Using special capacitors three experiments to search for a permanent electric dipole moment (EDM) of Cesium atom were completed. The electric susceptibility xe of Cs vapor varies in direct proportion to the density N, where xe =70 when N=7.37*1022 m-3! The relationship between xe of Cs vapor and the absolute temperatures T is xe =B/T, where the slope B=320(k) as polar molecules H2O(B=1.50(k)). Its capacitance C at different voltage V was measured. The C-V curve shows that the saturation polarization of Cs vapor has be observed when the field E=7.4*104V/m. Our measurements give the EDM of an Cs atom : dCs=2.97*10-29 C.m=1.86*10-8 e.cm. New example of CP (charge conjugation and parity) violation occurred in Cs atoms. Our results are easy to be repeated because the details of the experiment are described in the article.
We observe that when an ultracold ground state cesium (Cs) atom becomes bound within the electronic cloud of an extended Cs electronic orbit, ultralong-range molecules with giant (kilo-Debye) permanent electric dipole moments form. Large molecular permanent electric dipole moments are challenging to experimentally realize. Meeting this challenge has garnered significant interest because permanent electric dipole moments are important for understanding symmetry breaking in molecular physics, control of chemical reactions and realization of strongly correlated many-body quantum systems. These ne…
A research on a possibility of trapping a particle with permanent electric dipole in an electrostatic field has been conducted. For cylindrical coaxial electrodes, Keplerian orbits for some particles were revealed. The exact criterion of successful trapping on a closed orbit within the electrodes is expressed in dimensionless parameters. For more complicated cases where the exact solution is unknown, a useful tool for numerical solution -- local field map interpolation with continuous first derivatives -- is constructed.
Recently we demonstrated the formation of ultracold polar LiCs molecules in deeply bound levels of the X1S+ ground state, including the rovibrational ground state [J. Deiglmayr et al., Phys. Rev. Lett. 101, 133004 (2008)]. Here we report on the first experimental determination of the permanent electric dipole moment of deeply bound LiCs molecules. For X1S+,v"=2 and v"=3 we measure values of mu=5.5(2) Debye and 5.3(2) Debye respectively.
The ground-state permanent dipole moments (PDMs) and molecular dipole polarizabilities (DPs) of open-shell alkaline-earth monofluorides, and atomic DPs of alkaline-earth- and fluorine atoms are reported at the Kramers-restricted configuration interaction level of theory limited to single- and double excitations (KRCISD), using the finite-field approach. Sufficiently large basis sets such as quadruple-zeta (QZ) and augmented-QZ basis sets together with the generalized active space technique is employed to carry out the field dependent energy calculations at the KRCISD level. The PDMs and the co…
We find that two-color fields can induce field-free permanent dipoles in initially isotropic samples of chiral molecules via resonant electronic excitation in a one-$3ω$-photon vs. three-$ω$-photons scheme. These permanent dipoles are enantiosensitive and can be controlled via the relative phase between the two colors. When the two colors are linearly polarized perpendicular to each other, the interference between the two pathways induces excitation sensitive to the molecular handedness and orientation, leading to uniaxial orientation of the excited molecules and to an enantio-sensitive perman…
The interplay of the relativistic and correlation effects in the permanent electric dipole moments (PDMs) of the X2Σ+ (ν = 0) electronic ground states of the alkaline earth monoflourides (BeF, MgF, CaF, SrF and BaF) has been studied using a relativistic coupled cluster method (RCCM). The calculations were carried out using double, triple and quadruple zeta basis sets, and with no core orbitals frozen. The results are compared with those of other calculations available in the literature and with experiments. The correlation trends in the PDMs of these molecules are discussed in detail.
We report the results of a new experimental search for a permanent electric dipole moment of 199Hg utilizing a stack of four vapor cells. We find d(199Hg) = (0.49 \pm 1.29_stat \pm 0.76_syst) x 10^{-29} e cm, and interpret this as a new upper bound, |d(199Hg)| < 3.1 x 10^{-29} e cm (95% C.L.). This result improves our previous 199Hg limit by a factor of 7, and can be used to set new constraints on CP violation in physics beyond the standard model.
Longitudinal Zeeman slowers composed of arrays of compact discrete neodymium magnets are proposed. The general properties of these slowers, as well as specific designs of short spin-flip Zeeman slowers for Sr and Rb atoms are described. The advantages of these slowers are their simplicity, low cost and absence of consumed electrical power and corresponding water cooling. The smoothness of the magnetic field together with ease of adjustability makes it possible to operate these slowers near the theoretical limits of deceleration, making them more compact and efficient.
