Atomic Parity Nonconservation 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.

Investigation on the Cs 6S1/2 to 7D electric quadrupole transition via monochromatic two-photon process at 767 nm

We experimentally demonstrate the cesium electric quadrupole transition from the 6S1/2 ground state to the 7D3/2,5/2 excited state through a virtual level by using a single laser at 767 nm. The excited state energy level population is characterized by varying the laser power, the temperature of the vapor, and the polarization combinations of the laser beams. The optimized experimental parameters are obtained for a high resolution transition interval identification. The magnetic dipole coupling constant A and electric quadrupole coupling constant B for the 7D3/2,5/2 states are precisely determined by using the hyperfine levels intervals. The results, A = 7.39 (0.06) MHz, B = −0.19 (0.18) MHz for the 7D3/2 state, and A = −1.79 (0.05) MHz, B =1.05 (0.29) MHz for the 7D5/2 state, are in good agreement with the previous reported results. This work is beneficial for the determination of atomic structure information and parity non-conservation, which paves the way for the field of precision measurements and atomic physics.

Analysis of an Optical Lattice Methodology for Detection of Atomic Parity Nonconservation

We present an extension and a deepened analysis of a suggested experimental scheme for detecting atomic parity violation, previously published in Phys. Rev. A 2019, 100, 050101. The experimental concept is described in more detail and we compute new ab initio data necessary for assessing the plausibility of the approach. Original theoretical data for transition matrix elements on the electric dipole forbidden transition in caesium 6 s 2 S 1 / 2 – 5 d 2 D 3 / 2 are reported, as are a range of electric dipole matrix elements connected to the ground state 6s. The latter is used for an analysis of the wavelength-dependent light shift in Cs. A range of experimental details is presented, combined with a survey of realistic lasers parameters. These are adopted to project the feasibility of the scheme to eventually be capable of delivering data beyond the standard model of particle physics.

Determination of the Scalar and Vector Polarizabilities of the Cesium 6s^{2}S_{1/2}→7s^{2}S_{1/2} Transition and Implications for Atomic Parity Nonconservation.

Using recent high-precision measurements of electric dipole matrix elements of atomic cesium, we make an improved determination of the scalar (α) and vector (β) polarizabilities of the cesium 6s^{2}S_{1/2}→7s^{2}S_{1/2} transition calculated through a sum-over-states method. We report values of α=-268.82(30)a_{0}^{3} and β=27.139(42)a_{0}^{3} with the highest precision to date. We find a discrepancy between our value of β and the past preferred value, resulting in a significant shift in the value of the weak charge Q_{w} of the cesium nucleus. Future work to resolve the differences in the polarizability will be critical for interpretation of parity nonconservation measurements in cesium, which have implications for physics beyond the standard model.

Measurement of the radial matrix elements for the 6sS1/22→7pPJ2 transitions in cesium

We report measurements of the electric dipole matrix elements of the $^{133}$Cs $\ $ $6s\,^2S_{1/2} \rightarrow 7p\,^2P_{1/2}$ and $6s\,^2S_{1/2} \rightarrow 7p\,^2P_{3/2}$ transitions. Each of these determinations is based on direct, precise comparisons of the absorption coefficients between two absorption lines. For the $\langle 6s\,^2S_{1/2}||r|| 7p\,^2P_{3/2} \rangle$ matrix element, we measure the ratio of the absorption coefficient on this line with that of the D$_1$ transition, $6s\,^2S_{1/2} \rightarrow 6p\,^2P_{1/2}$. The matrix element of the D$_1$ line has been determined with high precision previously by many groups. For the $\langle 6s\,^2S_{1/2}||r|| 7p\,^2P_{1/2} \rangle$ matrix element, we measure the ratio of the absorption coefficient on this line with that of the $6s\,^2S_{1/2} \rightarrow 7p\,^2P_{3/2}$ transition. Our results for these matrix elements are $\langle 6s\,^2S_{1/2}||r|| 7p\,^2P_{3/2} \rangle = 0.57417 \: (57)~a_0$ and $\langle 6s\,^2S_{1/2}||r|| 7p\,^2P_{1/2} \rangle = 0.27810 \: (45)~a_0$. These measurements have implications for the interpretation of parity nonconservation in atoms.

