Parity Nonconserving Optical Rotation Research Articles

Fundamentals of cavity-enhanced polarimetry for parity-nonconserving optical rotation measurements: Application to Xe, Hg, and I

We present the theoretical basis of a cavity-enhanced polarimetric scheme for the measurement of parity-nonconserving (PNC) optical rotation. We discuss the possibility of detecting PNC optical rotation in accessible transitions in metastable Xe and Hg, and ground state I. In particular, the physics of the PNC optical rotation is presented, and we explore the lineshape effects on the expected PNC optical rotation signals. Furthermore, we present an analysis of the eigenpolarizations of the cavity-enhanced polarimeter, which is necessary for understanding the measurement procedure and the ability of employing robust background subtraction procedures using two novel signal reversals. Using recent atomic structure theoretical calculations, we present simulations of the PNC optical rotation signals for all proposed transitions, assuming a range of experimentally feasible parameters. Finally, the possibility of performing sensitive measurements of the nuclear-spin-dependent PNC effects is investigated, for the odd-neutron nuclei $^{129}$Xe and $^{199}$Hg, and the odd-proton nucleus $^{127}$I.

Calculation of parity-nonconserving optical rotation in iodine at 1315 nm

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 $\mu$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 anapole moment is feasible, and that a 1% PNC precision measurement should resolve the inconsistency between previous measurements in Cs and Tl.

Cavity-Enhanced Parity-Nonconserving Optical Rotation in Metastable Xe and Hg

We propose the measurement of cavity-enhanced parity-nonconserving (PNC) optical rotation in several transitions of metastable Xe and Hg, including Xe (2P(3/2)(o))6s(2)[3/2](2)(o)→(2P(1/2)(o))6s(2)[1/2](1)(o) and Hg 6s6p (3)P(2)(o)→6s6p (1)P(1)(o), with calculated amplitude ratios of E(1)(PNC)/M1=11×10(-8) and 10×10(-8), respectively. We demonstrate the use of a high-finesse bow-tie cavity with counterpropagating beams and a longitudinal magnetic field, which allows the absolute measurement of chiral optical rotation, with a path length enhancement of about 10(4), necessary for PNC measurement from available column densities of 10(14) cm(-2) for metastable Xe or Hg. Rapid PNC-signal reversal, allowing robust background subtraction, is achieved by shifting the cavity resonance to an opposite polarization mode or by inverting the magnetic field. The precise measurement of isotope and nuclear-spin dependent E(1)(PNC) amplitudes provides a sensitive low-energy test of the standard model.

Parity-nonconserving optical rotation on the6s6p3P0→6s6p1P1transition in atomic ytterbium

A new scheme to measure parity-nonconserving effects in atomic ytterbium is proposed. This method entails measuring parity-nonconserving optical rotation on the $1.28 \ensuremath{\mu}\mathrm{m} 6s6p{ }^{3}{P}_{0}\ensuremath{\rightarrow}6s6p{}^{1}{P}_{1}$ transition, for which optical rotation per unit absorption length is predicted to be an order of magnitude larger than that for transitions experimentally studied in thallium, lead, and bismuth. In the proposed experiment using a vapor cell filled with buffer gas, the lifetime of the lower metastable $6s6p{ }^{3}{P}_{0}$ state is limited by collisional de-excitation. Atoms are excited to the lower metastable state by, e.g., short $(\ensuremath{\sim}10 \mathrm{ns})$ near-resonant light pulses and spurious optical rotation is subtracted on a pulse by pulse basis. The potential sensitivity of this technique may enable precise measurements of electroweak parameters.

Measurement of the electric quadrupole amplitude within the 1283-nm6P1/2−6P3/2transition in atomic thallium

We have measured the ratio of the electric quadrupole $(E2)$ to magnetic dipole $(M1)$ transition amplitude within the ${6P}_{1/2}\ensuremath{\rightarrow}{6P}_{3/2}$ transition in atomic thallium. Defining $\ensuremath{\chi}$ to be this $E2$ to $M1$ amplitude ratio, we find that $\ensuremath{\chi}=0.2387(10)(38)$, where the first error is statistical and the second represents a combined systematic error. In addition to providing a stringent test of theoretical wave-function calculations in thallium, accurate knowledge of this quantity is essential for existing and future measurements of parity nonconserving optical rotation on this same 1283-nm line in thallium.

A measurement of parity non-conserving optical rotation in atomic lead

We report a measurement of parity non-conserving (PNC) optical rotation in the vicinity of the 1.279 magnetic dipole transition in atomic lead. We obtain a value for the conventional parameter, , with limits on the nuclear spin-dependent contribution set by the anapole constant . The experimental results, when combined with the relevant atomic calculations, lead to a value for the mass of the boson or, alternatively, place a limit on physics beyond the standard model through the isospin-conserving parameter, S.

