The atomic parity non-conservation(PNC) experiments has reached accuracies which have important implications for physics beyond the standard model. An optical rotation experiment to measure the atomic PNC of the 3P1(6s6p)--1P1(6s6p) in Yb was proposed recently. Our screened electron-electron coulomb potential multi-configuration Dirac-Fock calculation of th PNC induced E1 transition amplitude of this transition E1_PNC = -96.0 x 10^{-11}iea_0(-Q_W/N) of 171Yb is more than two orders of magnitude larger than E1_PNC(6s-7s) = -0.8991 x 10^{-11}iea_0(-Q_W/N) of 133Cs.
The connections between the Random Phase Approximation (RPA) and Many-Body Perturbation Theory (MBPT) and its all order generalisation, the Coupled- Cluster Theory (CCT) have been explored. Explicit expressions have been derived for the electric dipole amplitudes for allowed and forbidden transitions induced by the parity non-conserving neutral weak interaction. The Goldstone diagrams associated with the RPA terms in both cases are shown to arise in MBPT and CCT and the numerical verification of this relationship is made for the allowed electric dipole transitions.
We examine the feasibility of a parity non-conserving (PNC) optical rotation experiment for the $^2$P$_{3/2}\rightarrow ^2$P$_{1/2}$ transition of atomic iodine at 1315 nm. The calculated $E1_{\rm PNC}$ to $M1$ amplitude ratio is $R=0.80(16)\times 10^{-8}$. We show that very large PNC rotations (greater than 10 $μ$rad) are obtained for iodine-atom column densities of $\sim 10^{22}$ cm$^{-2}$, which can be produced by increasing the effective interaction pathlength by a factor of $\sim 10^4$ with a high-finesse optical cavity. The simulated signals indicate that measurement of the nuclear anapo…
As known, electron vacuum polarization by nuclear Coulomb field produces Uehling potential with the range $\hbar/2m_e c$. Similarly, neutrino vacuum polarization by $Z$ boson field produces long range potential $\sim G^2/r^5$ with the large range $\hbar/2m_νc$. Attempts to measure parity-conserving part of this potential produced only limits on this potential which are several orders of magnitude higher than the standard model predictions. We show that parity non-conserving (PNC) part of the neutrino exchange potential $W_L(r)$ gives a significant fraction of the observed PNC effects. Mixed $Z…
We formulate a parity-mixed coupled-cluster (PM-CC) approach for high-precision calculations of parity non-conserving amplitudes in mono-valent atoms. Compared to the conventional formalism which uses parity-proper (PP) one-electron orbitals, the PM-CC method is built using parity-mixed (PM) orbitals. The PM orbitals are obtained by solving the Dirac-Hartree-Fock equation with the electron-nucleus electroweak interaction included (PM-DHF). There are several advantages to such a PM-CC formulation: (i) reduced role of correlations, as for the most experimentally-accurate to date ${}^{133}{\rm Cs…
We use relativistic Hartree-Fock and correlation potential methods to calculate nuclear spin-dependent parity non-conserving amplitudes (dominated by the nuclear anapole moment) between hyperfine structure components of the ground state of odd isotopes of K, Rb, Cs, Ba+, Yb+, Tl, Fr, and Ra+. The results are to be used for interpretation of current and future measurements.
We present a method for measuring nuclear-spin-dependent atomic parity violation without nuclear-spin-independent background. Such measurements can be achieved by observing interference of parity-conserving and parity-violating two-photon J=0-to-1 transitions driven by collinear photons of the same frequency in the presence of an external static magnetic field.
We discuss the possibility of measuring nuclear anapole moments in atomic Zeeman transitions and perform the necessary calculations. Advantages of using Zeeman transitions include variable transition frequencies and the possibility of enhancement of parity nonconservation effects.
Atomic parity violation has been observed in the 6s^2 1S0 - 5d6s 3D1 408-nm forbidden transition of ytterbium. The parity-violating amplitude is found to be two orders of magnitude larger than in cesium, where the most precise experiments to date have been performed. This is in accordance with theoretical predictions and constitutes the largest atomic parity-violating amplitude yet observed. This also opens the way to future measurements of neutron skins and anapole moments by comparing parity-violating amplitudes for various isotopes and hyperfine components of the transition.
