New limit on the electron electric dipole moment

Relativistic Exact Two-Component Coupled-Cluster Study of Molecular Sensitivity Factors for Nuclear Schiff Moments

Relativistic exact two-component coupled-cluster calculations of molecular sensitivity factors for nuclear Schiff moments (NSMs) are reported. We focus on molecules containing heavy nuclei, especially octupole-deformed nuclei. Analytic relativistic coupled-cluster gradient techniques are used and serve as useful tools for identifying candidate molecules that sensitively probe for physics beyond the Standard Model in the hadronic sector. Notably, these tools enable straightforward "black-box" calculations. Two competing chemical mechanisms that contribute to the NSM are analyzed, illuminating the physics of ligand effects on NSM sensitivity factors.

Opportunities for fundamental physics research with radioactive molecules

Molecules containing short-lived, radioactive nuclei are uniquely positioned to enable a wide range of scientific discoveries in the areas of fundamental symmetries, astrophysics, nuclear structure, and chemistry. Recent advances in the ability to create, cool, and control complex molecules down to the quantum level, along with recent and upcoming advances in radioactive species production at several facilities around the world, create a compelling opportunity to coordinate and combine these efforts to bring precision measurement and control to molecules containing extreme nuclei. In this manuscript, we review the scientific case for studying radioactive molecules, discuss recent atomic, molecular, nuclear, astrophysical, and chemical advances which provide the foundation for their study, describe the facilities where these species are and will be produced, and provide an outlook for the future of this nascent field.

Engineering Field-Insensitive Molecular Clock Transitions for Symmetry Violation Searches

Molecules are a powerful platform to probe fundamental symmetry violations beyond the standard model, as they offer both large amplification factors and robustness against systematic errors. As experimental sensitivities improve, it is important to develop new methods to suppress sensitivity to external electromagnetic fields, as limits on the ability to control these fields are a major experimental concern. Here we show that sensitivity to both external magnetic and electric fields can be simultaneously suppressed using engineered radio frequency, microwave, or two-photon transitions that maintain large amplification of CP-violating effects. By performing a clock measurement on these transitions, CP-violating observables including the electron electric dipole moment, nuclear Schiff moment, and magnetic quadrupole moment can be measured with suppression of external field sensitivity of ≳100 generically, and even more in many cases. Furthermore, the method is compatible with traditional Ramsey measurements, offers internal co-magnetometry, and is useful for systems with large angular momentum commonly present in molecular searches for nuclear CP violation.

Axion-mediated electron-electron interaction in ytterbium monohydroxide molecule

The YbOH triatomic molecule can be efficiently used to measure the electron electric dipole moment, which violates time-reversal (T) and spatial parity (P) symmetries of fundamental interactions [Kozyryev and Hutzler, Phys. Rev. Lett. 119, 133002 (2017)]. We study another mechanism of the T, P-violation in the YbOH molecule-the electron-electron interaction mediated by the low-mass axionlike particle. For this, we calculate the molecular constant that characterizes this interaction and use it to estimate the expected magnitude of the effect to be measured. It is shown that this molecular constant has the same order of magnitude as the corresponding molecular constant corresponding to the axion-mediated electron-nucleus interaction. According to our estimation, an experiment on YbOH will allow one to set updated laboratory constraints on the CP-violating electron-axion coupling constants.

Approaching meV level for transition energies in the radium monofluoride molecule RaF and radium cation Ra+ by including quantum-electrodynamics effects

Highly accurate theoretical predictions of transition energies in the radium monofluoride molecule, ²²⁶RaF, and radium cation, ²²⁶Ra⁺, are reported. The considered transition X²Σ_1/2 → A²Π_1/2 in RaF is one of the main features of this molecule and can be used to laser-cool RaF for a subsequent measurement of the electron electric dipole moment. For molecular and atomic predictions, we go beyond the Dirac-Coulomb Hamiltonian and treat high-order electron correlation effects within the coupled cluster theory with the inclusion of quadruple and ever higher amplitudes. The effects of quantum electrodynamics (QED) are included non-perturbatively using the model QED operator that is now implemented for molecules. It is shown that the inclusion of the QED effects in molecular and atomic calculations is a key ingredient in resolving the discrepancy between the theoretical values obtained within the Dirac-Coulomb-Breit Hamiltonian and the experiment. The remaining deviation from the experimental values is within a few meV. This is more than an order of magnitude better than the "chemical accuracy," 1 kcal/mol = 43 meV, that is usually considered as a guiding thread in theoretical molecular physics.

