Electric dipole moments of diamagnetic atoms of experimental interest are calculated using the relativistic Hartree-Fock and random-phase approximation methods, the many-body perturbation theory and configuration interaction technique. We consider P,T-odd interactions which give rise to atomic electric dipole moment in the second order of the perturbation theory. These include nuclear Schiff moment, P,T-odd electron-nucleon interaction and electron electric dipole moment. Interpretation of a new experimental constraint of a permanent electric dipole moment of $^{199}$Hg [W. C. Griffith {\it et al.}, Phys. Rev. Lett. {\bf 102}, 101601 (2009)] is discussed.
The current status of electric dipole moments of diamagnetic atoms which involves the synergy between atomic experiments and three different theoretical areas -- particle, nuclear and atomic is reviewed. Various models of particle physics that predict CP violation, which is necessary for the existence of such electric dipole moments, are presented. These include the standard model of particle physics and various extensions of it. Effective hadron level combined charge conjugation (C) and parity (P) symmetry violating interactions are derived taking into consideration different ways in which a …
The exchange of an axion-like particle between atomic electrons and the nucleus may induce electric dipole moments (EDMs) of atoms and molecules. This interaction is described by a parity- and time-reversal-invariance-violating potential which depends on the product of a scalar $g^s$ and a pseudoscalar $g^p$ coupling constant. We consider the interaction with the specific combination of these constants, $g_e^s g_N^p$, which gives significant contributions to the EDMs of diamagnetic atoms. In this paper, we calculate these contributions to the EDMs of $^{199}$Hg, $^{129}$Xe, $^{211}$Rn and $^{2…
We have experimentally realized a hybrid trap for ultracold paramagnetic rubidium and diamagnetic ytterbium atoms by combining a bichromatic optical dipole trap for ytterbium with a Ioffe-Pritchard-type magnetic trap for rubidium. In this hybrid trap, sympathetic cooling of five different ytterbium isotopes through elastic collisions with rubidium was achieved. A strong dependence of the interspecies collisional cross section on the mass of the ytterbium isotope was observed.
The observation of electric dipole moments (EDMs) in atomic systems due to parity and time-reversal violating (P,T-odd) interactions can probe new physics beyond the standard model and also provide insights into the matter-antimatter asymmetry in the Universe. The EDMs of open-shell atomic systems are sensitive to the electron EDM and the P,T-odd scalar-pseudoscalar (S-PS) semi-leptonic interaction, but the dominant contributions to the EDMs of diamagnetic atoms come from the hadronic and tensor-pseudotensor (T-PT) semi-leptonic interactions. Several diamagnetic atoms like $^{129}$Xe, $^{171}$…
We perform model-independent analyses extracting limits for the electric dipole moment of the electron and the P,T-odd scalar-pseudoscalar (S-PS) nucleon-electron coupling from the most recent measurements with atoms and molecules. The analysis using paramagnetic systems, only, is improved substantially by the inclusion of the recent measurement on HfF+ ions, but complicated by the fact that the corresponding constraints are largely aligned, owing to a general relation between the coefficients for the two contributions. Since this same relation does not hold in diamagnetic systems, it is possi…
Postulating the existence of a fnite-mass mediator of T,P-odd coupling between atomic electrons and nucleons we consider its effect on permanent electric dipole moment (EDM) of diamagnetic atoms. We present both numerical and analytical analysis for such mediator-induced EDMs and compare it with EDM results for the conventional contact interaction. Based on this analysis we derive limits on coupling strengths and carrier masses from experimental limits on EDM of 199Hg atom.
