Calculation of the local environment of a barium monofluoride molecule in an argon matrix: A step towards using matrix-isolated BaF for determining the electron electric dipole moment
R. L. Lambo, G. K. Koyanagi, A. Ragyanszki, M. Horbatsch, R. Fournier, E. A. Hessels
备注：
6 pages, 3 figures. As published, with typos corrected in tables
本文计算了嵌入氩基质中 BaF 分子的局部环境，发现取代四个 Ar 原子最具优势，且低温下阻碍分子迁移与转动的势垒足以固定其位置和方向，为 EDM$^3$ 合作组精密测量电子电偶极矩提供了关键基础。
摘要：
本文计算了嵌入氩基质中的氟化钡（BaF）分子的局部环境。研究发现，用一个 BaF 分子取代四个 Ar 原子的方式比取代其他数量的 Ar 原子具有显著优势。通过最小化总能量，确定了 BaF 分子及其邻近 Ar 原子的平衡位置。计算了阻碍 BaF 分子在固体内部迁移的势垒以及阻碍其转动的势垒。在 EDM$^3$ 合作组所使用的低温环境下，这些势垒足够大，足以固定该分子的位置和方向。了解基质隔离 BaF 分子的局部环境对 EDM$^3$ 合作组至关重要，该合作组正利用这些分子进行电子电偶极矩的精密测量。
英文摘要：
The local environment of a barium monofluoride (BaF) molecule embedded in an argon matrix is calculated. A substitution of a BaF molecule for four Ar atoms is found to be strongly favoured compared to substitutions for other numbers of Ar atoms. The equilibrium positions of the BaF molecule and its nearby Ar neighbours are found by minimizing the total energy. The potential barrier that prevents the migration of the BaF molecule within the solid and the barrier that prevents its rotation are calculated. At the cryogenic temperatures used by the EDM$^3$ collaboration, these barriers are sufficiently large to fix the position and orientation of the molecule. Knowledge of the local environment of matrix-isolated BaF molecules is essential for the EDM$^3$ collaboration, which is using them in a precision measurement of the electron electric dipole moment.
We theoretically investigate the laser cooling of fermionic barium monofluoride (137BaF) molecules, which are promising candidates for precision studies of weak parity violation and nuclear anapole moments. This molecular species features two nuclear spins, resulting in a hyperfine structure that is considerably more complicated than the one found in the usual laser-cooled diatomics. We use optical Bloch equations and rate equations to show that optical cycling, sub-Doppler cooling and bichromatic forces can all be realized under realistically achievable experimental conditions.
We demonstrate one-dimensional Doppler cooling of a beam of buffer-gas cooled Barium monofluoride (BaF) molecules. The dependences of the cooling efficiency with the laser detuning, the bias filed and the laser intensity are carefully measured. We numerical simulate our experiment with a Monte Carlo method, and find the theoretic predictions consists with our experimental data. This result represents a key step towards further cooling and trapping of BaF molecules.
We report an experimental investigation on the Doppler-free saturated absorption spectroscopy of buffer-gas-cooled Barium monofluoride (BaF) molecules in a 4~K cryogenic cell. The obtained spectra with a resolution of 19~MHz, much smaller than previously observed in absorption spectroscopy, clearly resolve the hyperfine transitions. Moreover, we use these high-resolution spectra to fit the hyperfine splittings of excited $A(v=0)$ state and find the hyperfine splitting of the laser-cooling-relevant $A^2Π_{1/2}(v=0, J=1/2, +)$ state is about 18 MHz, much higher than the previous theoretically pr…
Calculations of the BaF-Ar triatomic system are performed with a relativistic Hamiltonian and coupled cluster theory at the CCSD(T) level for 1386 positions of the Ar atom relative to the BaF molecule. Calculations are repeated with increasing basis sets (double-, triple-, quadruple- and quintuple-zeta), and these are extrapolated to estimate the complete-basis-set limit. The resulting energies provide a potential energy for the interaction of an Ar atom with a BaF molecule. A fit is presented that parametrizes this potential. This work is needed for an understanding of the position, modes of …
A full density-matrix simulation is performed for optical deflection of a barium monofluoride (BaF) beam. Pairs of counter-propagating laser pulses are used for stimulated absorption followed by stimulated emission. The scheme produces a force which is nearly an order of magnitude larger than that obtainable using continuous-wave laser deflection, and yields a force-to-spontaneous-decay ratio which is more than an order of magnitude larger. The large reduction in spontaneous decay is key to optical deflection of molecules, where branching ratios to other vibrational states do not allow for cyc…
We demonstrate buffer-gas cooling, high-resolution spectroscopy and cycling fluorescence of cold barium monofluoride (BaF) molecules. Our source produces an intense and internally cold molecular beam containing the different BaF isotopologues with a mean forward velocity of 190 m/s. For a well-collimated beam of 138BaF we observe a flux of more than 1e10 molecules/sr/pulse in the X2Sigma, N=1 state in our downstream detection region. Studying the absorption line strength of the intermediate A'Delta state we infer a lifetime of 790+\-346 ns, significantly longer than previously estimated. Final…
Heavy-atom alkaline earth monofluoride molecules are considered as prospective systems to study spatial parity or spatial parity and time-reversal symmetry violating effects such as the nuclear anapole moment or the electron electric dipole moment. Comprehensive and highly accurate theoretical study of the electronic structure properties and transition energies in such systems can simplify the preparation and interpretation of the experiments. However, almost no attempts to calculate quantum electrodynamics (QED) effects contribution into characteristics of neutral heavy-atom molecules have be…
The interplay of the relativistic and correlation effects in the permanent electric dipole moments (PDMs) of the X2Σ+ (ν = 0) electronic ground states of the alkaline earth monoflourides (BeF, MgF, CaF, SrF and BaF) has been studied using a relativistic coupled cluster method (RCCM). The calculations were carried out using double, triple and quadruple zeta basis sets, and with no core orbitals frozen. The results are compared with those of other calculations available in the literature and with experiments. The correlation trends in the PDMs of these molecules are discussed in detail.