Probing Low-Mass Vector Bosons with Parity Nonconservation and Nuclear Anapole Moment Measurements in Atoms and Molecules.

In the presence of P-violating interactions, the exchange of vector bosons between electrons and nucleons induces parity-nonconserving (PNC) effects in atoms and molecules, while the exchange of vector bosons between nucleons induces anapole moments of nuclei. We perform calculations of such vector-mediated PNC effects in Cs, Ba^{+}, Yb, Tl, Fr, and Ra^{+} using the same relativistic many-body approaches as in earlier calculations of standard-model PNC effects, but with the long-range operator of the weak interaction. We calculate nuclear anapole moments due to vector-boson exchange using a simple nuclear model. From measured and predicted (within the standard model) values for the PNC amplitudes in Cs, Yb, and Tl, as well as the nuclear anapole moment of ^{133}Cs, we constrain the P-violating vector-pseudovector nucleon-electron and nucleon-proton interactions mediated by a generic vector boson of arbitrary mass. Our limits improve on existing bounds from other experiments by many orders of magnitude over a very large range of vector-boson masses.

Effect of nuclear quadrupole moments on parity nonconservation in atoms

Nuclei with spin $I \ge 1$ have a weak quadrupole moment which leads to tensor contribution to the parity non-conserving interaction between nuclei and electrons. We calculate this contribution for Yb$^+$, Fr and Ra$^+$ and found it to be small. In contrast, in many lanthanides (e.g., Nd, Gd, Dy, Ho, Er, Pr, Sm) and Ra close levels of opposite parity lead to strong enhancement of the effect making it sufficiently large to be measured. Another possibility is to measure the PNC transitions between the hyperfine components of the ground state of Bi. Since nuclear weak charge is dominated by neutrons this opens a way of measuring quadrupole moments of neutron distribution in nuclei.

Magic and tune-out wavelengths for atomic francium

The frequency dependent polarizabilities of the francium atom are calculated from the available data of energy levels and transition rates. Magic wavelengths for the state insensitive optical dipole trapping are identified from the calculated light shifts of the $7s~^2S_{1/2}$, $7p~^2P_{1/2, 3/2}$ and $8s~^{2}S_{1/2}$ levels of the $7s~^{2}S_{1/2}-7p~^{2}P_{1/2,3/2}$ and $7s~^{2}S_{1/2}-8s~^{2}S_{1/2}$ transitions, respectively. Wavelengths in the ultraviolet, visible and near infrared region is identified that are suitable for cooling and trapping. Magic wavelengths between 600-700~nm and 700-1000~nm region, which are blue and red detuned with the $7s-7p$ and $7s-8s$ transitions are feasible to implement as lasers with sufficient power are available. In addition, we calculated the tune-out wavelengths where the ac polarizability of the ground $7s~^{2}S_{1/2}$ state in francium is zero. These results are beneficial as laser cooled and trapped francium has been in use for fundamental symmetry investigations like searches for an electron permanent electric dipole moment in an atom and for atomic parity non-conservation.