Manifestation of the nuclear anapole moment in the M1 transitions in bismuth

Results of the ab initio calculation of the parity non-conserving optical rotation caused by the weak charge and the anapole moment of the nucleus are given for the 876 nm and 648 nm transitions in atomic bismuth.

Precise Measurement of Parity Nonconserving Optical Rotation in Atomic Thallium

We report a new measurement of parity nonconserving (PNC) optical rotation on the ${6p}_{1/2}$- ${6p}_{3/2}$ transition in atomic thallium near 1283 nm. The result expressed in terms of the quantity $R\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}\mathrm{Im}{{E1}^{\mathrm{PNC}}/M1}$ is $\ensuremath{-}(15.68\ifmmode\pm\else\textpm\fi{}0.45)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}8}$, and is consistent with current calculations based on the standard model. In addition, limits have been set on the much smaller nuclear spin-dependent rotation amplitude at ${R}_{S}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}(0.04\ifmmode\pm\else\textpm\fi{}0.20)\ifmmode\times\else\texttimes\fi{}1{0}^{\ensuremath{-}8}$; this is consistent with theoretical estimates which include a nuclear anapole contribution.

High-precision measurement of parity nonconserving optical rotation in atomic lead.

We have completed a new measurement of parity nonconserving (PNC) optical rotation near the 1.279 \ensuremath{\mu}m magnetic dipole absorption line in lead, improving earlier results on this line by a factor of 20. We find the ratio of the PNC E1 amplitude to the M1 amplitude to be scrR=(-9.86\ifmmode\pm\else\textpm\fi{}0.12)\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}8}$, consistent with theoretical predictions. Difficulties in the atomic theory of lead presently limit the extent to which our result tests the standard model of electroweak interactions. The amplitude of the nuclear spin-dependent PNC rotation is found to be less than 2\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}2}$ of the nuclear spin-independent rotation.

An experimental search for enhanced parity non-conserving optical rotation in samarium

The authors have made a preliminary study of several allowed M1 transitions within the 4f66s2 ground state configuration of samarium with the aim of observing enhanced parity non-conserving (PNC) optical rotation. No evidence for R=Im(E1)PNC/(M1) greater than 10-6 has been found. They conclude that, although opposite parity states are comparatively close (ca 200 cm-1) in the cases studied, the strength of the admixed E1 transitions is low thereby reducing any potential enhancement. This also complicates any theoretical analysis since there is no single dominant E1 component in the admixture, and in any case calculations of oscillator strengths for samarium with its complicated level structure are notoriously difficult. Finally, the reactivity of metallic samarium poses considerable experimental difficulties in achieving sufficiently high vapour pressures.

Precise measurement of parity nonconserving optical rotation at 876 nm in atomic bismuth.

We report the first precise measurements of parity nonconserving (PNC) optical rotation in atoms, carried out on the 876-nm M1 transition in bismuth. We obtain ${\mathit{R}}_{\mathit{i}}$=Im(E${1}_{\mathrm{PNC}}^{\mathit{i}}$/M1)=(-10.12\ifmmode\pm\else\textpm\fi{}0.20)\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}8}$, where E${1}_{\mathrm{PNC}}^{\mathit{i}}$ is the E1 amplitude mixed into the transition by the nuclear spin-independent PNC interaction. The result is in excellent agreement with the standard model of the electroweak interaction. The amplitude of nuclear spin-dependent PNC rotation is found to be less than 1.5\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}2}$ of that due to the nuclear spin-independent interaction.

On the feasibility of detecting parity non-conserving optical rotation at 639 nm in Sm I

An experimental study has been made of the nearly degenerate, opposite parity states 4f 66s6p 7G1 and 4f 65d6s 7G1 in samarium to assess the feasibility of using the forbidden M1 transition from the 4f 66s 2 7F0 ground state to the 4f 65d6s 7G1 state for measuring parity non-conserving (PNC) effects. The authors conclude that detection of the PNC optical rotation is not feasible because of the high background rotation present at the M1 wavelength and also because the PNC signal itself would be significantly smaller than in existing PNC experiments. Consideration has also been given to the possibility of a novel optical rotation experiment on this transition, using crossed electric and magnetic fields. However, this too is concluded not to be feasible due to the difficulty in achieving a sufficiently large PNC signal. A general comment on the future of rare earth elements for PNC studies is made.

