Parity Nonconservation Experiments Research Articles

Studies of the weak interaction in atomic systems: towards measurements of atomic parity non-conservation in francium

Tests of the standard model of particle physics should be carried out over the widest possible range of energies. Here we present our plans and progress for an atomic parity non-conservation experiment using the heaviest alkali, francium (Z = 87), which has no stable isotope. Low-energy tests of this kind have sensitivity complementary to higher energy searches, e.g. at the large hadron collider.

Interaction between single frequency two photon and one photon transitions in a V system

In this experimental work we address the issue of interaction between non-resonant two photon absorption (5S1/2→ 5D5/2) and a resonant one photon transition (5S1/2→5P3/2) in a Doppler broadened medium of hot Rubidium atoms under the V type coupling scheme 5D5/2← 5S1/2→5P3/2. For a particular Rb isotope, suppression of one and two photon absorptions (sharing same ground state hyperfine component) are observed. At the same time increment in two photon absorption for the same isotope involving other ground state hyperfine component is noticed. The two photon transition is studied by monitoring the blue fluorescence emitted in 5D5/2→6P3/2→ 5S1/2 spontaneous decay route. The recorded blue light is the measure of population in 5D state; thus indicating the relative strength of absorption. Transparency observed in this case is due to coupling field saturation and quantum interference. The even parity-odd parity (dipole forbidden–dipole allowed) V type linkage exhibits presence of coherent control under three level configuration. Our studies may find application in optical communication, negative energy study and indirectly to parity non-conservation experiments, where S→S transitions are used.

Efficient inter-trap transfer of cold francium atoms

We report on the status of the FrPNC experiments and summarize our plans for measurements of parity non-conservation (PNC) in a sample of cold francium. The FrPNC collaboration has commissioned a laser cooling apparatus at the TRIUMF accelerator that collects and cools francium atoms for PNC experiments. We have recently demonstrated the robust, high efficiency transfer (50 %) of laser cooled francium atoms to a second laser cooling apparatus, located 0.7 m below the first, where the PNC experiments will be conducted.

Measurements of the ground-state polarizabilities of Cs, Rb, and K using atom interferometry

We measured the ground-state static electric-dipole polarizabilities of Cs, Rb, and K atoms using a three-nanograting Mach-Zehnder atom beam interferometer. Our measurements provide benchmark tests for atomic structure calculations and thus test the underlying theory used to interpret atomic parity non-conservation experiments. We measured $\alpha_{\mathrm{Cs}} = 4\pi\epsilon_0 \times 59.45(11) \AA^3$, $\alpha_{\mathrm{Rb}} = 4\pi\epsilon_0 \times 47.44(9) \AA^3$, and $\alpha_{\mathrm{K}} = 4\pi\epsilon_0 \times 42.97(8) \AA^3$. In atomic units, these measurements are $\alpha_{\mathrm{Cs}} = 401.2(7)$, $\alpha_{\mathrm{Rb}} = 320.1(6)$, and $\alpha_{\mathrm{K}} = 290.0(5)$. We report ratios of polarizabilities $\alpha_{\mathrm{Cs}}/\alpha_{\mathrm{Rb}} = 1.2532(10)$, $\alpha_{\mathrm{Cs}}/\alpha_{\mathrm{K}} = 1.3835(9)$, and $\alpha_{\mathrm{Rb}}/\alpha_{\mathrm{K}} = 1.1040(9)$ with smaller fractional uncertainty because the systematic errors for individual measurements are largely correlated. Since Cs atom beams have short de Broglie wavelengths, we developed measurement methods that do not require resolved atom diffraction. Specifically, we used phase choppers to measure atomic beam velocity distributions, and we used electric field gradients to give the atom interference pattern a phase shift that depends on atomic polarizability.