Measurement of the magnetic dipole hyperfine constant Ahfs of cesium 7S1/2 state

Hyperfine-structure (HFS) of atoms results from the interactions between the nuclear magnetic dipole moment and the magnetic field generated by the electrons (related to the magnetic dipole hyperfine constant Ahfs), and between the nuclear electric quadrupole moment and the electric field gradient due to the distribution of charge within atoms (related to the electric quadrupole hyperfine constant Bhfs), so the accurate measurement of HFS is of interest in many fields, including atomic parity nonconservation, tests of fundamental physics, electron-nucleus interaction, and high resolution spectrum and so on. Generally, in order to obtain the atomic spectra, the frequency of laser needs to be scanned over the hyperfine transitions of atoms, so the nonlinear effect from the laser frequency scanning often limits the measurement accuracy of hyperfine splitting. In this paper, we solve this problem, and demonstrate a novel method to measure the hyperfine splitting of atoms. Taking cesium (Cs) for example, based on the Cs 6S1/2-6P3/2-7S1/2 (852.3 nm + 1469.9 nm) ladder-type atomic system, three sets of optical-optical double resonance (OODR) spectra are obtained in a room-temperature vapor cell, when the 852.3 nm laser is tuned to the 6S1/2 (F=4)-6P3/2 (F'=4) resonant transition, and the carriers of 1469.9 nm probe laser accompanied with1 sidebands from a phase-type electro-optical modulator (EOM) are scanned over the whole 6P3/2-7S1/2 hyperfine transitions. Owing to the Doppler effect, some of the hyperfine transitions in these three sets of OODR spectra overlap with the narrowest linewidth only when the frequency of the signal driving EOM equals the value of hyperfine splitting 7S1/2 state. Using this phenomenon which can effectively avoid the nonlinear influence on the measurement during the frequency scanning process of 1469.9 nm laser, we measure the hyperfine splitting of 7S1/2 state to be (2183.720.23) MHz, and the magnetic dipole hyperfine constant Ahfs to be (545.930.06) MHz, which are consistent with previously reported experimental results. This technique provides a robust and simple method of measuring hyperfine splitting with a high precision, which is significant to provide the useful information about atomic structure for developing a more accurate theoretical model describing the interaction within an atom.

Noise-immune cavity-enhanced optical heterodyne molecular spectrometry on N₂O 1.283 μm transition based on a quantum-dot external-cavity diode laser.

To access the wavelength within the 1.1-1.3 μm region, we have developed a quantum-dot (QD) laser with an external-cavity configuration and a linewidth of kilohertz at a 1 ms integration time. The residual electroluminescence, due to the inhomogeneous broadening of the QD gain medium, was observed and filtered out using a grating. While a fiber-coupled electro-optical modulator was employed, this laser system was locked to a high-finesse (F∼18,500) optical cavity, and noise-immune cavity-enhanced optical heterodyne molecular spectroscopy was used to observe weak transitions. The Doppler-broadened spectra of a weak N(2)O transition at 1.283 μm are obtained with a signal-to-noise ratio of 30 for a gas pressure of 54 mTorr. The minimum noise-equivalent absorption coefficient is 5.3×10(-10) cm(-1) Hz(-1/2). This system can be a powerful and stable light source for atomic parity nonconservation measurements using thallium, ytterbium, lead, and iodine.

Francium trapping at the INFN-LNL facility

A brief review of the Francium trapping experiments at the INFN-LNL facility is presented in the wide context of Atomic Parity-Nonconservation (APNC), which, as long as acquiring more precise and new spectroscopic data on the Francium isotopes, is the ultimate goal of the experiment. Due to its instability, Francium atoms must be produced continuously by a nuclear fusion–evaporation reaction into a heated Gold target hit by a beam of accelerated oxygen ions. Francium is then extracted in the ionic form and guided by an electrostatic line to the actual science chamber, where the ions are neutralized. Atoms are then cooled down and trapped in a Magneto-Optical Trap (MOT) to ensure both the availability of a sufficiently populated and stable atomic sample and to eliminate the Doppler broadening which would affect the precision of the measurements. A review of the recent improvements to the experimental apparatus and to the detection techniques that led to a sensitivity better than five atoms is presented. The final part of this paper deals with a summary of the recent results obtained by our collaboration and a short outlook for the immediate future.

Commissioning of the Francium Trapping Facility at TRIUMF

We report on the successful commissioning of the Francium Trapping Facility at TRIUMF. Large laser-cooled samples of francium are produced from a francium ion beam delivered by the ISAC radioactive ion beam facility. The ion beam is neutralized on an yttrium foil, which is subsequently heated to transfer the atoms into the magneto-optical trapping region. We have successfully trapped 207Fr, 209Fr and 221Fr, with a maximum of 2.5 × 105 209Fr atoms. The neutral cold atoms will be used in studies of the weak interaction through measurements of atomic parity non-conservation.