Measurement of parity non-conserving optical rotation in the 648 nm transition in atomic bismuth

Parity non-conserving (PNC) optical rotation has been measured by laser polarimetry in the 648 nm magnetic dipole transition (6p3 J=3/2 to 6p3 J'=5/2) in atomic bismuth. The experiment involves finding the small differences in rotation between selected frequency points in the vicinity of the F=6 to F'=7 hyperfine component. Faraday rotation, which can be distinguished from PNC rotation by its wavelength dependence, is used in locking the laser frequency and calibrating the PNC effect. Results obtained over a six-year period are summarised; a detailed discussion of error sources and associated tests is given. The final result for the PNC parameter of the 648 nm transition is R=(-9.3+or-1.4)*10-8. This is an agreement with the measurements of Birich et al (1984) but not with those of Barkov and Zolotorev (1980). It is also consistent with the standard model of the electroweak interaction, but the uncertainty in the atomic theory is now the limiting factor in the comparison.

Parity-Nonconserving Optical Rotation in Atomic Lead

Etude de la transition dipolaire magnetique 3 P 0 − 3 P 1 a 1,28 μm: assez bon accord de la valeur experimentale de R=Im (E1/M1)=(−9,9±2,5).10 −8 avec la valeur prevue par la theorie de Weinberg-Salam-Glashow

Calculation of parity-nonconserving optical rotation in atomic bismuth

A Dirac-Hartree-Fock potential has been used to evaluate all zeroth- and first-order effects on the parity-nonconserving optical rotation for the 876-nm and 648-nm transitions in Bi. For the 876-nm transition, the zeroth-order result is -9.6\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}8}$ for the ratio $R=\frac{\mathrm{Im}(E1)}{M1}$, and the result after addition of the first-order effect is -7.0\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}8}$. The ratios for the 648-nm transition are -12.8\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}8}$, respectively. To obtain more accurate results, the parity-nonconserving parts of the orbitals were then obtained in a self-consistent procedure by including the weak parity-nonconserving interaction in the one-particle Hamiltonian of the Hartree-Fock equations. Similarly, the electric-dipole functions were modified by taking into account the shielding of the external electric field due to a polarization of the core electrons. Re-evaluation of the first-order diagrams using these functions changes the ratio to $R=\ensuremath{-}8.3\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}8}$ for the 876-nm transition and to $R=\ensuremath{-}11.1\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}8}$ for the 648-nm transition.

Measurement of Parity Nonconservation in Atomic Bismuth

Parity-nonconserving optical rotation has been observed and measured on the 8757-\AA{}A magnetic-dipole absorption line in atomic bismuth vapor. The result, $R\ensuremath{\equiv}\mathrm{Im}(\frac{{E}_{1}}{{M}_{1}})=(\ensuremath{-}10.4\ifmmode\pm\else\textpm\fi{}1.7)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}8}$, is of the approximate size calculated with use of the Weinberg-Salam theory of the weak neutral-current interaction with ${{sin}^{2}\ensuremath{\theta}}_{\mathrm{W}}=0.23$.

Dirac-Hartree-Fock Calculations for Bismuth Including the Parity-Violating Operator in the Potential

The neutral-current induced parity non-conserving optical rotation in Bi has been calculated using a local potential and a Dirac-Hartree-Fock potential giving the values - 18 × 10-8 and - 10 × 10-8, respectively for the ratio R = Im (E1)/M1. When the parity-violating parts of all orbitals were considered in the Dirac-Hartree-Fock calculation, the value - 17 × 10-8 was obtained.

Calculation of Parity-Nonconserving Optical Rotation in Atomic Bismuth

Using results of the Weinberg-Salam model, we have calculated in lowest order the magnitude of the optical rotation parameter $\mathrm{Im}(\frac{E1}{M1})$ in atomic bismuth for the four allowed $M1$ transitions from the ground state within the configuration $6{s}^{2}6{p}^{3}$. Results based on Dirac-Hartree-Fock orbitals are found to vary significantly according to the form used for the electric dipole operator in the $E1$ matrix element. This is interpreted as evidence for large correlation effects.

Atomic shielding and PNC optical rotation in bismuth

It is pointed out that shielding by the outer electrons may significantly reduce the neutral current induced parity non-conserving optical rotation in atomic bismuth. A self-consistent calculation gives a reduction of order 50% in R=Im E1PNC/M1 and leads to values -14*10-8 and -12*10-8 for the 648 nm and 876 nm transitions respectively.

Upper Limit on Parity-Nonconserving Optical Rotation in Atomic Bismuth

We have searched for optical rotation near the 8757-\AA{} magnetic-dipole absorption line in atomic bismuth vapor. The experiment is sensitive to parity nonconservation in the weak neutral-current interaction between electrons and nucleons in atoms. We find $R\ensuremath{\equiv}\mathrm{Im}(\frac{{E}_{1}}{{M}_{1}})=(\ensuremath{-}0.7\ifmmode\pm\else\textpm\fi{}3.2)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}8}$, which is considerably smaller than the value $R=\ensuremath{-}2.5\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}7}$ obtained by central-field calculations for this bismuth line using the Weinberg-Salam theory of neutral currents.