We have considered a mechanism for inducing a time-reversal violating electric dipole moment (EDM) in atoms through the interaction of a nuclear EDM (d_N) with the hyperfine interaction, the "magnetic moment effect". We have derived the operator for this interaction and presented analytical formulas for the matrix elements between atomic states. Induced EDMs in the diamagnetic atoms 129Xe, 171Yb, 199Hg, 211Rn, and 225Ra have been calculated numerically. From the experimental limits on the atomic EDMs of 129Xe and 199Hg, we have placed the following constraints on the nuclear EDMs, |d_N(129Xe)|…
We address the quantum estimation of the diamagnetic, or $A^2$, term in an effective model of light-matter interaction featuring two coupled oscillators. First, we calculate the quantum Fisher information of the diamagnetic parameter in the interacting ground state. Then, we find that typical measurements on the transverse radiation field, such as homodyne detection or photon counting, permit to estimate the diamagnetic coupling constant with near-optimal efficiency in a wide range of model parameters. Should the model admit a critical point, we also find that both measurements would become as…
We calculate the effect of the P, CP-odd electron-nucleon interaction on the electric dipole moment of the $^{199}$Hg atom by evaluating the nuclear spin matrix elements in terms of the nuclear shell model. It is found that the neutron spin matrix element of the $^{199}$Hg nucleus is $\langle Ψ|\, σ_{nz} | Ψ\rangle \approx -0.4$ with a dominant configuration of $p_{1/2}$ orbital neutron. We also derive constraints on the CP phases of Higgs-doublet models, supersymmetric models, and leptoquark models from the latest experimental limit $|d_{\rm Hg}| < 7.4 \times 10^{-30}e$ cm.
Parity and time invariance violating electric dipole moment of $^{205}$Tl is calculated using the relativistic Hartree-Fock and configuration interaction methods and the many-body perturbation theory. Contributions from the interaction of the electron electric dipole moments with internal electric field and scalar-pseudoscalar electron-nucleon (T,P)-odd interaction are considered. The results are $d(^{205}{\rm Tl})=-582(20) d_e$ or $d(^{205}{\rm Tl})=-7.0(2)\times 10^{-18}C^{SP} e {\rm cm}$. Interpretation of the measurements are discussed. The results of similar calculations for $^{133}$Cs ar…
We report the calculation of the isovector CP-odd $πN$ interaction generated by the Weinberg operator, the CP violating three-gluon operator. This enables to restrict models which induce the operator by using experimental data of atomic electric dipole moment. The QCD sum rules are used to determine the matrix element required to assess the CP-odd $πN$ interactions. The relation between the Weinberg operator and the Hg and Xe EDMs is clarified, and the constraint on the Weinberg operator is obtained using the experimental data for the Hg EDM.
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 …
Parity and time invariance violating ($P,T$-odd) atomic electric dipole moments (EDM) are induced by interaction between atomic electrons and nuclear $P,T$-odd moments which are produced by $P,T$-odd nuclear forces. The nuclear EDM is screened by atomic electrons. The EDM of a non-relativistic atom with closed electron subshells is induced by the nuclear Schiff moment. For heavy relativistic atoms EDM is induced by the nuclear local dipole moments which differ by 10-50% from the Schiff moments calculated previously. We calculate the local dipole moments for ${^{199}{\rm Hg}}$ and ${^{205}{\rm …
We have calculated the atomic electric dipole moments (EDMs) induced in ^{199}Hg, ^{129}Xe, ^{223}Rn, ^{225}Ra, and ^{239}Pu by their respective nuclear Schiff moments S. The results are (in units 10^{-17}S(e {fm}^{3})^{-1}e cm): d(^{199}Hg)=-2.8, d(^{129}Xe)=0.38, d(^{223}Rn)=3.3, d(^{225}Ra)=-8.5, d(^{239}Pu)=-11. We have also calculated corrections to the parity- and time-invariance-violating (P,T-odd) spin-axis interaction constant in TlF. These results are important for the interpretation of atomic and molecular experiments on EDMs in terms of fundamental P,T-odd parameters.