Precision measurement of branching fractions ofBa138+: Testing many-body theories below the 1% level

The branching fractions from the excited state $6P_{1/2}$ of singly charged barium ion has been measured with a precision $0.05%$ in an ion trap experiment. This measurement along with the known value of the upper state life-time allowed the determination of the dipole matrix elements for the transitions $P-S$ and $P-D$ to below one percent level. Therefore, for the first time it is now possible to compare the many body calculations of these matrix elements at level which is of significance to any parity non-conservation experiment on barium ion. Moreover, these dipole matrix elements are the most significant contributors to the parity violating matrix element between the $S-D$ transition, contributing upto $90%$ to the total. Our results on the dipole matrix elements are $3.306\pm0.014$ and $3.036\pm0.016$ for the $S-P$ and $P-D$ transitions respectively.

Parity-violating interactions of cosmic fields with atoms, molecules, and nuclei: Concepts and calculations for laboratory searches and extracting limits

We propose methods and present calculations that can be used to search for evidence of cosmic fields by investigating the parity-violating effects, including parity nonconservation amplitudes and electric dipole moments, that they induce in atoms. The results are used to constrain important fundamental parameters describing the strength of the interaction of various cosmic fields with electrons, protons, and neutrons. Candidates for such fields are dark matter (including axions) and dark energy, as well as several more exotic sources described by standard-model extensions. Existing parity nonconservation experiments in Cs, Dy, Yb, and Tl are combined with our calculations to directly place limits on the interaction strength between the temporal component, b_0, of a static pseudovector cosmic field and the atomic electrons, with the most stringent limit of |b_0^e| < 7*10^(-15) GeV, in the laboratory frame of reference, coming from Dy. From a measurement of the nuclear anapole moment of Cs, and a limit on its value for Tl, we also extract limits on the interaction strength between the temporal component of this cosmic field, as well as a related tensor cosmic-field component d_00, with protons and neutrons. The most stringent limits of |b_0^p| < 4*10^(-8) GeV and |d_00^p| < 5*10^(-8) for protons, and |b_0^n| < 2*10^(-7) GeV and |d_00^n| < 2*10^(-7) for neutrons (in the laboratory frame) come from the results using Cs. Axions may induce oscillating P- and T-violating effects in atoms and molecules through the generation of oscillating nuclear magnetic quadrupole and Schiff moments, which arise from P- and T-odd intranuclear forces and from the electric dipole moments of constituent nucleons. Nuclear-spin-independent parity nonconservation effects may be enhanced in diatomic molecules possessing close pairs of opposite-parity levels in the presence of time-dependent interactions.

Method for measuring the6S1/2↔5D3/2magnetic-dipole-transition moment in Ba+

We propose a method for measuring the magnetic dipole ($M1$) transition moment of the $6{S}_{1/2}(m=\ensuremath{-}1/2)\ensuremath{\leftrightarrow}5{D}_{3/2}(m=\ensuremath{-}1/2)$ transition in single trapped Ba${}^{+}$ by exploiting different symmetries in the electric quadrupole ($E2$) and $M1$ couplings between the states. The technique is adapted from a previously proposed method for measuring atomic parity nonconservation in a single trapped ion [N. Fortson, Phys. Rev. Lett. 70, 2383 (1993)]. Knowledge of $M1$ is crucial for any parity nonconservation measurement in Ba${}^{+}$, as laser coupling through $M1$ can mimic the parity-violating signal. The magnetic moment for the transition has been calculated by atomic theory and found to be dominated by electron-electron correlation effects [B. K. Sahoo et al., Phys. Rev. A 74, 062504 (2006)]. To date the value has not been verified experimentally. This proposed measurement is therefore an essential step toward a parity nonconservation experiment in the ion that will also test current many-body theory. The technique can be adapted for similar parity nonconservation experiments using other atomic ions, where the magnetic dipole moment could present similar complications.

Single frequency 1070 nm Nd:GdVO_4 laser using a volume Bragg grating

We demonstrate a single frequency diode-pumped Nd:GdVO(4) laser at 1070 nm using a volume Bragg grating as the output coupler of a short plano-concave cavity. The TEM(00) output had a maximum power of 300 mW and a linewidth less than 23 MHz. The beam propagation parameter M2 and the divergence angle at 200 mW were 1.2 and 0.37°, respectively. The single frequency tuning range was 5.1 GHz at 100 mW. Upon locking the laser frequency to a confocal reference cavity, a relative stability of 7.58 kHz was achieved. If frequency doubled, such as using a periodically-poled lithium niobate (PPLN) crystal, this laser offers an excellent light source for parity non-conservation experiments of atomic thallium.

