Electric and Magnetic Field Control for Electric Dipole Moment Searches

Permanent Electric Dipole Moments (EDMs) would violate the symmetries of parity and time-reversal, and with validity of CPT symmetry they would also violate the combined CP symmetry. EDMs have been suggested in many speculative extensions to the Standard Model of particle physics. The purpose of the NL-eEDM experiment is to search for a permanent electron Electric Dipole Moment (eEDM). The experiment entails a BaF molecular beam moving through an interaction zone with a homogeneous electric and a homogeneous magnetic field. A non-zero eEDM would reveal itself in a different spin precession behavior for parallel and anti-parallel electric and magnetic fields.The emphasis of this work lies on the design, implementation, evaluation and use of the interaction zone for this new experiment. The design is informed by calculations with COMSOL software. The implementation consists of Indium Tin Oxide (ITO) coated glass plates for homogeneous electric field generation at several kV/cm scale. A homogeneous magnetic field of O(nT) is realized by a novel designed double cosine coil, which resides in a 5 layer µ-metal shield with O(10^6) shielding surrounded by rectangular compensation coils.This work in combination with work on a BaF source, laser systems, a quantum mechanical description of the measurement process, data acquisition and analysis provides the first complete eEDM setup at the VSI in Groningen. Measurements have been performed with spin precession on BaF molecules in order to quantify the capabilities of the setup. These show that the setup of the interaction zone suffices for a competitive eEDM search

Precision Tests of Discrete Symmetries at Low Energies

Low energy precision measurements provide for precise testing of the Standard Model, e.g., in searches for violations of the discrete symmetries charge conjugation (C), parity (P), and time reversal (T) as well as their combinations CP and CPT. We focus here on new experiments concerning atomic parity violation (APV) and searches for a permanent electric dipole moment (EDM) in atoms. In particular, we address precision APV experiments on Ba+ and Ra+ single ions that will enable the extraction of the Weinberg angle at lowest presently accessible momentum transfer. They are expected to contribute towards searches for new particles such as dark Z-bosons. We also review experimental programmes in which an EDM is searched for and we compare them in a common framework. We describe latest EDM searches in heavy effective two-electron atoms such as Xe and Hg. We also indicate possible future prospects of searches for a permanent EDM of the electron using molecules with large enhancement factors

High accuracy theoretical investigations of CaF, SrF, and BaF and implications for laser-cooling

The NL-eEDM collaboration is building an experimental setup to search for the permanent electric dipole moment of the electron in a slow beam of cold barium fluoride molecules [Eur. Phys. J. D, 72, 197 (2018)]. Knowledge of molecular properties of BaF is thus needed to plan the measurements and in particular to determine an optimal laser-cooling scheme. Accurate and reliable theoretical predictions of these properties require incorporation of both high-order correlation and relativistic effects in the calculations. In this work theoretical investigations of the ground and the lowest excited states of BaF and its lighter homologues, CaF and SrF, are carried out in the framework of the relativistic Fock-space coupled cluster (FSCC) and multireference configuration interaction (MRCI) methods. Using the calculated molecular properties, we determine the Franck-Condon factors (FCFs) for the $A^2\Pi_{1/2} \rightarrow X^2\Sigma^{+}_{1/2}$ transition, which was successfully used for cooling CaF and SrF and is now considered for BaF. For all three species, the FCFs are found to be highly diagonal. Calculations are also performed for the $B^2\Sigma^{+}_{1/2} \rightarrow X^2\Sigma^{+}_{1/2}$ transition recently exploited for laser-cooling of CaF; it is shown that this transition is not suitable for laser-cooling of BaF, due to the non-diagonal nature of the FCFs in this system. Special attention is given to the properties of the $A'^2\Delta$ state, which in the case of BaF causes a leak channel, in contrast to CaF and SrF species where this state is energetically above the excited states used in laser-cooling. We also present the dipole moments of the ground and the excited states of the three molecules and the transition dipole moments (TDMs) between the different states.Comment: Minor changes; The following article has been submitted to the Journal of Chemical Physics. After it is published, it will be found at https://publishing.aip.org/resources/librarians/products/journals

Systematic study and uncertainty evaluation of P, T-odd molecular enhancement factors in BaF

A measurement of the magnitude of the electric dipole moment of the electron (eEDM) larger than that predicted by the Standard Model (SM) of particle physics is expected to have a huge impact on the search for physics beyond the SM. Polar diatomic molecules containing heavy elements experience enhanced sensitivity to parity (P) and time-reversal (T)-violating phenomena, such as the eEDM and the scalar-pseudoscalar (S-PS) interaction between the nucleons and the electrons, and are thus promising candidates for measurements. The NL-eEDM collaboration is preparing an experiment to measure the eEDM and S-PS interaction in a slow beam of cold BaF molecules [P. Aggarwal et al., Eur. Phys. J. D 72, 197 (2018)]. Accurate knowledge of the electronic structure parameters, Wd and Ws, connecting the eEDM and the S-PS interaction to the measurable energy shifts is crucial for the interpretation of these measurements. In this work, we use the finite field relativistic coupled cluster approach to calculate the Wd and Ws parameters in the ground state of the BaF molecule. Special attention was paid to providing a reliable theoretical uncertainty estimate based on investigations of the basis set, electron correlation, relativistic effects, and geometry. Our recommended values of the two parameters, including conservative uncertainty estimates, are 3.13 ±0.12×1024Hzecm for Wd and 8.29 ± 0.12 kHz for W

Narrow linewidth diode lasers for narrow Ba+ ion transitions

Precision measurements on atomic parity violation (APV) can be conducted using narrow optical transitions in the Ba+ ion. Narrow linewidth lasers are essential for the success of such experiments. For this purpose we use a Pound-Drever-Hall locking scheme for stabilizing the frequency of a diode laser to a Fabry Perot cavity. An importan role plays the electronics employed for fast feedback. We have explored two viable, a FET controlled fast current bypass and a bias-T configuration. Laser frequency drifts at slow time scales are compensated by stabilizing an optical using light from an optical frequency comb. The laser linewidth could be reduced to 10 kHz, which is sufficient to measure APV