Microscopic study of low-lying states in odd-mass nuclei for atomic electric dipole moment searches
School of Physics and Astronomy, Sun Yat-sen University（中山大学物理学院）；Guangdong Provincial Key Laboratory of Quantum Metrology and Sensing, Sun Yat-Sen University（中山大学广东省量子计量与传感重点实验室）
$^{129}$Xe is an important candidate for the searches of electric dipole moments due to violations of time-reversal and parity violations in diamagnetic atoms. In view of the similarities between the electric dipole moment and the polarizability from the point of view of many-body theory, we have performed rigorous calculations of the ground state polarizability of $^{129}$Xe using a self consistent relativistic coupled-cluster method and the relativistic normal coupled-cluster method. The discrepancy between the results from these two methods is two percent, but each of them differs from the …
Combining the recently reported electric dipole moment (EDM) of $^{199}$Hg atom due to breaking of parity and time-reversal symmetries with the improved relativistic atomic calculations, precise limits on the tensor-pseudotensor (T-PT) electron-nucleus (e-N) coupling coefficient and the nuclear Schiff moment (NSM) interactions are determined. Using these limits with the nuclear calculations, we infer limits on the EDMs of neutron and proton as $d_n < 2.2 \times 10^{-26} |e| \rm{cm}$ and $d_p < 2.1 \times 10^{-25} |e| \rm{cm}$, respectively, and on the quantum chromodynamics (QCD) parameter and…
The contribution of the CP violating three-gluon Weinberg operator, $\frac{1}{3!} w f^{abc} ε^{νραβ} G^a_{μν} G^b_{αβ} G^{c μ}_ρ$, to the atomic and nuclear EDMs is estimated using QCD sum rules. After calculating the transition matrix element between the pion and the vacuum through the Weinberg operator, we obtain the long-range CP-odd nuclear force by determining the isovector CP-odd pion-nucleon vertex, using chiral perturbation theory at NLO. The EDMs of $^{199}$Hg, $^{129}$Xe, $^{225}$Ra, $^2$H, and $^3$He are finally given including comprehensive uncertainty analysis. While the leading c…
The parity (P) and time-reversal (T) odd coupling constant associated with the tensor-pseudotensor (T-PT) electron-nucleus interaction and the nuclear Schiff moment (NSM) have been determined by combining the result of the measurement of the electric dipole moment (EDM) of ^{129}Xe atom and calculations based on the relativistic coupled-cluster (RCC) theory. Calculations using various relativistic many-body methods have been performed at different levels of approximation and their accuracies are estimated by comparing the results of the calculated dipole polarizability of the ground state of t…
We review the current status of the study of parity and time invariance violation in atoms, nuclei and molecules. We focus on parity non-conservation in cesium and three of the most promising areas of research: (i) parity non-conservation in a chain of isotopes, (ii) search for nuclear anapole moments, and (iii) search for permanent electric dipole moments (EDMs) of atoms and molecules, which in turn are caused by either an electron EDM or nuclear $T,P$-odd moments such as a nuclear EDM or nuclear Schiff moment.
We have calculated the atomic electric dipole moments (EDMs) induced in 229Pa and 225Ac by their respective nuclear Schiff moments S. The results are d(229Pa)= - 9.5 10^{-17} [S/(e fm)] e cm= - 1.1 10^{-20} ηe cm; d(225Ac})=- 8.6 10^{-17} [S/(e fm)] e cm=- 0.8 10^{-21} ηe cm. EDM of 229 Pa is 3 10^4 times larger than 199Hg EDM and 40 times larger than 225Ra EDM. Possible use of actinides in solid state experiments is also discussed. The T,P-odd spin-axis interaction in RaO molecule is 500 times larger than in TlF.