The permanent electric dipole moment of the X 2 Σ+ electronic ground state of the strontium monofluoride molecule is calculated using a relativistic coupled cluster method. Our result is compared with those of other calculations and that of experiment. Individual contributions arising from different physical effects are presented. The result obtained suggests that the relativistic coupled cluster method used in the present work is capable of yielding accurate results for the permanent electric dipole moments of molecules for which relativistic effects cannot be ignored.
We propose indium (In) as a possible candidate for observing the permanent electric dipole moment (EDM) arising from the violations of parity (P) and time-reversal (T) symmetries. This atom has been laser cooled and therefore the measurement of its EDM has the potential of improving on the current best EDM limit for a paramagnetic atom which comes from thallium. We report the results of our calculations of the EDM enhancement factor due to the electron EDM and the ratio of the atomic EDM to the electron-nucleus scalar-pseudoscalar (S-PS) interaction coupling constant in In in the framework of …
Searches for permanent electric dipole moments (EDMs) of fundamental particles render the possibility to discover New Physics beyond present Standard Theory. New ideas for experiments have come up recently which may allow to lower present limits substantially or even find unambiguous effects. Such are predicted by a variety of speculative models. The identification of potential sources for CP and T-violation will require to study several systems, which all have different sensitivity to possible mechanisms generating EDMs.
We report on a new measurement of the CP-violating permanent Electric Dipole Moment (EDM) of the neutral $^{129}$Xe atom. Our experimental approach is based on the detection of the free precession of co-located nuclear spin-polarized $^3$He and $^{129}$Xe samples. The EDM measurement sensitivity benefits strongly from long spin coherence times of several hours achieved in diluted gases and homogeneous weak magnetic fields of about 400~nT. A finite EDM is indicated by a change in the precession frequency, as an electric field is periodically reversed with respect to the magnetic guiding field. …
This paper describes the results of the most recent measurement of the permanent electric dipole moment (EDM) of neutral $^{199}$Hg atoms. Fused silica vapor cells containing enriched $^{199}$Hg are arranged in a stack in a common magnetic field. Optical pumping is used to spin-polarize the atoms orthogonal to the applied magnetic field, and the Faraday rotation of near-resonant light is observed to determine an electric-field-induced perturbation to the Larmor precession frequency. Our results for this frequency shift are consistent with zero; we find the corresponding $^{199}$Hg EDM $d_{Hg} …
We present the first results of a new search for a permanent electric dipole moment of the ^{199}Hg atom using a UV laser. Our measurements give d(Hg)= - (1.06 +/- 0.49 +/- 0.40) 10^{-28} e cm. We interpret the result as an upper limit |d(Hg)| < 2.1 10^{-28} e cm (95% C.L.), which sets new constraints on theta_{QCD}, chromo-EDMs of the quarks, and CP violation in Supersymmetric models.
The influence of large permanent dipoles on molecular orbital tomography via high-order harmonic generation (HHG) is investigated in this work. It is found that, owing to the modification of the angle-dependent ionization rate resulting from the Stark shift, the one-side-recollision condition for the tomographic imaging can not be satisfied even with the few-cycle driving pulses. To overcome this problem, we employ a tailored driving pulse by adding a weak low-frequency pulse to the few-cycle laser pulse to control the HHG process and the recollision of the continuum electrons are effectively …
Quantum mechanics thinks that all atoms do not have permanent electric dipole moment (EDM) because of their spherical symmetry. Therefore, there is no polar atom in nature except for polar molecules. The electric susceptibility Xe caused by the orientation of polar substances is inversely proportional to the absolute temperature T while the induced susceptibility of atoms is temperature independent. Using special capacitors our experiments discovered that directional motion of Rb atoms in a non-uniform electric field and ground state Rb atom is polar atom with a large EDM: d(Rb) =2.72*10-29C.m…
We report results of a new technique to measure the electric dipole moment of $^{129}$Xe with $^3$He comagnetometry. Both species are polarized using spin-exchange optical pumping, transferred to a measurement cell, and transported into a magnetically shielded room, where SQUID magnetometers detect free precession in applied electric and magnetic fields. The result from a one week measurement campaign in 2017 and a 2.5 week campaign in 2018, combined with detailed study of systematic effects, is $d_A(^{129}\mathrm{Xe}) = (1.4 \pm 6.6_\mathrm{stat} \pm 2.0_\mathrm{syst})\times10^{-28}~e\,\mathr…
Using special capacitors our experiments discovered that the ground state K, Rb or Cs atom is polar atom with a large permanent electric dipole moment (EDM) of the order of eao (ao is Bohr radius) as excited state of hydrogen atom. But we can not calculate the EDM of an atom using Boltzmann constant. The mechanism of polar atoms by which orientation polarization arises completely differs from polar molecules. The orientation polarization of polar molecule, such as HCl or H2O etc, is a molecule as a whole turned toward the direction of an external field. Unlike polar molecules, the orientation …
