Space-time parity violation and magnetoelectric interactions in antiferromagnets

The properties of antiferromagnetic materials with violated space-time parity are considered. Particular attention is given to the bismuth ferrite BiFeO₃ ferroelectric magnet. This material is distinguished from other antiferromagnets in that the inversion center is absent in its crystal and magnetic structures. This circumstance gives rise to diversified and unusual properties, namely, to the appearance of a spatially modulated spin structure and to the unique possibility of the linear magnetoelectric effect coexisting with a weak ferromagnetic moment. The magnetic-induced phase transitions accompanied by the suppression of the modulated spin structure and appearance of a number of new and unusual effects are considered. These are the linear magnetoelectric effect and the appearance of a toroidal moment and a weak ferromagnetic moment of the magnetoelectric nature.     

Theoretical overview of atomic parity violation

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( ^133Cs ) = - 72.65(28)_expt(36)_theor , agrees with the prediction of the standard model at 1σ level. Further improved interpretation is limited by an accuracy of solving the basic correlation problem of the 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, electric-dipole matrix elements, and hyperfine-structure constants of Cs are presented.     

Radium ion: a candidate for measuring atomic parity violation

Parity Non Conservation (PNC) in atomic systems can be observed in experiments using a single trapped ion and intense laser fields. The original proposal is based on a single barium ion. Here, we study the feasibility for carrying out similar experiment with a single radium ion. Since the PNC effect in atomic system increases faster than the Z ³, where Z is the atomic number, radium is a natural choice. The advantages and disadvantages of measuring atomic parity violation in radium ion are discussed.     

Ra+ ion trapping: toward an atomic parity violation measurement and an optical clock

A single Ra⁺ ion stored in a Paul radio frequency ion trap has excellent potential for a precision measurement of the electroweak mixing angle at low momentum transfer and as the most stable optical clock. The effective transport and cooling of singly charged ions of the isotopes ²⁰⁹Ra to ²¹⁴Ra in a gas filled radio frequency quadrupole device is reported. The absolute frequencies of the transition 7s²S_1/2–7d²D_3/2 at wavelength 828 nm have been determined in ^212–214Ra⁺ with ≤19 MHz uncertainty using laser spectroscopy on small samples of ions trapped in a linear Paul trap at the online facility Trapped Radioactive Isotopes: µicrolaboratories for fundamental Physics (TRIµP) of the Kernfysisch Versneller Instituut.     

Measurements of complex third-order optical susceptibility in a collinear pump-probe experiment

We demonstrate simultaneous measurement of the real and the imaginary parts of third-order susceptibilities by use of a collinear pump-probe technique. This technique allows for good results and simple implementation. The signal analysis is based on the particular oscillatory signature versus the pump-probe delay allowed by the collinear configuration. Results are compared with interferometric measurements of a SF59 (Schott) glass sample.     

Pump-probe measurement of atomic parity violation in cesium with a precision of 2.6%

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 20ns. 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 magnetic dipole transition moment is observed for the first time, and used for in situ determination of the electric field. The result, ImE ₁ ^pv = (- 808±21)×10^-14 ea ₀ , is in perfect agreement with the corresponding, more precise measurement obtained by the Boulder group. A transverse field configuration with large probe amplification could bring atomic parity violation measurements to the 0.1% accuracy level.     

Observation of a parity violation in cesium

We have measured a parity violation in the 6S–7S transition of Cs in an electric field. Our result is Im $\text{E}{}_1{}^{\mathrm{<mtext>pv</mtext>}}\text{β}\text{= -1.34 ± 0.22}$$\text{(}\text{rms statistical deviation}\text{) ± ～0.11 (}\text{systematic uncertainty}\text{)}\text{mV}\text{cm;}\text{E}{}_1{}^{\mathrm{<mtext>pv</mtext>}}$ is the parity violating electric dipole amplitude, ß is the vector polarizability. This result is consistent with the Weinberg-Salam prediction.     