Isotopic tuning of the 2 3P0−2 1S0 and 2 3P1−2 1S0 transition energies in He-like ions for future parity-nonconservation experiments

Crossings of opposite-parity levels in He-like ions for particular values of the atomic number Z offer excellent conditions for precise experimental tests of parity-nonconservation (PNC). Such tests may be performed by inducing, through intense lasers, transitions that are only allowed in presence of PNC. Several spectroscopy experiments have been proposed in the past, but only now, with the advent of high-intensity laser facilities (e.g. PHELIX at GSI or POLARIS at Jena), their feasibility is within reach. In this paper, we use relativistic many-body perturbation theory (RMBPT) to calculate accurately the crossing conditions of the excited levels (1s2s) 1S0 and (1s2p) 3P0 and of (1s2s) 1S0 and (1s2p) 3P1 in intermediate and heavy He-like ions. Moreover, we show the dependence of the energy splittings upon the choice of the nuclear isotope.

Nuclear structure effects in parity non-conservation in heavy ions

We calculate the binding energy, charge radii in 129Ba-143Ba and 214Ra-228Ra 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 these isotopes 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 nonconservation experiments and atomic structure calculations on Ba+ and Ra+.

Relativistic configuration-interaction study of the nuclear-spin-dependent parity-nonconserving electron-nucleus interaction constantWAin BaF

A fully relativistic restricted active space configuration-interaction method is employed to compute the $P$-odd electron-nucleus interaction constant ${W}_{\text{A}}$ for the ground $({^{2}\ensuremath{\Sigma}}_{1/2})$ state of BaF, which yields the result of ${W}_{\text{A}}=160\text{ }\text{Hz}$. Our present estimated result of the $P$-odd interaction constant ${W}_{\text{A}}$ is in reasonable agreement with previous calculations. This result will be useful for the interpretation of the nuclear-spin-dependent parity-nonconservation experiment on BaF.

Systematic studies of properties of nuclei by parity violating electron scattering

Two investigations by the parity violating electron scattering are performed theoretically: one is to investigate the properties of the surface for neutron-rich nuclei such as $^{124}\mathrm{Sn}$ and $^{208}\mathrm{Pb}$, and the other is to predict the parity violating asymmetries for some isotopic chains, such as Ba and Pb, which have been proposed for the atomic parity nonconservation experiments. For the first topic, the neutron and proton densities are taken to be the 2pF distributions. Results show that the parity violating asymmetries are very sensitive to the type of neutron density. It means that the parity violating electron scattering can be used to verify the type of neutron distribution in neutron-rich stable nuclei. For the second topic, the neutron and proton densities are obtained from the relativistic mean-field (RMF) theory. By combining the results for these two topics, we find that for various proton and neutron densities the amplitudes of the parity violating asymmetries correspond to the distances between the minima of the proton and neutron form factors. Our results can provide useful references for future experiments.

Relativistic Coupled-Cluster Theory of Atomic Parity Nonconservation: Application toBa+137

We report the result of our ab initio calculation of the 6s2S1/2-->5d2D3/2 parity nonconserving electric dipole transition amplitude in 137Ba+ based on relativistic coupled-cluster theory. Considering single, double, and partial triple excitations, we have achieved an accuracy of less than 1%. 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 nonaccelerator test of the standard model of particle physics.