Large Long-Distance Contributions to the Electric Dipole Moments of Charged Leptons in the Standard Model

We reevaluate the electric dipole moment (EDM) of charged leptons in the standard model using hadron effective models. We find unexpectedly large EDM generated by the hadron level long-distance effect, d_{e}=5.8×10^{-40}, d_{μ}=1.4×10^{-38}, and d_{τ}=-7.3×10^{-38}  e cm, with an error bar of 70%, exceeding the conventionally known four-loop level elementary contribution by several orders of magnitude.

Electron Electric Dipole Moment Searches Using Clock Transitions in Ultracold Molecules

Permanent electric dipole moments (EDMs) of fundamental particles such as the electron are signatures of parity and time-reversal violation occurring in physics beyond the standard model. EDM measurements probe new physics at energy scales well beyond the reach of present-day colliders. Recent advances in assembling molecules from ultracold atoms have opened up new opportunities for improving the reach of EDM experiments. However, the magnetic field sensitivity of such ultracold molecules means that new measurement techniques are needed before these opportunities can be fully exploited. We present a technique that takes advantage of magnetically insensitive hyperfine clock transitions in polar molecules, offering a way to improve both the precision and accuracy of EDM searches with ultracold assembled molecules.

P , T -Violating and Magnetic Hyperfine Interactions in Atomic Thallium

We present state-of-the-art string-based relativistic general-excitation-rank configuration interaction and coupled cluster calculations of the electron electric dipole moment, the nucleon–electron scalar-pseudoscalar, and the magnetic hyperfine interaction constants ( α d e , α C S , A | | , respectively) for the thallium atomic ground state 2 P 1 / 2 . Our present best values are α d e = − 558 ± 28 , α C S = 6.77 ± 0.34 [ 10 − 18 e cm], and A | | = 21172 ± 1059 [MHz]. The central value of the latter constant agrees with the experimental result to within 0.7% and serves as a measurable probe of the P , T -violating interaction constants. Our findings lead to a significant reduction of the theoretical uncertainties for P , T -odd interaction constants for atomic thallium but not to stronger constraints on the electron electric dipole moment, d e , or the nucleon–electron scalar-pseudoscalar coupling constant, C S .

Actinide and lanthanide molecules to search for strong CP-violation

Actinide and lanthanide molecules are prospective candidates to search for the violation of fundamental symmetries and test grand unification theories.

Optical Rotation Approach to Search for the Electric Dipole Moment of the Electron

The P , T -odd Faraday effect (i.e., rotation of the polarization plane of light propagating through a medium in presence of the external electric field due to P , T symmetry violating interactions) is considered for several atomic species: Ra, Pb, Tl, Hg, Cs, and Xe. Corresponding theoretical simulation of P , T -odd Faraday experiment, with already achieved intracavity absorption spectroscopy characteristics and parameters, is performed. The results show that the magnetic dipole transitions in the Tl and Pb atoms as well as the electric dipole transitions in the Ra, Hg and Cs atoms are favorable for the observation of the P , T -odd Faraday optical rotation. The estimation of the rotation angle of the light polarization plane demonstrates that recently existing boundaries for the electron electric dipole moment can be improved by one-two orders of magnitude.

Relativistic coupled-cluster investigation of parity (P) and time-reversal (T ) symmetry violations in HgF

We employ the Z-vector method in the four-component relativistic coupled-cluster framework to calculate the parity (P) and time-reversal (T ) symmetry violating scalar-pseudoscalar nucleus-electron interaction constant (W_s), the effective electric field (E_eff) experienced by the unpaired electron, and the nuclear magnetic quadrupole moment-electron interaction constant (W_M) in the open-shell ground electronic state of HgF. The molecular frame dipole moment and the magnetic hyperfine structure (HFS) constant of the molecule are also calculated at the same level of theory. The outcome of our study is that HgF has a high value of E_eff (115.9 GV/cm), W_s (266.4 kHz), and W_M (3.59 × 10³³ Hz/e cm²), which shows that it can be a possible candidate for the search of new physics beyond the standard model. Our results are in good agreement with the available literature values. Furthermore, we investigate the effect of the basis set and the virtual energy functions on the computed properties. The role of the high-energy virtual spinors is found to be significant in the calculation of the HFS constant and the P,T-odd interaction coefficients.