P odd anapole moment of the deuteron is found in the chiral limit, $m_π \to 0$. The contact current generated by the P odd pion exchange does not contribute to the deuteron anapole. Being combined with usual radiative corrections to the weak electron -- deuteron interaction, our calculation results in a sufficiently accurate theoretical prediction for the corresponding effective constant $C_{2d}$. The experimental measurement of this constant would give valuable information on the P odd $π$NN constant and on the $s$-quark content of nucleons. We calculate also in the same limit $m_π \to 0$ the…
The existence of a nuclear electric octupole moment (EOM) requires both parity and time invariance violation. The EOMs of odd $Z$ nuclei that are induced by a particular T- and P-odd interaction are calculated. We compare such octupole moments with the collective EOMs that can occur in nuclei having a static octupole deformation. A nuclear EOM can induce a parity and time invariance violating atomic electric dipole moment, and the magnitude of this effect is calculated. The contribution of a nuclear EOM to such a dipole moment is found, in most cases, to be smaller than that of other mechanism…
It is demonstrated that the TaN molecule is the best candidate to search for T,P-violating nuclear magnetic quadrupole moment (MQM), it also looks promising to search for other T,P-odd effects. We report results of coupled-cluster calculations of T,P-odd effects in TaN produced by the Ta nucleus MQM, electron electric dipole moment (EDM), scalar$-$pseudoscalar nucleus$-$electron interactions, also of the molecule-axis hyperfine structure constant and dipole moment. Nuclear calculations of $^{181}$Ta MQM are performed to express the T,P-odd effect in terms of the strength constants of T,P-odd n…
Toroidal Transitions in Hydrogenic and Alkali Atoms
Centre for Quantum Technologies, Nanyang Technological University（南洋理工大学量子技术中心）；Centre for Disruptive Photonic Technologies, SPMS, The Photonics Institute, Nanyang Technological University（南洋理工大学光波研究中心、理学院光子学研究所）；MajuLab, International Joint Research Unit IRL 3654, CNRS, Université Côte d’Azur, Sorbonne Université, National University of Singapore, Nanyang Technological University（马久实验室，国际联合研究单位IRL 3654，法国国家科学研究中心，蔚蓝海岸大学，索邦大学，新加坡国立大学，南洋理工大学）；Centre for Quantum Technologies, National University of Singapore（新加坡国立大学量子技术中心）
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 accurac…
Parity and time-reversal violating electric dipole moment (EDM) of $^{171}$Yb is calculated accounting for the electron correlation effects over the Dirac-Hartree-Fock (DHF) method in the relativistic Rayleigh-Schrödinger many-body perturbation theory, with the second (MBPT(2) method) and third order (MBPT(3) method) approximations, and two variants of all-order relativistic many-body approaches, in the random phase approximation (RPA) and coupled-cluster (CC) method with singles and doubles (CCSD method) framework. We consider electron-nucleus tensor-pseudotensor (T-PT) and nuclear Schiff mom…
We discuss the nuclear anapole moment, a new P odd, T even electromagnetic multipole. Its discovery in the cesium experiment gives a first-rate information on parity-nonconserving nuclear forces. New prospects in the field are considered. Upper limits on the electric dipole moments, which are P odd, T odd multipoles, of elementary particles and atoms are presented, and their physical implications discussed. The atomic experiments are demonstrated to be as informative in this respect as the neutron ones. Tremendous progress in the field can be expected from experiments at ion storage rings and …
We consider a mechanism by which dyons (electrically charged magnetic monopoles) can produce both a T- and P-odd (i.e. time reversal invariance and parity violating) mixed polarizability beta [defined by Delta E = -beta E.B, where Delta E is the energy change when electric (E) and magnetic (B) fields are applied to a system] and a T- and P-odd interaction between two particles: psi_1-bar gamma_5 psi_1 psi_2-bar psi_2, where the psi_i are electron and quark spinors. The latter can create atomic and neutron electric dipole moments (EDMs). From experimental bounds on these we find limits on the p…
Recent relativistic coupled-cluster (RCC) calculations of electric dipole moments (EDMs) of diamagnetic atoms due to parity and time-reversal violating (P,T-odd) interactions, that are essential ingredients for probing new physics beyond the standard model of particle interactions, differ substantially from the previous theoretical results. It is therefore necessary to perform an independent test of the validity of these results. In view of this, the normal coupled-cluster (NCC) method has been extended to the relativistic regime to calculate the EDMs of atoms by simultaneously incorporating t…
The multiconfiguration Dirac-Hartree-Fock (MCDHF) method has been employed to calculate atomic electric dipole moments (EDM) of 225^Ra, 199^Hg, and 171^Yb. For the calculations of the matrix elements we extended the relativistic atomic structure package GRASP2K. The extension includes programs to evaluate matrix elements of (P, T)-odd e-N tensor-pseudotensor and pseudoscalar-scalar interactions, the atomic electric dipole interaction, the nuclear Schiff moment, and the interaction of the electron electric dipole moment with nuclear magnetic moments. The interelectronic interactions were accoun…
A concept of CP-violating (T,P-odd) permanent molecular magnetic moments $μ^{CP}$ is introduced. We relate the moments to the electric dipole moment of electron (eEDM) and estimate $μ^{CP}$ for several diamagnetic polar molecules. The moments exhibit a steep, Z^5, scaling with the nuclear charge Z of the heavier molecular constituent. A measurement of the CP-violating magnetization of a polarized sample of heavy molecules may improve the present limit on eEDM by several orders of magnitude.
