We report first ab initio relativistic correlation calculations of potential curves for ten low-lying electronic states, effective electric field on the electron and hyperfine constants for the ^3Δ_1 state of cation of a heavy transition metal fluoride, HfF^+, that is suggested to be used as the working state in experiments to search for the electric dipole moment of the electron. It is shown that HfF^+ has deeply bound ^1Σ^+ ground state, its dissociation energy is D_e=6.4 eV. The ^3Δ_1 state is obtained to be the relatively long-lived first excited state lying about 0.2 eV higher. The calculated effective electric field E_eff=W_d|Ω| acting on an electron in this state is 5.84*10^{24}Hz/(e*cm)
计算了$^{177}$ Hf $^{19}$ F $^+$和$^{179}$ Hf $^{19}$ F $^+$中由核磁四极矩（MQM）、电子电偶极矩（EDM）和标量$-$赝标核$-$电子中性流（SP）相互作用产生的CP破坏效应.超精细相互作用的作用进行了研究。结果表明，由于MQM位移与超精细子能级的隐式依赖关系，MQM位移可以与电子EDM和SP位移区分开来。MQM效应用质子EDM、QCD真空角$θ$和夸克色EDM表示。
Nuclei with a quadrupole deformation such as $^{177}$Hf have enhanced weak quadrupole moment which induces the tensor weak electron-nucleus interaction in atoms and molecules. Corresponding parity non-conserving (PNC) effect is strongly enhanced in the $^3Δ_1$ electronic state of the $^{177}$HfF$^+$ cation which has very close opposite parity levels mixed by this tensor interaction. In the present paper we perform relativistic many-body calculations of this PNC effect. It is shown that the tensor weak interaction induced by the weak quadrupole moment gives the dominating contribution to the PN…
Updated constraints on $\mathcal{T}$,$\mathcal{P}$-violating axionlike-particle-mediated electron-electron and electron-nucleus interactions from HfF$^+$ experiment
Experiments with paramagnetic ground or metastable excited states of molecules (ThO, HfF$^+$, YbF, YbOH, BaF, PbO, etc.) provide strong constraints on electron electric dipole moment (EDM) and coupling constant $C_{SP}$ of contact semileptonic interaction. We compute new contributions to $C_{SP}$ arising from the nucleon EDMs due to combined electric and magnetic electron-nucleon interaction. This allows us to improve limits from the experiments with paramagnetic molecules on the $CP$-violating parameters, such as the proton EDM, $|d_p|< 1.1\times 10^{-23} e\cdot $cm, the QCD vacuum angle, $|\…
We use our recent electric dipole moment (EDM) measurement data to constrain the possibility that the HfF$^+$ EDM oscillates in time due to interactions with candidate dark matter axion-like particles (ALPs). We employ a Bayesian analysis method which accounts for both the look-elsewhere effect and the uncertainties associated with stochastic density fluctuations in the ALP field. We find no evidence of an oscillating EDM over a range spanning from 27 nHz to 400 mHz, and we use this result to constrain the ALP-gluon coupling over the mass range $10^{-22}-10^{-15}$ eV. This is the first laborat…
We demonstrate a spin-precession method to observe and analyze multi-level coherence between all hyperfine levels in the $X ^2Σ^+,N=0$ ground state of barium monofluoride ($^{138}$Ba$^{19}$F). The signal is sensitive to the state-preparation Rabi frequency and external electric and magnetic fields applied in searches for a permanent electric dipole moment (EDM). In the obtained interference spectrum, the electric field and Rabi frequency become observable simultaneously with the EDM. This method reduces systematic biases and the number of auxiliary measurements for such precision measurements.
TaN molecule as a candidate to search for New physics
结果表明，TaN分子是寻找T，P-破坏的核磁四极矩（MQM）的最佳候选者，它也有希望寻找其他T，P-奇效应。本文报道了Ta核MQM、电子电偶极矩（EDM）、标量$-$和赝标量核$-$电子相互作用产生的T，P奇效应，以及分子轴超精细结构常数和偶极矩的耦合簇计算结果。用T，P奇核力强度常数、质子和中子EDM、QCD参数$θ$和夸克色模EDM对$^{181}$ Ta MQM进行了核计算，以表达T，P奇效应.
Permanent electric dipole moments (EDMs) of fundamental particles such as the electron are signatures of parity and time-reversal violation due to 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. But better measurement techniques, that are not limited by the magnetic field sensitivity of such molecules, are necessary before these opportunities can be fully exploited. We pre…
Statistics and systematics of electron EDM searches with BaF
Nikhef, National Institute for Subatomic Physics（尼赫夫国家亚原子物理研究所）；Department of Physics and Astronomy, LaserLaB, Vrije Universiteit（自由大学物理与天文学系激光实验室）；Institute for Theoretical Physics, University of Amsterdam（阿姆斯特丹大学理论物理研究所）
The current best upper limit for electron electric dipole moment (EDM), $|d_e|<1.1\times10^{-29}\,$e$\cdot$cm ($90$% confidence), was set by the ACME collaboration in 2018. The ACME experiment uses a spin-precession measurement in a cold beam of ThO molecules to detect $d_e$. An improvement in statistical uncertainty would be possible with more efficient use of molecules from the cryogenic buffer gas beam source. Here, we demonstrate electrostatic focusing of the ThO beam with a hexapole lens. This results in a factor of $16$ enhancement in the molecular flux detectable downstream, in a beamli…
CP-violating interaction of the nuclear magnetic quadrupole moment (MQM) with electrons in the ytterbium mono-hydroxide molecule, $^{173}$YbOH, is considered. Both the magnetic quadrupole moment (MQM) of the $^{173}$Yb nucleus and the molecular interaction constant WM are estimated. Electron correlation effects are taken into account within the relativistic Fock-space coupled cluster method. Results are interpreted in terms of the strength constants of CP-violating nuclear forces, neutron EDM, QCD vacuum angle $θ$, quark EDM and chromo-EDM.