Quantum mechanics thinks that atoms do not have permanent electric dipole moment (EDM) because of their spherical symmetry. Therefore, there is no polar atom in nature except for polar molecules. The electric susceptibility Xe caused by the orientation of polar substances is inversely proportional to the absolute temperature T while the induced susceptibility of atoms is temperature independent. This difference in temperature dependence offers a means of separating the polar and non-polar substances experimentally. Using special capacitor our experiments discovered that the relationship betwee…
We give a derivation for the indirect interaction between two magnetic dipoles induced by the quantized electromagnetic field. It turns out that the interaction between permanent dipoles directly returns to the classical form; the interaction between transition dipoles does not directly return to the classical result, yet returns in the short-distance limit. In a finite volume, the field modes are highly discrete, and both the permanent and transition dipole-dipole interactions are changed. For transition dipoles, the changing mechanism is similar with the Purcell effect, since only a few numb…
We show that combined permanent and induced electric dipole interactions of polar and polarizable molecules with collinear electric fields lead to a sui generis topology of the corresponding Stark energy surfaces and of other observables - such as alignment and orientation cosines - in the plane spanned by the permanent and induced dipole interaction parameters. We find that the loci of the intersections of the surfaces can be traced analytically and that the eigenstates as well as the number of their intersections can be characterized by a single integer index. The value of the index, distinc…
Searches for permanent electric-dipole moments (EDM) of atoms provide important constraints on competing extensions to the standard model of elementary particles. Recently proposed experiment with liquid $^{129}$Xe [M.V. Romalis and M.P. Ledbetter, Phys. Rev. Lett. \textbf{87}, 067601 (2001)] may significantly improve present limits on the EDMs. To interpret experimental data in terms of CP-violating sources, one must relate measured atomic EDM to various model interactions via electronic-structure calculations. Here we study density dependence of atomic EDMs. The analysis is carried out in th…
In this work the inhomogeneous (zero-phonon line) and homogeneous line widths, and one projection of the permanent electric dipole moment change for the Ce 4f-5d transition in Y_2SiO_5 were measured in order to investigate the possibility for using Ce as a sensor to detect the hyperfine state of a spatially close-lying Pr or Eu ion. The experiments were carried out on Ce doped or Ce-Pr co-doped single Y_2SiO_5 crystals. The homogeneous line width was measured to be about 3 MHz, which is essentially limited by the excited state lifetime. Based on the line width measurements, the oscillator stre…
We describe a new technique to measure the EDM of $^{129}$Xe with $^3$He comagnetometry. Both species are polarized using spin-exchange optical pumping, transferred to a measurement cell, and transported into a magnetically shielded room, where SQUID magnetometers detect free precession in applied electric and magnetic fields. The result of a one week run combined with a detailed study of systematic effects is $d_A(^{129}\mathrm{Xe}) = (0.26 \pm 2.33_\mathrm{stat} \pm 0.72_\mathrm{syst})\times10^{-27}~e\,\mathrm{cm}$. This corresponds to an upper limit of $|d_A(^{129}\mathrm{Xe})| < 4.81\times…
The parity of atomic wave functions prevents neutral atoms from having permanent electric-dipole moment. Electric-dipole moment is induced in an atom when exposed to strong light, the electric field of the light. Hence the optical trapping of neutral atoms relies on the induced dipole moment. Here we present the calculated numerical values of the detuning, potential depth, minimum laser power required to trap $^{87}$Rb ($D_2$ line) atoms using lasers of wavelength 1064 nm, 850 nm, 820 nm and 800 nm and beam waists 50$μ$m, 100$μ$m and 200$μ$m.
The classical theory of electrodynamics is built upon Maxwell's equations and the concepts of electromagnetic field, force, energy and momentum, which are intimately tied together by Poynting's theorem and the Lorentz force law. Whereas Maxwell's macroscopic equations relate the electric and magnetic fields to their material sources (i.e., charge, current, polarization and magnetization), Poynting's theorem governs the flow of electromagnetic energy and its exchange between fields and material media, while the Lorentz law regulates the back-and-forth transfer of momentum between the media and …
We report calculations of Born-Oppenheimer potential energy curves of the chromium-rubidium heteronuclear molecule 52Cr-87Rb, and the long-range dispersion coefficient for the interaction between ground state Cr and Rb atoms. Our calculated van der Waals coefficient (C6=1770 a.u.) has an expected error of 3%. The ground state 6Sigma+ molecule at its equilibrium separation has a permanent electric dipole moment of de (Re=3.34 A) = 2.90 D. We investigate the hyperfine and dipolar collisions between trapped Cr and Rb atoms, finding elastic to inelastic cross section ratio of 100-1000.