We present a method for measuring atomic parity violation in the absence of static external electric and magnetic fields. Such measurements can be achieved by observing the interference of parity conserving and parity violating two-photon transition amplitudes between energy eigenstates of zero electronic angular momentum. General expressions for induced two-photon transition amplitudes are derived. The signal-to-noise ratio of a two-photon scheme using the 6s^2 1S0 to 6s6p 3P0 transition in ytterbium is estimated.
We present calculations of nuclear-spin-dependent and nuclear-spin-independent parity violating amplitudes in Ba, Ra, Ac+, Th and Pa. Parity nonconservation in these systems is greatly enhanced due to the presence of very close electronic energy levels of opposite parity, large nuclear charge, and strong nuclear enhancement of parity-violating effects. The presented amplitudes constitute several of the largest atomic parity-violating signals predicted so far. Experiments using these systems may be performed to determine values for the nuclear anapole moment, a P-odd T-even nuclear moment given…
We calculate the binding energy, charge radii in $^{126}$Ba--$^{140}$Ba and $^{214}$Ra--$^{228}$Ra using the relativistic mean field theory which includes scalar and vector mesons. We then evaluate the nuclear structure corrections to the weak charges for a series of isotopes of these atoms using different parameters and estimate their uncertainty in the framework of this model. Our results will have important implication for the ongoing and planned parity non-conservation experiments and atomic structure calculations on Ba$^+$ and Ra$^+$.
We have calculated parity nonconserving 7s - 6d_{3/2} amplitude E_PNC in 223Ra+ using high-precision relativistic all-order method where all single and double excitations of the Dirac-Fock wave functions are included to all orders of perturbation theory. Detailed study of the uncertainty of the parity nonconserving (PNC) amplitude is carried out; additional calculations are performed to estimate some of the missing correlation corrections. A systematic study of the parity conserving atomic properties, including the calculation of the energies, transition matrix elements, lifetimes, hyperfine c…
Feasibility of extracting the proton weak charge from quantum-control measurements of atomic parity violation on the $2s-3s$ or $2s-4s$ transition in hydrogen
本文提出通过氢的 $2s-3s$ 或 $2s-4s$ 跃迁量子控制方案测量原子宇称破坏，以提取质子弱电荷，应对近期 W 玻色子质量异常，并评估了相关计算近似的准确度。
Studying the violation of parity and time-reversal invariance in atomic systems has proven to be a very effective means for testing the electroweak theory at low energy and searching for physics beyond it. Recent developments in both atomic theory and experimental methods have led to the ability to make extremely precise theoretical calculations and experimental measurements of these effects. Such studies are complementary to direct high-energy searches, and can be performed for just a fraction of the cost. We review the recent progress in the field of parity and time-reversal violation in ato…
We estimate the relative contribution of nuclear structure and new physics couplings to the parity non-conserving spin-independent effects in atomic systems, for both single isotopes and isotopic ratios. General expressions are presented to assess the sensitivity of isotopic ratios to neutron skins and to couplings beyond standard model at tree level. The specific coefficients for these contributions are calculated assuming Fermi distribution for proton and neutron nuclear densities for isotopes of Cs, Ba, Sm, Dy, Yb, Pb, Fr, and Ra. The present work aims to provide a guide to the choice of th…
We discuss the propagation of hydrogen atoms in static electric and magnetic fields in a longitudinal atomic beam spin echo (lABSE) apparatus. Depending on the choice of the external fields the atoms may acquire both dynamical and geometrical quantum mechanical phases. As an example of the former, we show first in-beam spin rotation measurements on atomic hydrogen, which are in excellent agreement with theory. Additional calculations of the behaviour of the metastable 2S states of hydrogen reveal that the geometrical phases may exhibit the signature of parity-(P-)violation. This invites for po…
Atomic Parity Violation provides the rare opportunity of a low energy window into possible new fundamental processes at very high mass scales normally investigated at large high energy accelerators. Precise measurements on atomic systems are currently the most sensitive probes of many kinds of new physics, and complement high energy experiments. Present atomic experiments are beginning to reach their limits of precision due to either sensitivity, systematics or atomic structure uncertainties. An experiment in a single trapped Barium ion can improve on all of these difficulties. This experiment…
