Recently, there have been great interest and advancement in the field of laser cooling and magneto-optical trapping of molecules. The rich internal structure of molecules naturally lends themselves to extensive and exciting applications. In this paper, the radical , as a promising candidate for laser cooling and magneto-optical trapping, is discussed in detail. The highly diagonal Franck–Condon factors between the and states are first confirmed with three different methods. Afterwards, with the effective Hamiltonian approach and irreducible tensor theory, the hyperfine structure of the state is calculated accurately. A scheme for laser cooling is given clearly. Besides, the Zeeman effects of the upper ( ) and lower ( ) levels are also studied, and their respective g factors are obtained under a weak magnetic field. Its large g factor of the upper state is advantageous for magneto-optical trapping. Finally, by studying Stark effect of BaF in the , we investigate the dependence of the internal effective electric field on the applied electric field. It is suggested that such a laser-cooled BaF is also a promising candidate for precision measurement of electron electric dipole moment.
For laser-cooling considerations, we have theoretically investigated the electronic, rovibrational, and hyperfine structures of the BaF molecule. The highly diagonal Franck-Condon factors and the branching ratios for all possible transitions within the lowest-lying four electronic states have also been calculated. Meanwhile, the mixing between the metastable ${A}^{{\ensuremath{'}}^{2}}\mathrm{\ensuremath{\Delta}}$ and ${A}^{2}\mathrm{\ensuremath{\Pi}}$ states and, further, the lifetime of the $\mathrm{\ensuremath{\Delta}}$ state have been estimated since the loss procedure via the $\mathrm{\ensuremath{\Delta}}$ state might fatally break the main quasicycling $\mathrm{\ensuremath{\Sigma}}\ensuremath{-}\mathrm{\ensuremath{\Pi}}$ transition for cooling and trapping. The resultant hyperfine splittings of each rovibrational state in the ${X}^{2}{\mathrm{\ensuremath{\Sigma}}}^{+}$ state provide benchmarks for sideband modulations of the cooling and repumping lasers and the remixing microwaves to address all necessary levels. The calculated Zeeman shift and
g factors for both
X and
A states serve as benchmarks for selection of the trapping laser polarizations. Our study paves the way for future laser cooling and magneto-optical trapping of the BaF molecule.
More recently, laser cooling of the diatomic radical magnesium monofluoride (
24Mg19F) is being experimentally preformed [Appl. Phys. Express 8, 092701 (2015) and Opt. Express 22, 28645 (2014)] and was also studied theoretically [Phys. Rev. A 91, 042511 (2015)]. However, some important problems still remain unsolved, so, in our paper, we perform further theoretical study for the feasibility of laser cooling and trapping the
24Mg19F molecule. At first, the highly diagonal Franck-Condon factors of the main transitions are verified by the closed-form approximation, Morse approximation, and Rydberg-Klein-Rees inversion methods, respectively. Afterwards, we investigate the lower $X{\phantom{\rule{0.16em}{0ex}}}^{2}{\mathrm{\ensuremath{\Sigma}}}_{1/2}^{+}$ hyperfine manifolds using a quantum effective Hamiltonian approach and obtain the zero-field hyperfine spectrum with an accuracy of less than 30 $\mathrm{kHz}\phantom{\rule{0.16em}{0ex}}\ensuremath{\sim}5\phantom{\rule{0.28em}{0ex}}\ensuremath{\mu}\text{K}$ compared with the experimental results, and then find out that one cooling beam and one or two repumping beams with their first-order sidebands are enough to implement an efficient laser slowing and cooling of
24Mg19F. Meanwhile, we also calculate the accurate hyperfine structure magnetic
g factors of the rotational state ($X{\phantom{\rule{0.16em}{0ex}}}^{2}{\mathrm{\ensuremath{\Sigma}}}_{1/2}^{+},N=1$) and briefly discuss the influence of the external fields on the hyperfine structure of
24Mg19F as well as its possibility of preparing three-dimensional magneto-optical trapping. Finally we give an explanation for the difference between the Stark and Zeeman effects from the perspective of parity and time reversal symmetry. Our study shows that, besides appropriate excitation wavelengths, the short lifetime for the first excited state $A{\phantom{\rule{0.16em}{0ex}}}^{2}{\mathrm{\ensuremath{\Pi}}}_{1/2}$, and lighter mass, the
24Mg19F radical could be a good candidate molecule amenable to laser cooling and magneto-optical trapping.