Nuclear-Spin Comagnetometer Based on a Liquid of Identical Molecules

Atomic comagnetometers are used in searches for anomalous spin-dependent interactions. Magnetic field gradients are one of the major sources of systematic errors in such experiments. Here we describe a comagnetometer based on the nuclear spins within an ensemble of identical molecules. The dependence of the measured spin-precession frequency ratio on the first-order magnetic field gradient is suppressed by over an order of magnitude compared to a comagnetometer based on overlapping ensembles of different molecules. Our single-species comagnetometer is capable of measuring the hypothetical spin-dependent gravitational energy of nuclei at the 10^{-17}  eV level, comparable to the most stringent existing constraints. Combined with techniques for enhancing the signal such as parahydrogen-induced polarization, this method of comagnetometry offers the potential to improve constraints on spin-gravity coupling of nucleons by several orders of magnitude.

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.

Precision Measurement of the Electron's Electric Dipole Moment Using Trapped Molecular Ions

We describe the first precision measurement of the electron's electric dipole moment (d_{e}) using trapped molecular ions, demonstrating the application of spin interrogation times over 700 ms to achieve high sensitivity and stringent rejection of systematic errors. Through electron spin resonance spectroscopy on ^{180}Hf^{19}F^{+} in its metastable ^{3}Δ_{1} electronic state, we obtain d_{e}=(0.9±7.7_{stat}±1.7_{syst})×10^{-29}  e cm, resulting in an upper bound of |d_{e}|<1.3×10^{-28}  e cm (90% confidence). Our result provides independent confirmation of the current upper bound of |d_{e}|<9.4×10^{-29}  e cm [J. Baron et al., New J. Phys. 19, 073029 (2017)NJOPFM1367-263010.1088/1367-2630/aa708e], and offers the potential to improve on this limit in the near future.

Transparent electrodes for high E-field production using a buried indium tin oxide layer

We present a design and characterization of optically transparent electrodes suitable for atomic and molecular physics experiments where high optical access is required. The electrodes can be operated in air at standard atmospheric pressure and do not suffer electrical breakdown even for electric fields far exceeding the dielectric breakdown of air. This is achieved by putting an indium tin oxide coated dielectric substrate inside a stack of dielectric substrates, which prevents ion avalanche resulting from Townsend discharge. With this design, we observe no arcing for fields of up to 120 kV/cm. Using these plates, we directly verify the production of electric fields up to 18 kV/cm inside a quartz vacuum cell by a spectroscopic measurement of the dc Stark shift of the 5(2)S(1/2) → 5(2)P(3/2) transition for a cloud of laser cooled rubidium atoms. We also report on the shielding of the electric field and on the residual electric fields that persist within the vacuum cell once the electrodes are discharged. In addition, we discuss observed atom loss that results from the motion of free charges within the vacuum. The observed asymmetry of these phenomena on the bias of the electrodes suggests that field emission of electrons within the vacuum is primarily responsible for these effects and may indicate a way of mitigating them.

Laser frequency locking with 46 GHz offset using an electro-optic modulator for magneto-optical trapping of francium atoms

We demonstrate frequency offset locking between two laser sources using a waveguide-type electro-optic modulator (EOM) with 10th-order sidebands for magneto-optical trapping of Fr atoms. The frequency locking error signal was successfully obtained by performing delayed self-homodyne detection of the beat signal between the repumping frequency and the 10th-order sideband component of the trapping light. Sweeping the trapping-light and repumping-light frequencies with keeping its frequency difference of 46 GHz was confirmed over 1 GHz by monitoring the Doppler absorption profile of I₂. This technique enables us to search for a resonance frequency of magneto-optical trapping of Fr.

Transportation of a radioactive ion beam for precise laser-trapping experiments

Francium is the heaviest species among the alkali elements. Due to its properties, francium is said to be of advantage in measurements of tiny observations, such as atomic parity violation and electric dipole moment. Before executing experiments with francium, it must be produced artificially because it is one of the most unstable elements. We produced francium with the nuclear fusion reaction of an oxygen beam and gold target, ionized the produced francium through a thermal ionization process, and extracted the ion with electrostatic fields. However, the thermal ionization process is known to ionize not only an objective atom but also other atomic species. Therefore, a Wien filter was installed to analyze the composition of the ion beam and purify the beam. This allowed us to improve the beam purity from ∼10(-6) to ∼10(-3).

Calculation of P,T-odd interaction constant of PbF using Z-vector method in the relativistic coupled-cluster framework

The effective electric field experienced by the unpaired electron in the ground state of PbF, which is a potential candidate in the search of electron electric dipole moment due to some special characteristics, is calculated using Z-vector method in the coupled cluster single- and double- excitation approximation with four component Dirac spinor. This is an important quantity to set the upper bound limit of the electron electric dipole moment. Further, we have calculated molecular dipole moment and parallel magnetic hyperfine structure constant (A‖) of (207)Pb in PbF to test the accuracy of the wavefunction obtained in the Z-vector method. The outcome of our calculations clearly suggests that the core electrons have significant contribution to the "atom in compound" properties.