We present a detailed description of experimental studies of the parity violation effect in an isotopic chain of atomic ytterbium (Yb), whose results were reported in a recent Letter [Antypas et al., Nat. Phys. 15, 120 (2019)]. We discuss the principle of these measurements, made on the Yb 6s$^2$ $^1$S$_0 \rightarrow $5d6s $^3$D$_1$ optical transition at 408 nm, describe the experimental apparatus, and give a detailed account of our studies of systematic effects in the experiment. Our results offer the first direct observation of the isotopic variation in the atomic parity violation effect, a …
Currently the theoretical uncertainty limits the interpretation of the atomic parity non-conservation (PNC) measurements. We calculate the PNC $5s$ - $6s$ electric dipole transition amplitude in rubidium and demonstrate that rubidium is a good candidate to search for new physics beyond the standard model since accuracy of the atomic calculations in rubidium can be higher than in cesium. PNC in cesium is currently the best low-energy test of the standard model, therefore, similar measurements for rubidium present a good option for further progress in the field. We also calculate nuclear spin-de…
Precision measurements of parity non-conserving (PNC) interactions in atoms, molecules and ions can lead to the discovery of new physics beyond the standard model and understanding of weak-force induced interactions in the nucleus. In this paper, we propose and analyze a novel atomic parity violation measurement scheme for a forbidden transition where we combine a two-pathway coherent control mechanism with probe gain techniques. We detail a feasible experimental geometry for $6S_{1/2}\rightarrow 7S_{1/2}$ transitions in a cesium vapor cell, and consider the statistical noise of such a measure…
We propose using a Stark interference technique to directly measure the odd-parity c_{0j} components of the electron sector c_{μν} tensor of the Standard-Model Extension. This technique has been shown to be a sensitive probe of parity violation in atomic dysprosium in a low-energy, tabletop experiment, and may also be straightforwardly applied to test Lorentz invariance. We estimate that such an experiment may be sensitive to c_{0j} coefficients as small as 10^{-18}.
Recent reanalyses of the atomic physics effects on the weak charge in cesium have led to a value in much closer agreement with predictions of the Standard Model. We review precision electroweak tests, their implications for upper bounds on the mass of the Higgs boson, possible ways in which these bounds may be circumvented, and the requirements placed upon accuracy of future atomic parity violation experiments by these considerations.
We discuss the propagation of hydrogen atoms in static electric and magnetic fields in a longitudinal atomic beam spin echo (lABSE) apparatus. There the atoms acquire geometric (Berry) phases that exhibit a new manifestation of parity-(P-)violation in atomic physics. We provide analytical as well as numerical calculations of the behaviour of the metastable 2S states of hydrogen. The conditions for electromagnetic field configurations that allow for adiabatic evolution of the relevant atomic states are investigated. Our results provide the theoretical basis for the discussion of possible measur…
Recent advances in interpreting the most accurate to-date measurement of atomic parity violation in Cs are reviewed. The inferred nuclear weak charge, Q_W = - 72.65(28)_expt (36)_theor, agrees with the prediction of the standard model at 1 sigma level. Further improved interpretation is limited by an accuracy of solving basic correlation problem of atomic structure. We report on our progress in solving this problem within the relativistic coupled-cluster formalism. We include single-, double- and triple- electronic excitations in the coupled-cluster expansion. Numerical results for energies, e…
In a recent Letter [B. K. Sahoo, B. P. Das, and H. Spiesberger, Phys. Rev. D 103, L111303 (2021)], a calculation of the parity violating 6S-7S E1 amplitude in Cs is reported, claiming an uncertainty of just 0.3%. In this Comment, we point out that key contributions have been omitted, and the theoretical uncertainty has been significantly underestimated. In particular, the contribution of missed QED radiative corrections amounts to several times the claimed uncertainty.