We report results of ab initio calculation of the spin-rotational Hamiltonian parameters including P- and P,T-odd terms for the BaF molecule. The ground state wave function of BaF molecule is found with the help of the Relativistic Effective Core Potential method followed by the restoration of molecular four-component spinors in the core region of barium in the framework of a non-variational procedure. Core polarization effects are included with the help of the atomic Many Body Perturbation Theory for Barium atom. For the hyperfine constants the accuracy of this method is about 5-10%.
We reported a detailed experimental study of the cold collision of Barium monofluoride (BaF) with buffer gas and the high-resolution spectroscopy relevant with direct laser cooling. BaF molecules are efficiently produced with laser ablation and buffer-gas cooled in a cryogenic apparatus. The laser cooling relevant transition $|X^2Σ, v=0, N=1\rangle$ to $|A^2Π, v'=0, J'=1/2\rangle$ is identified. The collision cross section with buffer gas is measured to be $1.4(7)\times10^{-14} cm^{-2}$, which is very suitable for buffer gas cooling. Both rotational and vibrational temperatures are effectively…
We investigate the merits of a measurement of the permanent electric dipole moment of the electron ($e$EDM) with barium monofluoride molecules, thereby searching for phenomena of CP violation beyond those incorporated in the Standard Model of particle physics. Although the BaF molecule has a smaller enhancement factor in terms of the effective electric field than other molecules used in current studies (YbF, ThO and ThF$^+$), we show that a competitive measurement is possible by combining Stark-deceleration, laser-cooling and an intense primary cold source of BaF molecules. With the long coher…
The particular advantages of using the diatomic molecule radium monofluoride (RaF) as a versatile molecular probe for physics beyond the Standard Model are highlighted. i) RaF was previously suggested as being potentially amenable to direct cooling with lasers. As shown in the present work, RaF's energetically lowest electronically excited state is of ${}^{2}Π$ symmetry (in contrast to BaF), such that no low-lying ${}^{2}Δ$ state prevents efficient optical cooling cycles. ii) The effective electric field acting on the unpaired electron in the electronic ground state of RaF is estimated larger …
A cryogenic apparatus with a rotatable substrate for matrix isolation spectroscopy of BaF in neon crystals down to 3.2 K
Istituto Nazionale di Fisica Nucleare（意大利国家核物理研究所）；University of Ferrara（费拉拉大学）；University of Padua（帕多瓦大学）；National Quantum Science and Technology Institute（国家量子科学与技术研究所）
Specular reflection of polar molecules from a simple multi-cylinder electrostatic mirror: a method for separating BaF molecules produced in a buffer-gas-cooled laser-ablation source from other ablation products
This work presents an experimental protocol conceived to determine the vibrational distribution of barium monofluoride molecules seeded in a supersonic beam of argon. Here, as in many cases, the detection signal is related to the number of molecules by an efficiency involving several parameters that may be difficult to determine properly. In particular, this efficiency depends on the vibrational level of the detected molecules. Our approach avoids these complications by comparing different detection signals generated by different vibrational excitations. Such an excitation is made possible by …
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 st…
Heavy polar diatomic molecules are currently among the most promising probes of fundamental physics. Constraining the electric dipole moment of the electron (eEDM), in order to explore physics beyond the Standard Model, requires a synergy of molecular experiment and theory. Recent advances in experiment in this field have motivated us to implement a finite field coupled cluster approach (FFCC). This work has distinct advantages over the theoretical methods that we had used earlier in the analysis of eEDM searches. We used the relativistic FFCC to calculate molecular properties of interest to e…
