perform calculations of T, P-odd effects in the molecules TaN, ThO, ThF+, HfF+, YbF, HgF, and BaF induced by MQMs. We compare our results with those for the diamagnetic TlF molecule, where the T, P-odd effects are produced by the nuclear Schiff moment. We argue that measurements in molecules with MQMs may provide improved limits on the strength of T, P-odd nuclear forces, on the proton, neutron, and quark EDMs, on quark chromo-EDMs, and on the QCD θ term and CP-violating quark interactions.