We report on progress towards performing precision measurements of parity violation in Yb, in which the theoretical prediction for a strong weak-interaction-induced effect in the 6s^{2} ^{1}S_{0} \rightarrow 5d6s ^{3}D_{1} optical transition at 408 nm has already been confirmed, with a measurement of the effect at the \approx 10 % level of accuracy. With a new atomic-beam apparatus offering enhanced sensitivity, we are aiming at precisely determining the parity violation observable in Yb, which will allow us to probe the distributions of neutrons in different isotopes, investigate physics beyo…
Single trapped and laser cooled Radium ion as a possible candidate for measuring the parity violation induced frequency shift has been discussed here. Even though the technique to be used is similar to that proposed by Fortson [1], Radium has its own advantages and disadvantages. The most attractive part of Radium ion as compared to that of Barium ion is its mass which comes along with added complexity of instability as well as other issues which are discussed here
We propose a nuclear mechanism which can induce an atomic electric dipole moment (EDM). Parity and time reversal violating (P,T-odd) nuclear forces generate a mixed P,T-odd nuclear polarizability beta_{ik} (defined by an energy shift U = -beta_{ik} E_{i}H_{k}, E is electric field and H magnetic field). The interaction of atomic electrons with beta_{ik} produces an atomic EDM. We performed an analytical calculation of the P,T-odd nuclear polarizability and estimated the value for the induced atomic EDM. The measurements of atomic EDMs can provide information about P,T-odd nuclear forces and tes…
We present the atomic parity violation measurements made in Cs vapour using a pump-probe scheme. After pulsed excitation of the 6S-7S forbidden transition in the presence of a longitudinal electric field, a laser beam resonant with one of the 7S-6P transitions stimulates the 7S atom emission for a duration of 20 ns. The polarisation of the amplified probe beam is analysed. A seven-fold signature allows discrimination of the parity violating linear dichroism, and real-time calibration by a similar, known, parity conserving linear dichroism. The zero-field linear dichroism signal due to the magn…
This is a personal recollection of the time when the search for APV was beginning. In spite of today's remarkable results, summarized here, there are still important goals to be achieved. I indicate a possible way to tackle the remaining experimental challenges, by adapting methods now of frequent use in precision metrology.
We report the result of our {\it ab initio} calculation of the $6s ^2S_{1/2} \to 5d ^2D_{3/2}$ parity nonconserving electric dipole transition amplitude in $^{137}\text{Ba}^+$ based on relativistic coupled-cluster theory. Considering single, double and partial triple excitations, we have achieved an accuracy of less than one percent. If the accuracy of our calculation can be matched by the proposed parity nonconservation experiment in Ba$^+$ for the above transition,then the combination of the two results would provide an independent non accelerator test of the Standard Model of particle physi…
We consider the implication of the recent measurement of the W-boson mass $M_W$ [Science 376, 170 (2022)] for atomic parity violation experiments. We show that the change in $M_W$ shifts the Standard Model prediction for the ${}^{133}$Cs nuclear weak charge to $Q_W({}^{133}{\rm Cs})=-72.85(6)$, i.e. by $5.5σ$ from its current value. This brings existing experimental result for $Q_W({}^{133}{\rm Cs})$ into an essential agreement with the Standard Model. Using our revised value for $Q_W({}^{133}{\rm Cs})$, we readjust constraints on physics beyond the Standard Model.
Anapole moments are parity-odd, time-reversal-even moments of the E1 projection of the electromagnetic current. Although it was recognized, soon after the discovery of parity violation in the weak interaction, that elementary particles and composite systems like nuclei must have anapole moments, it proved difficult to isolate this weak radiative correction. The first successful measurement, an extraction of the nuclear anapole moment of 133Cs from the hyperfine dependence of the atomic parity violation, was obtained only recently. An important anapole moment bound in Tl also exists. We discuss…
We perform calculations for the neutron skin of nuclei and its contribution to atomic parity non-conservation (PNC) in many isotopes of Cs, Ba, Sm, Dy, Yb, Tl, Pb, Bi, Fr, Ra. Three problems are addressed: i) Neutron-skin induced errors to single-isotope PNC, ii) Possibility to measure neutron skin using atomic PNC, iii) Neutron-skin induced errors for ratios of PNC effects in different isotopes. In the latter case the correlations in the neutron skin values for different isotopes lead to cancelations of the errors; this makes the isotopic ratio method a competitive tool in a search for new ph…
The next generation of "intensity frontier" facilities will bring a significant increase in the intensity of sub-relativistic beams of $μ^-$. We show that the use of these beams in combination with thin targets of $Z\sim 30$ elements opens up the possibility of testing parity-violating interactions of muons with nuclei via direct radiative capture of muons into atomic 2S orbitals. Since atomic capture preserves longitudinal muon polarization, the measurement of the gamma ray angular asymmetry in the single photon $2S_{1/2}$-$1S_{1/2}$ transition will offer a direct test of parity. We calculate…