New manifestation of atomic parity violation in cesium: a chiral optical gain induced by linearly polarized 6S-7S excitation

We have detected, by using stimulated emission, an atomic parity violation (APV) in the form of a chiral optical gain of a cesium vapor on the 7S-6P(3/2) transition, consecutive to linearly polarized 6S-7S excitation. We demonstrate the validity of this detection method of APV, by presenting a 9% accurate measurement of expected sign and magnitude. We stress several advantages of this new approach which fully exploits the cylindrical symmetry of the setup. Future measurements at the percent level will provide an important cross-check of an existing more precise result obtained by a different method.     

New observation of a parity violation in cesium

The parity violation induced by weak neutral currents is measured in a ΔF=1 hyperfine component of the 6S–7S transition of the Cs atom. The measured value (statistical rms deviation) ±0.12 (systematic uncertainty) mV/cm, agrees with our previous measurement in a ΔF=0 component, and constitutes an important cross-check. Our result excludes a parity violation induced by a purely axial hadronic neutral current.     

Longitudinal atomic beam spin echo experiments: a possible way to study parity violation in hydrogen

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 possible future lABSE experiments, focusing on P-violating geometrical phases in the lightest of all atoms.     

Atomic parity violation in a single trapped radium ion

Atomic parity violation (APV) experiments are sensitive probes of the electroweak interaction at low energy. These experiments are competitive with and complementary to high-energy collider experiments. The APV signal is strongly enhanced in heavy atoms and it is measurable by exciting suppressed (M1, E2) transitions. The status of APV experiments and theory are reviewed as well as the prospects of an APV experiment using one single trapped Ra^?+? ion. The predicted enhancement factor of the APV effect in Ra^?+? is about 50 times larger than in Cs atoms. However, certain spectroscopic information on Ra^?+? needed to constrain the required atomic many-body theory, was lacking. Using the AGOR cyclotron and the TRI??P facility at KVI in Groningen, short-lived ^212???214Ra^?+? ions were produced and trapped. First ever excited-state laser spectroscopy was performed on the trapped ions. These measurements provide a benchmark for the atomic theory required to extract the electroweak mixing angle to sub-1% accuracy and are an important step towards an APV experiment in a single trapped Ra^?+? ion.     

Search for a parity violation induced by neutral currents in the 6S–7S transition of atomic cesium

Parity violating, time-reversal invariant, weak neutral currents can induce an electric dipole transition moment, E₁^p.v., between atomic states of same parity. We report here on the preliminary results of an experiment designed to measure E₁^p.v. in the 6S–7S transition of atomic cesium, using a polarization effect characteristic of the interference of E₁^p.v. with the electric dipole transition moment E₁^ind. induced by a d.c. electric field. At a 90% confidence level we find the upper limit: |E₁^p.v.| < 2.0 × 10^?9|e|a₀. As a consequence the coupling constant of the electron-nucleon interaction involving the product of an axial electronic neutral current by a vector nucleonic one must be less than 44 G_F.     

Relativistic theory of parity violation in many-electron atoms

We present a theoretical framework for the calculation of parity-mixing effects of the weak interaction in many-electron atoms which is based on first principles. The starting point is an external-field no-pair Hamiltonian H₊ which allows for a consistent treatment of effects coming from virtual electron-positron pairs and can be used as a basis for a systematic program of calculations. We show that the matrix element $\text{M}$ for parity-violating E1 transitions, given by quantum electrodynamics, gets an appreciable contribution $\text{M}$^pair from states involving an extra electron-positron pair. However on eliminating the velocity operator α in favor of the length operator iωr, we find cancellations which result in an accurate formula for $\text{M}$ involving only the positive-energy N-electron eigenstates of H₊ as intermediate states and the length form, iωr · ?, of the dipole operator. We discuss the implications of our results for calculations of amplitudes for parity-violating radiative E1 transitions in many-electron atoms. Our analysis includes a study of the effects coming from the weak electron-electron interaction as well as those arising from the weak electron-nucleus interaction.