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

eEDM sensitive searches with BaF molecules

eEDM sensitive searches form a probe into the Standard Model of particle physics and its extensions. A BaF supersonic beam with a velocity of around 600 m/s, moving in a controlled 10 kV/cm electric field and nT magnetic field, forms an experimental setup for eEDM sensitive searches. The emphasis lies on characterizing and controlling the electric and magnetic fields. Not only of interest are these fields themselves, but in particular (the use of) the sensitivity of the BaF quantum system in such fields. This provides multiple handles on statistical and systematic effects, critical in EDM searches. With this we aim to complete a first measurement step with the supersonic BaF beam in the coming year at a sensitivity level 10^-28 ecm

eEDM sensitive searches with BaF molecules

eEDM sensitive searches form a probe into the Standard Model of particle physics and its extensions. A BaF supersonic beam with a velocity of around 600 m/s, moving in a controlled 10 kV/cm electric field and nT magnetic field, forms an experimental setup for eEDM sensitive searches. The emphasis lies on characterizing and controlling the electric and magnetic fields. Not only of interest are these fields themselves, but in particular (the use of) the sensitivity of the BaF quantum system in such fields. This provides multiple handles on statistical and systematic effects, critical in EDM searches. With this we aim to complete a first measurement step with the supersonic BaF beam in the coming year at a sensitivity level 10^-28 ecm

eEDM sensitive searches with BaF molecules

eEDM sensitive searches form a probe into the Standard Model of particle physics and its extensions. A BaF supersonic beam with a velocity of around 600 m/s, moving in a controlled 10 kV/cm electric field and nT magnetic field, forms an experimental setup for eEDM sensitive searches. The emphasis lies on characterizing and controlling the electric and magnetic fields. Not only of interest are these fields themselves, but in particular (the use of) the sensitivity of the BaF quantum system in such fields. This provides multiple handles on statistical and systematic effects, critical in EDM searches. With this we aim to complete a first measurement step with the supersonic BaF beam in the coming year at a sensitivity level 10^-28 ecm

eEDM sensitive searches with BaF molecules

eEDM sensitive searches form a probe into the Standard Model of particle physics and its extensions. A BaF supersonic beam with a velocity of around 600 m/s, moving in a controlled 10 kV/cm electric field and nT magnetic field, forms an experimental setup for eEDM sensitive searches. The emphasis lies on characterizing and controlling the electric and magnetic fields. Not only of interest are these fields themselves, but in particular (the use of) the sensitivity of the BaF quantum system in such fields. This provides multiple handles on statistical and systematic effects, critical in EDM searches. With this we aim to complete a first measurement step with the supersonic BaF beam in the coming year at a sensitivity level 10^-28 ecm

Interaction Zone for an eEDM measurement with a BaF beam

The measurement of an electron electric dipole moment (eEDM) with high precision using BaF, benefits from fine control over several key parameters. These parameters include a vacuum, lasers and an electric and magnetic field. Measurements employing a BaF supersonic beam, are planned. These measurements, happening in an Interaction Zone, will use a large electric field of 10 kV/cm, and a small magnetic field of order 6 nT, with small field gradients. In addition, control and understanding of molecular states using lasers and spectroscopy are crucial for a successful experiment. This poster discusses how to reach an electromagnetic field in the Interaction Zone, useful for an eEDM measurement

Interaction Zone for an eEDM measurement with a BaF beam

The measurement of an electron electric dipole moment (eEDM) with high precision using BaF, benefits from fine control over several key parameters. These parameters include a vacuum, lasers and an electric and magnetic field. Measurements employing a BaF supersonic beam, are planned. These measurements, happening in an Interaction Zone, will use a large electric field of 10 kV/cm, and a small magnetic field of order 6 nT, with small field gradients. In addition, control and understanding of molecular states using lasers and spectroscopy are crucial for a successful experiment. This poster discusses how to reach an electromagnetic field in the Interaction Zone, useful for an eEDM measurement

Interaction Zone for an eEDM measurement with a BaF beam

The measurement of an electron electric dipole moment (eEDM) with high precision using BaF, benefits from fine control over several key parameters. These parameters include a vacuum, lasers and an electric and magnetic field. Measurements employing a BaF supersonic beam, are planned. These measurements, happening in an Interaction Zone, will use a large electric field of 10 kV/cm, and a small magnetic field of order 6 nT, with small field gradients. In addition, control and understanding of molecular states using lasers and spectroscopy are crucial for a successful experiment. This poster discusses how to reach an electromagnetic field in the Interaction Zone, useful for an eEDM measurement

Interaction Zone for an eEDM measurement with a BaF beam

The measurement of an electron electric dipole moment (eEDM) with high precision using BaF, benefits from fine control over several key parameters. These parameters include a vacuum, lasers and an electric and magnetic field. Measurements employing a BaF supersonic beam, are planned. These measurements, happening in an Interaction Zone, will use a large electric field of 10 kV/cm, and a small magnetic field of order 6 nT, with small field gradients. In addition, control and understanding of molecular states using lasers and spectroscopy are crucial for a successful experiment. This poster discusses how to reach an electromagnetic field in the Interaction Zone, useful for an eEDM measurement