The Francium Trapping Facility at TRIUMF

The study of weak interactions in atoms started soon after the discovery of parity nonconservation PNC [1]. Its small size remained a challenge, but the Bouchiats [2] recognized that in an appropriate interference experiment the size of the effect of atomic parity noncon servation (APNC) scales faster than Z3, with Z the atomic number. This strong scaling has made possible not only to observe PNC effects in atoms, but to measure weak interaction coupling constants, at very low energies.

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.

Quantum electrodynamics corrections to energies, transition amplitudes, and parity nonconservation in Rb, Cs, Ba+, Tl, Fr, and Ra+

We use the previously developed radiative potential method to calculate quantum electrodynamic (QED) corrections to energy levels and electric dipole transition amplitudes for atoms which are used for the study of the parity nonconservation (PNC) in atoms. The QED shift in energies and dipole amplitudes leads to noticeable change in the PNC amplitudes. This study compliments the previously considered QED corrections to the weak matrix elements. We demonstrate that the QED corrections due to the change in energies and dipole matrix elements are comparable in value to those due to the change in weak matrix elements and therefore must be included.

Parity-nonconservation effects on the radiative recombination of heavy hydrogenlike ions

Based on the theoretical analysis of the radiative recombination of heavy hydrogen-like ions with unpolarized electrons, a scheme is proposed for observing atomic parity nonconservation (PNC). The scheme employs the sensitivity of the polarization properties of recombination photons on the PNC-induced mixing of opposite-parity ionic levels. For the electron capture into the $1s2p\phantom{\rule{0.16em}{0ex}}{}^{3}{P}_{0}$ state of helium-like ions, in particular, the PNC leads to a rotation of the photon linear polarization on the angle, directly proportional to the $1s2p\phantom{\rule{0.16em}{0ex}}{}^{3}{P}_{0}$--$1s2s\phantom{\rule{0.16em}{0ex}}{}^{1}{S}_{0}$ mixing parameter. Owing to the recent advances in the development of x-ray polarimeters, the observation of such a rotation angle and, hence, the corresponding parity mixing is likely to become feasible in the future.

Atomic parity non-conservation: the francium anapole project of the FrPNC collaboration at TRIUMF

We present a method for measuring the nuclear anapole in a string of francium isotopes. The anapole is a parity non-conserving electromagnetic moment that enables parity-forbidden transitions between ground state hyperfine levels of an atom. The experiment is run by the FrPNC collaboration and relies on a beam of artificially-produced francium from the ISAC facility at TRIUMF.

Fundamental Symmetries and Conservation Laws

I discuss recent progress in low-energy tests of symmetries and conservation laws, including parity nonconservation in atoms and nuclei, electric dipole moment tests of time-reversal invariance, β-decay correlation studies, and decays violating separate (family) and total lepton number.

Polarized atoms in a far-off-resonance yttrium-aluminum-garnet-laser optical dipole trap

Optical trapping of radioactive atoms has a great potential in precision measurements for testing fundamental physics such as electric-dipole moment, atomic parity nonconservation, and parity-violating $\ensuremath{\beta}$-decay correlation coefficients. One challenge that remains is to polarize the atoms to a high degree, and to measure the polarization of the sample and its evolution over time. In this paper we report on the polarization study of Rb atoms in a yttrium-aluminum-garnet (YAG)-laser optical dipole trap using both Faraday rotation polarimetry and resolved Zeeman spectroscopy techniques. We have prepared a cold cloud of polarized atoms and observed that its spin relaxation due to light scattering is suppressed in the YAG dipole trap. The spin polarization is further purified and maintained when the two-body collision loss rate between atoms in mixed spin states is greater than the one-body trap loss. These advancements are an important step toward a new generation of precision measurement with polarized trapped atoms.

Calculations of the neutron skin and its effect in atomic parity violation

We perform calculations for the neutron skin of nuclei and its contribution to atomic parity nonconservation (PNC) in many isotopes of Cs, Ba, Sm, Dy, Yb, Tl, Pb, Bi, Fr, and Ra. Three problems are addressed: (i) neutron-skin-induced errors to single-isotope PNC, (ii) the possibility of measuring neutron skin using atomic PNC, and (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 cancellations of the errors; this makes the isotopic ratio method a competitive tool in a search for new physics beyond the standard model.