Exploring CP violation in the MSSM

We explore the prospects for observing CP violation in the minimal supersymmetric extension of the Standard Model (MSSM) with six CP-violating parameters, three gaugino mass phases and three phases in trilinear soft supersymmetry-breaking parameters, using the CPsuperH code combined with a geometric approach to maximise CP-violating observables subject to the experimental upper bounds on electric dipole moments. We also implement CP-conserving constraints from Higgs physics, flavour physics and the upper limits on the cosmological dark matter density and spin-independent scattering. We study possible values of observables within the constrained MSSM (CMSSM), the non-universal Higgs model (NUHM), the CPX scenario and a variant of the phenomenological MSSM (pMSSM). We find values of the CP-violating asymmetry [Formula: see text] in [Formula: see text] decay that may be as large as 3 %, so future measurements of [Formula: see text] may provide independent information about CP violation in the MSSM. We find that CP-violating MSSM contributions to the [Formula: see text] meson mass mixing term [Formula: see text] are in general below the present upper limit, which is dominated by theoretical uncertainties. If these could be reduced, [Formula: see text] could also provide an interesting and complementary constraint on the six CP-violating MSSM phases, enabling them all to be determined experimentally, in principle. We also find that CP violation in the [Formula: see text] and [Formula: see text] couplings can be quite large, and so may offer interesting prospects for future [Formula: see text], [Formula: see text], [Formula: see text] and [Formula: see text] colliders.

QCD and strongly coupled gauge theories: challenges and perspectives

We highlight the progress, current status, and open challenges of QCD-driven physics, in theory and in experiment. We discuss how the strong interaction is intimately connected to a broad sweep of physical problems, in settings ranging from astrophysics and cosmology to strongly coupled, complex systems in particle and condensed-matter physics, as well as to searches for physics beyond the Standard Model. We also discuss how success in describing the strong interaction impacts other fields, and, in turn, how such subjects can impact studies of the strong interaction. In the course of the work we offer a perspective on the many research streams which flow into and out of QCD, as well as a vision for future developments.

New classes of systematic effects in gas spin comagnetometers

Atomic comagnetometers are widely used in precision measurements searching for spin interactions beyond the standard model. We describe a new (3)He-(129)Xe comagnetometer probed by Rb atoms and use it to identify two general classes of systematic effects in gas comagnetometers, one associated with diffusion in second-order magnetic-field gradients and another due to temperature gradients. We also develop and confirm experimentally a general and practical approach for calculating spin relaxation and frequency shifts due to arbitrary magnetic-field gradients.

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.

Limit on the electron electric dipole moment using paramagnetic ferroelectric Eu0.5Ba0.5TiO3

We report on the results of a search for the electron electric dipole moment d(e) using paramagnetic ferroelectric Eu(0.5)Ba(0.5)TiO(3). The electric polarization creates an effective electric field that makes it energetically favorable for the spins of the seven unpaired 4f electrons of the Eu(2+) to orient along the polarization, provided that d(e) ≠ 0. This interaction gives rise to sample magnetization, correlated with its electric polarization, and is therefore equivalent to a linear magnetoelectric effect. A SQUID magnetometer is used to search for the resulting magnetization. We obtain d(e) = (-1.07 ± 3.06(stat) ± 1.74(syst)) × 10(-25) ecm, implying an upper limit of |d(e)|<6.05 × 10(-25) ecm (90% confidence).

Liquid-state nuclear spin comagnetometers

We discuss nuclear spin comagnetometers based on ultralow-field nuclear magnetic resonance in mixtures of miscible solvents, each rich in a different nuclear spin. In one version thereof, Larmor precession of protons and 19F nuclei in a mixture of thermally polarized pentane and hexafluorobenzene is monitored via a sensitive alkali-vapor magnetometer. We realize transverse relaxation times in excess of 20 s and suppression of magnetic field fluctuations by a factor of 3400. We estimate it should be possible to achieve single-shot sensitivity of about 5×10(-9)  Hz, or about 5×10(-11)  Hz in ≈1 day of integration. In a second version, spin precession of protons and 129Xe nuclei in a mixture of pentane and hyperpolarized liquid xenon is monitored using superconducting quantum interference devices. Application to spin-gravity experiments, electric dipole moment experiments, and sensitive gyroscopes is discussed.

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.