As a heavy molecule, barium monofluoride (BaF) presents itself as a promising candidate for measuring permanent electric dipole moment. Here we report the realization of three-dimensional magneto-optical trapping (MOT) of BaF molecules. Through the repumping of all the vibrational states up to v=3, and rotational states up to N=3, we effectively close the transition to a leakage level lower than 10^{-5}. This approach enables molecules to scatter a sufficient number of photons required for laser cooling and trapping. By employing a technique that involves chirping the slowing laser frequency, BaF molecules are decelerated to near-zero velocity, resulting in the capture of approximately 3×10^{3} molecules in a MOT. Our findings represent a significant step towards the realization of ultracold BaF molecules and the conduct of precision measurements with cold molecules.
Abstract A method for manipulating molecules without suitable electronic properties to be viable candidates for laser cooling is described. Only a few natural molecules have a highly diagonal Franck–Condon factor (FCF) for the laser cooling scheme. Thus, we manipulate the FCFs by using an electric field identified by an optimized method based on linear regression. The details and the validity of the method are demonstrated using the CsH molecule. The different angles between the electric field and the molecular axis are considered, and the potential energy surfaces dependent on the electric field and angle are constructed. The vibrational energies and FCFs dependent on the angles are obtained, and the corresponding laser cooling schemes relative to the angles are built, which induce the accumulated FCFs of each scheme to exceed 0.999. The schemes can exert work at the angle between the molecular axis and the electric field is 1080° with five pumping lasers with center wavelengths of 473.74, 499.58, 527.72, 540.22, and 571.62 nm. In principle, the present method can be extended to any diatomic molecules without highly diagonal FCFs under natural conditions, providing a theoretical basis for studying physical and chemical problems involving cold molecules.
Laser cooling and magneto-optical trapping of molecules typically involves multiple transitions driven by several laser frequencies. We analyze how magneto-optical trapping forces depend on the angular momenta, F l and F u , and the g -factors, g l and g u , of the lower and upper states. When the polarizations must be reversed relative to cases where The correct choice of circular polarization depends on the sign of g u but not on the sign of g l . If g u is zero there is no trapping force, and the trapping force is very weak whenever g u is small compared to g l , which it usually is when the cooling transition is the to transition of a molecule. For some molecules, mixing of the excited state with a nearby excited state can greatly increase g u , leading to stronger trapping forces. A strong trapping force can also be produced by rapidly and synchronously reversing both the magnetic field and the laser polarizations. We simulate a recent experiment on magneto-optical trapping of SrF molecules, and suggest that an alternative choice of laser beam polarizations will strengthen the trapping force.
Laser cooling molecules to the ultracold regime is the prerequisite for many novel science and technologies. It is desirable to take advantage of theoretical approaches to explore polyatomic molecular candidates, which are capable of being cooled to the ultracold regime. In this work, we explore two polyatomic candidates, CaNC and SrNC, which are suitable for laser cooling. These molecules possess impressively large permanent dipole moments (∼6 Debye), which is preferred for applications using an external electric field. High-level ab initio calculations are carried out to reveal electronic structures of these molecules, and the calculated spectroscopic constants agree very well with the available experimental data. For each molecule, the Franck-Condon factor matrix is calculated and shows a diagonal distribution. The radiative lifetimes for CaNC and SrNC are estimated to be 15.5 and 15.8 ns, respectively. Based upon the features of various electronic states and by choosing suitable spin-orbit states, we construct two feasible laser cooling schemes for the two molecules, each of which allows scattering nearly 10000 photons for direct laser cooling. These indicate that CaNC and SrNC are excellent ultracold polyatomic candidates with strong polarity.