Parity violation in astrophysics

Core collapse supernovae are gigantic explosions of massive stars that radiate 99% of their energy in neutrinos. This provides a unique opportunity for large scale parity or charge conjugation violation. Parity violation in a strong magnetic field could lead to an asymmetry in the neutrino radiation and recoil of the newly formed neutron star. Charge conjugation violation in the neutrino-nucleon interaction reduces the ratio of neutrons to protons in the neutrino driven wind above the neutron star. This is a problem for r-process nucleosynthesis in this wind. On earth, parity violation is an excellent probe of neutrons because the weak charge of a neutron is much larger than that of a proton. The Parity Radius Experiment (PREX) at Jefferson Laboratory aims to precisely measure the neutron radius of $^{208}$Pb with parity violating elastic electron scattering. This has many implications for astrophysics, including the structure of neutron stars, and for atomic parity nonconservation experiments.}

Radio frequency spectroscopy with a trapped Ba+ ion: recent progress andprospects for measuring parity violation

We have employed the method of shelving to measure Zeeman resonances of asingle trapped Ba+ ion in low magnetic fields, and have observed radio frequencytransitions with linewidths of 5 Hz, limited by magnetic-field noise. We have alsoobserved the shift in the Zeeman frequency when the ion is illuminated byoff-resonant light. A simultaneous measurement of such light shifts in two atomicstates of Ba+ will permit a precise determination of the ratio of transition matrixelements. Furthermore, using this method with an ion in a standing lightwave, aproposed parity nonconservation (PNC) measurement with Ba+ or Ra+could be realized. In this paper we review methods and the status of theseexperiments and discuss the remaining challenges of the PNC experiment.

Estimate of contribution from p–d mixing in atomic PNC

We investigate possible contributions to future atomic parity nonconservation (PNC) experiments from parity admixtures between single-electron atomic states with total angular momentum j=3/2. We develop new formalism for studying these admixtures between atomic p and d states, which enter only when finite nuclear size effects are considered and have been neglected in the literature to date. We use analytic approximations to provide an order-of-magnitude estimate of the contribution from these admixtures, and identify a dimensionless ratio which sets the scale of the correction. Using realistic numerical wavefunctions in Ba+ we confirm the results of our analytic expressions, and conclude quantitatively that these novel admixtures are likely to be negligible in essentially all cases.

Measurement of the forbidden6s21S0→5d6s3D1magnetic-dipole transition amplitude in atomic ytterbium

We report on a measurement of a highly forbidden magnetic-dipole transition amplitude in ytterbium using the Stark-interference technique. This amplitude is important in interpreting a future parity nonconservation experiment that exploits the same transition. We find $|〈{5d6s}^{3}{D}_{1}|M1|{6s}^{21}{S}_{0}〉|{=1.33(6)}_{\mathrm{Stat}}{(20)}_{\ensuremath{\beta}}\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}4}{\ensuremath{\mu}}_{0},$ where the larger uncertainty comes from the previously measured vector transition polarizability $\ensuremath{\beta}.$ The $M1$ amplitude is small and should not limit the precision of the parity nonconservation experiment.

Neutron density distributions for atomic parity nonconservation experiments

Nuclear structure corrections to the weak charge in atomic parity nonconservation (PNC) experiments are analyzed. Measurement of PNC effects along an isotope chain might represent a useful method to circumvent the present atomic theory uncertainty in tests of the Standard model of electroweak interactions. Neutron distributions of Cs, Ba, Yb and Pb isotopes are calculated with the relativistic Hartree-Bogoliubov model, and the uncertainty of the calculated isotope shifts of neutron radii is analyzed.

Neutron density distributions for atomic parity nonconservation experiments

The neutron distributions of Cs, Ba, Yb and Pb isotopes are described in the framework of relativistic mean-field theory. The self-consistent ground state proton and neutron density distributions are calculated with the relativistic Hartree-Bogoliubov model. The binding energies, the proton and neutron radii, and the quadrupole deformations are compared with available experimental data, as well as with recent theoretical studies of the nuclear structure corrections to the weak charge in atomic parity nonconservation experiments.

Effects of neutron spatial distributions on atomic parity nonconservation in cesium

We have examined modifications to the nuclear weak charge due to small differences between the spatial distributions of neutrons and protons in the Cs nucleus. We derive approximate formulae to estimate the value and uncertainty of this modification based only on nuclear rms neutron and proton radii. Present uncertainties in neutron distributions in Cs are difficult to quantify, but we conclude that they should not be neglected when using atomic parity nonconservation experiments as a means to test the Standard Model.