Rydberg-atom ensembles are switched from a weakly- into a strongly-interacting regime via adiabatic transformation of the atoms from an approximately non-polar into a highly dipolar quantum state. The resultant electric dipole-dipole forces are probed using a device akin to a field ion microscope. Ion imaging and pair-correlation analysis reveal the kinetics of the interacting atoms. Dumbbell-shaped pair correlation images demonstrate the anisotropy of the binary dipolar force. The dipolar $C_3$ coefficient, derived from the time dependence of the images, agrees with the value calculated from …
Trapped diatomic molecular ions could prove to be a sensitive probe for a permanent electron electric dipole moment (eEDM). We propose to use a ground or metastable $^3Δ_1$ level, due to its high polarizability and large EDM enhancement factor. Ions allow for simple trapping and long interrogation times, but require a time-varying electric bias field in order to probe the eEDM. We discuss experimental design as well as challenges in performing a precision spectroscopic measurement in rapidly time-varying electric fields.
We study the quantum properties of Rydberg atoms in a magnetic Ioffe-Pritchard trap which is superimposed by a homogeneous electric field. Trapped Rydberg atoms can be created in long-lived electronic states exhibiting a permanent electric dipole moment of several hundred Debye. The resulting dipole-dipole interaction in conjunction with the radial confinement is demonstrated to give rise to an effectively one-dimensional ultracold Rydberg gas with a macroscopic interparticle distance. We derive analytical expressions for the electric dipole moment and the critical linear density of Rydberg at…
Heavy polar diatomic molecules are the primary tools for searching for the T-violating permanent electric dipole moment of the electron (eEDM). Valence electrons in some molecules experience extremely large effective electric fields due to relativistic interactions. These large effective electric fields are crucial to the success of polar-molecule-based eEDM search experiments. Here we report on the results of relativistic ab initio calculations of the effective electric fields in a series of molecules that are highly sensitive to an eEDM, the mercury monohalides (HgF, HgCl, HgBr,and HgI). We …
We calculate the potential energy curves, the permanent dipole moment curves, and the lifetimes of the ground and excited vibrational states of the heteronuclear alkali dimers XY (X, Y = Li, Na, K, Rb, Cs) in the X1Σ+ electronic state using the coupled cluster with singles doubles and triples (CCSDT) method. All-electron quadruple-ζ basis sets with additional core functions are used for Li and Na, and small-core relativistic effective core potentials with quadruple-ζ quality basis sets are used for K, Rb and Cs. The inclusion of the coupled cluster non-perturbative triple excitations is shown …
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.
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 review current status of the study of parity and time invariance phenomena in atoms, nuclei and molecules. We focus on three 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 (EDM) of atoms and molecules which are caused by either, electron EDM or nuclear $T,P$-odd moments such as nuclear EDM and nuclear Schiff moment.
A new potential energy surface for the electronic ground state of the simplest triatomic anion H3- is determined for a large number of geometries. Its accuracy is improved at short and large distances compared to previous studies. The permanent dipole moment surface of the state is also computed for the first time. Nine vibrational levels of H3- and fourteen levels of D3- are obtained, bound by at most ~70 cm^{-1} and ~ 126 cm^{-1} respectively. These results should guide the spectroscopic search of the H3- ion in cold gases (below 100K) of molecular hydrogen in the presence of H3- ions.
We present models for a heteronuclear diatomic molecular ion in a linear Paul trap in a rigid-rotor approximation, one purely classical, the other where the center-of-mass motion is treated classically while rotational motion is quantized. We study the rotational dynamics and their influence on the motion of the center-of-mass, in the presence of the coupling between the permanent dipole moment of the ion and the trapping electric field. We show that the presence of the permanent dipole moment affects the trajectory of the ion, and that it departs from the Mathieu equation solution found for a…
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…
The electric dipole moment of atomic $^{199}$Hg induced by the nuclear Schiff moment and tensor-pseudotensor electron-nucleus interactions has been calculated. For this, we have developed and employed a novel method based on the relativistic coupled-cluster theory. The results of our theoretical calculations combined with the latest experimental result of $^{199}$Hg electric dipole moment, provide new bounds on the T reversal or CP violation parameters $θ_{\rm QCD}$, the tensor-pseudotensor coupling constant $C_T$ and $(\widetilde{d}_u - \widetilde{d}_d)$. This is the most accurate calculation…
Heteronuclear alkali-metal dimers represent the class of molecules of choice for creating samples of ultracold molecules exhibiting an intrinsic large permanent electric dipole moment. Among them, the KCs molecule, with a permanent dipole moment of 1.92~Debye still remains to be observed in ultracold conditions. Based on spectroscopic studies available in the literature completed by accurate quantum chemistry calculations, we propose several optical coherent schemes to create ultracold bosonic and fermionic KCs molecules in their absolute rovibrational ground level, starting from a weakly boun…
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 …
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…
