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

Novel spin-precession method for sensitive EDM searches

We demonstrate a spin-precession method to observe and analyze multi-level coherence between all hyperfine levels in the $X ^2\Sigma^+,N=0$ ground state of barium monofluoride ($^{138}$Ba$^{19}$F). The signal is sensitive to the state-preparation Rabi frequency and external electric and magnetic fields applied in searches for a permanent electric dipole moment (EDM). In the obtained interference spectrum, the electric field and Rabi frequency become observable simultaneously with the EDM. This method reduces systematic biases and the number of auxiliary measurements for such precision measurements

Novel spin-precession method for sensitive EDM searches

We demonstrate a spin-precession method to observe and analyze multi-level coherence between all hyperfine levels in the $X ^2\Sigma^+,N=0$ ground state of barium monofluoride ($^{138}$Ba$^{19}$F). The signal is sensitive to the state-preparation Rabi frequency and external electric and magnetic fields applied in searches for a permanent electric dipole moment (EDM). In the obtained interference spectrum, the electric field and Rabi frequency become observable simultaneously with the EDM. This method reduces systematic biases and the number of auxiliary measurements for such precision measurements

Novel spin-precession method for sensitive EDM searches

We demonstrate a spin-precession method to observe and analyze multi-level coherence between all hyperfine levels in the $X ^2\Sigma^+,N=0$ ground state of barium monofluoride ($^{138}$Ba$^{19}$F). The signal is sensitive to the state-preparation Rabi frequency and external electric and magnetic fields applied in searches for a permanent electric dipole moment (EDM). In the obtained interference spectrum, the electric field and Rabi frequency become observable simultaneously with the EDM. This method reduces systematic biases and the number of auxiliary measurements for such precision measurements

Novel spin-precession method for sensitive EDM searches

We demonstrate a spin-precession method to observe and analyze multi-level coherence between all hyperfine levels in the $X ^2\Sigma^+,N=0$ ground state of barium monofluoride ($^{138}$Ba$^{19}$F). The signal is sensitive to the state-preparation Rabi frequency and external electric and magnetic fields applied in searches for a permanent electric dipole moment (EDM). In the obtained interference spectrum, the electric field and Rabi frequency become observable simultaneously with the EDM. This method reduces systematic biases and the number of auxiliary measurements for such precision measurements

Novel spin-precession method for sensitive EDM searches

We demonstrate a spin-precession method to observe and analyze multi-level coherence between all hyperfine levels in the $X ^2\Sigma^+,N=0$ ground state of barium monofluoride ($^{138}$Ba$^{19}$F). The signal is sensitive to the state-preparation Rabi frequency and external electric and magnetic fields applied in searches for a permanent electric dipole moment (EDM). In the obtained interference spectrum, the electric field and Rabi frequency become observable simultaneously with the EDM. This method reduces systematic biases and the number of auxiliary measurements for such precision measurements

Deceleration and Trapping of SrF Molecules

We report on the electrostatic trapping of neutral SrF molecules. The molecules are captured from a cryogenic buffer-gas beam source into the moving traps of a 4.5 m long traveling-wave Stark decelerator. The SrF molecules in $X^2\Sigma^+(v=0, N=1)$ state are brought to rest as the velocity of the moving traps is gradually reduced from 190 m/s to zero. The molecules are held for up to 50 ms in multiple electric traps of the decelerator. The trapped packets have a volume (FWHM) of 1 mm$^{3}$ and a velocity spread of 5(1) m/s which corresponds to a temperature of $60(20)$ mK. Our result demonstrates a factor 3 increase in the molecular mass that has been Stark-decelerated and trapped. Heavy molecules (mass$>$100 amu) offer a highly increased sensitivity to probe physics beyond the Standard Model. This work significantly extends the species of neutral molecules of which slow beams can be created for collision studies, precision measurement and trapping experiments

A supersonic laser ablation beam source with narrow velocity spreads

A supersonic beam source for SrF and BaF molecules is constructed by combining the expansion of carrier gas (a mixture of 2% SF6 and 98% argon) from an Even-Lavie valve with laser ablation of a barium/strontium metal target at a repetition rate of 10 Hz. Molecular beams with a narrow translational velocity spread are produced at relative values of Δv/v = 0.053(11) and 0.054(9) for SrF and BaF, respectively. The relative velocity spread of the beams produced in our source is lower in comparison with the results from other metal fluoride beams produced in supersonic laser ablation sources. The rotational temperature of BaF is measured to be 3.5 K. The source produces 6 × 108 and 107 molecules per steradian per pulse in the X2ς+ (ν = 0, N = 1) state of BaF and SrF molecules, respectively, a state amenable to Stark deceleration and laser cooling

Lifetime measurements of the A (2)Pi(1/2) and A (2)Pi(3/2) states in BaF

Time resolved detection of laser induced fluorescence from pulsed excitation of electronic states in barium monofluoride (BaF) molecules has been performed in order to determine the lifetimes of the $A^2\Pi_{1/2}$ and $A^2\Pi_{3/2}$ states. The method permits control over experimental parameters such that systematic biases in the interpretation of the data can be controlled to below $10^{-3}$ relative accuracy. The statistically limited values for the lifetimes of the $A^2\Pi_{1/2}(\nu=0)$ and $A^2\Pi_{3/2}(\nu=0)$ states are 57.1(3) ns and 47.9(7)~ns, respectively. The ratio of these values is in good agreement with scaling for the different excitation energies. The investigated molecular states are of relevance for an experimental search for a permanent electric dipole moment (EDM) of the electron in BaF