The prospects for a new search for the electron electric dipole moment in solid Gadolinium iron garnet ceramics
我们解决了一些问题，固态电子电偶极矩（EDM）的实验，专注于钆铁石榴石（简称GdIG，化学式Gd $_3$ Fe $_5$ O $_{12}$）作为可能的样品材料。GdIG保持其高磁化率低至4.2 K，这增强了置于电场中的样品的EDM诱导磁化。我们估计晶格极化率产生的EDM增强因子约为20。我们还计算了各种样品的几何形状和磁导率的退磁场的效果。固有的GdIG磁化噪声的测量，和波动耗散定理是用来比较我们的数据与GdIG磁导率的虚部在4.2 K的测量，显示出良好的协议以上的频率的几个赫兹。我们还观察到退磁场如何抑制噪声引起的磁通量，证实了我们的计算。基于固体GdIG样品的EDM搜索的统计灵敏度估计与目前的实验极限处于同一水平。考虑到所涉及的完全不同的方法和系统，这种测量是有价值的。在这样的实验中最重要的系统是磁滞和磁电效应。我们的分析表明，在统计敏感性水平上控制这些是可能的。
在当前最佳极限|d_e| < 1.05 e-27 e cm的几个数量级内测量电子的非零电偶极矩（EDM）将是物理学超出标准模型的指示。ACME合作正在寻找一种电子EDM，通过使用缓慢的低温束在一氧化钍（ThO）的亚稳态H状态下进行电子自旋进动的精确测量。我们讨论了实验的现状。基于在2天的时间内从14小时的运行时间获得的数据集，我们已经实现了1-sigma统计不确定性为1 e-28 e cm/T^（1/2），其中T是以天为单位的运行时间。
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…
The relativistic coupled-cluster (RCC) method is a powerful many-body method, particularly in the evaluation of electronic wave functions of heavy atoms and molecules, and can be used to calculate various atomic and molecular properties. One such atomic property is the enhancement factor (R) of the atomic electric dipole moment (EDM) due to an electron EDM needed in electron EDM searches. The EDM of the electron is a sensitive probe of CP-violation, and its search could provide insights into new physics beyond the Standard Model, as well as open questions in cosmology. Electron EDM searches us…
The present constraint on the space parity ($\mathcal{P}$) and time reflection invariance ($\mathcal{T}$) violating electron electric dipole moment ($e$EDM) is based on the observation of the electron spin precession in an external electric field using the ThO molecule. We propose an alternative approach: observation of the $\mathcal{P}$,~$\mathcal{T}$-odd Faraday effect in an external electric field using the cavity-enhanced polarimetric scheme in combination with a molecular beam crossing the cavity. Our theoretical simulation of the proposed experiment with the PbF and ThO molecular beams s…
Experiments searching for the electric dipole moment (EDM) of the electron $d_e$ utilise atomic/molecular states with one or more uncompensated electron spins, and these paramagnetic systems have recently achieved remarkable sensitivity to $d_e$. If the source of $CP$ violation resides entirely in the hadronic sector, the two-photon exchange processes between electrons and the nucleus induce $CP$-odd semileptonic interactions, parametrised by the Wilson coefficient $C_{SP}$, and provide the dominant source of EDMs in paramagnetic systems instead of $d_e$. We evaluate the $C_{SP}$ coefficients …
The CP-violating interaction of the nuclear magnetic quadrupole moment (MQM) of the $^{175}$Lu nucleus with electrons in the molecular cation LuOH$^+$ is studied. The resulting effect is expressed in terms of CP-odd parameters, such as quantum chromodynamics angle $\barθ$, quark electric dipole moment (EDM) and chromo-EDM. For this we have performed a calculation of the nuclear MQM as well as the molecular constant that characterises the interaction of this MQM of $^{175}$Lu with electrons. Additionally, we predict the hyperfine structure constants for the ground electronic state of LuOH$^+$. …
Proposed search for an electric-dipole moment using laser-cooled $^{171}$Yb atoms
我们提出了一个实验，寻找一个永久的原子电偶极矩（EDM）使用激光冷却的$^{171}$ Yb原子发射在原子喷泉。用均匀B场作为量子化轴，用Ramsey分离振荡场方法测量原子的塞曼旋进频率。适当偏振的激光束用于在给定的磁性子级中进行制备和检测。EDM的签名是与大E场的应用相关的拉姆齐共振的偏移。精度预计将至少比目前的限制好20倍，因为冷原子束的使用允许应用比蒸汽室大10倍的E场，并且与E场的相互作用时间比热束大200倍。电子束实验中系统误差的主要来源，（E x v/c）运动磁场，由于通过E场区域的上下轨迹之间的速度几乎完全反转而大大减少。