An experiment to search for the electron electric dipole moment (\eEDM) on the metastable $H^3Δ_1$ state of ThO molecule was proposed and now in the final stage of preparation by the ACME collaboration [http://www.electronedm.org]. To interpret the experiment in terms of \eEDM\ and dimensionless constant $k_{T,P}$ characterizing the strength of the scalar T,P-odd electron-nucleus neutral current interaction, an accurate theoretical study of effective electric field on electron, Eeff, and $W_{T,P}$ constants is required. We report calculation of \Eeff\ (84 GV/cm) and a parameter of T,P-odd scal…
Highly correlated pure {\it{ab initio}} relativistic configuration interaction theory is in the present paper applied to the calculation of the tensor-pseudotensor ${\cal{(P,T)}}$-violating nucleon-electron interaction constant in the electronic ground states of atomic mercury and radium. The final best obtained results are $R_T$(Hg) = $-4.43$\, [$10^{-20}$ $\left<σ_N\right>$ $e$ cm] and $R_T$(Ra) = $-15.0$\, [$10^{-20}$ $\left<σ_N\right>$ $e$ cm]. The accuracy of the employed electronic-structure models are confirmed by determining the static electric dipole polarizability $α_d$(Hg) = $35.7$ …
In the quest to find a favourable triatomic molecule for detecting electric dipole moment of an electron (eEDM), we identify mercury hydroxide (HgOH) as an extremely attractive candidate from both experimental and theoretical viewpoints. Our calculations show that there is a four-fold enhancement in the effective electric field of HgOH compared to the recently proposed ytterbium hydroxide (YbOH) [Phys. Rev. Lett. 119, 133002 (2017)] for eEDM measurement. Thus, in the (010) bending state associated with the electronic ground state, it could provide better sensitivity than YbOH from a theoretica…
Present limit on the electron electric dipole moment ($e$EDM) is based on the electron spin precession measurement. We propose an alternative approach - observation of the $\mathcal{P}$,$\mathcal{T}$-odd Faraday effect in an external electric field on atoms and molecules using cavity-enhanced polarimetric scheme in combination with molecular (atomic) beam crossing the cavity. Our calculations of the effective electric fields and theoretical simulation of the proposed experiment on Tl and Pb atoms, PbF, YbF, ThO, and YbOH show that the present limit on the $e$EDM can be improved by 6-7 orders o…
We place new limits on potential T- and P- violating monopole-dipole interactions between unpolarized nucleons and neutrons using dual species magnetic resonance in polarzed Xe gas. Free-induction decay transients with relaxation times ~20 s allow high precision measurements of the NMR frequencies, whose ratios cancel magnetic fluctuations. The new limits on the product gsgp improve on previous laboratory work by 2 orders of magnitude.
Ab initio calculation of the hyperfine, P-odd, and P,T-odd constants for the YbF molecule was performed with the help of the recently developed technique, which allows to take into account correlations and polarization in the outercore region. The ground state electronic wave function of the YbF molecule is found with the help of the Relativistic Effective Core Potential method followed by the restoration of molecular four-component spinors in the core region of ytterbium in the framework of a non-variational procedure. Core polarization effects are included with the help of the atomic Many Bo…
