Theoretical Investigation Of The Alkaline-earth-metal Monohydrides Toward Laser Cooling

Laser cooling and trapping of neutral atoms has made substantial progress in the past few decades.Compared with atoms,molecules have more complex energy level structures,thus bringing great challenges to direct laser cooling and trapping.On the other side,cold molecules show great advantages in cold molecular collisions and cold chemistry,as well as the applications in many-body interactions and fundamental physics such as the searches for fundamental symmetry violations.In recent years,polar diatomic molecules such as SrF,YO,and CaF have been demonstrated experimentally in direct laser cooling techniques and magneto-optical traps(MOTs),all of which require a comprehensive understanding of their molecular internal level structures.Other suitable candidates have also been proposed,such as YbF,MgF,BaF,HgF or even SrOH and YbOH,some of which already find their important roles in the search for changing fundamental constants and the measurement of the electron's Electric Dipole Moment(eEDM).Alkaline-earth-metal monohydrides(AEMHs)MH(M=Be,Mg,Ca,Sr and Ba)are widely found in sunspots,stars,nebulae and the interstellar medium,whose spectral data are quite important in astrophysical analysis and simulation.For example,in the spectral analysis of dwarf stars,scientists use the CaH's low-gravity spectral characteristics as an age indicator to observe and analyze the spectra of various dwarf stars to study the upper limit of their remaining ages.More importantly,they are considered as candidates for laser cooling and trapping,and may contribute to probing exotic quantum phases and eEDM due to their large permanent dipole moments.In previous studies,AEMHs have been analyzed theoretically using ab initio quantitative method to comprehend their potential energy curves,vibrational transitions,and Franck-Condon factors.However,these data are far from enough to carry out theoretical simulation or even experiment of laser cooling depth.In this paper,we have been studied the key information of laser cooling in detail,such as the hyperfine energy level of the X2?1/2 state of AEMHS molecule,the hyperfine transition branching ratio of A2?1/2 ?X2?1/2 transition and the ground state Zeeman effect.In this paper,we have theoretically investigated the molecular properties of the alkaline-earth-metal monohydrides MH(M=Be,Mg,Ca,Sr,and Ba)toward laser cooling and trapping.The highly diagonal Franck—Condon factors in the major cooling channel X2?1/2-A2?1/2 were first examined via the Morse potential method,the closed-form approximation method,and the RKR inversion method respectively,indicating that sum of f00,f01,and f02 for each molecule is greater than 0.9999 and almost 1 × 104 photons can be scattered to slow the molecules with merely three lasers.The molecular hyperfine structures of X2?1/2,as well as the transitions and associated hyperfine branching ratios in A2?1/2(J'=1/2,+)?X2?1/2(N=1,-)of MgH,CaH,SrH and BaH,are later evaluated via the effective Hamiltonian approach.The results not only confirm the consistency with the experimental hyperfine transitions of MgH and CaH,but also provide the calculated hyperfine frequencies of the least explored SrH and BaH.Based on these,we proposed the sideband modulation schemes that at least two EOMs should be required for CaH and SrH,three EOMs for MgH and BaH,in order to fully cover the hyperfine manifold originating from |X,N=1,-)while detuning within 3? of the respective hyperfine transition.In the end,we analyzed the Zeeman structures in the |X,N=1,->state and the associated magnetic g factors with or without J mixing.The results of this study show that:(i)the AEMHs show the highly diagonal Franck-Condon factors;(ii)short lifetime of the excited state;(iii)no intervening electronic states(except BaH)in the X2?1/2 ?A2?1/2 transition;(iv)the total nuclear spins of MH(M=24Mg,40Ca,88Sr,138Ba)are all 1/2,and the hyperfine level structure is not complicated;(v)the linearity of the ground state Zeeman structures are very high in a weak magnetic field.These results further suggest that AEMHs could be as candidates for laser cooling experiments or even MOT experiments.In addition,AEMHs require much less saturation irradiance than AEMFs MF(M=Mg,Ca,Sr,Ba),and can benefit more from the continuous diode lasers that are commercially available.Further studies even revealed that the heavier AEMH systems like SrH and BaH can have fairly large permanent electric dipole moment,leading to impressive experimental sensitivity for precision measurement under long coherence time.It is not easy to find suitable candidates for molecular laser cooling because of the demanding conditions.Based on the investigation of a large number of diatomic molecules and combined with a series of methods used in the study of AEMHs,we found that CdH molecules meet the requirements of laser cooling conditions,such as the highly diagonal Franck-Condon factors(A-X transition),short excited state lifetime,and etc.In addition,the linearity of the Zeeman structure of the ground state of CdH molecule is very high,which is very beneficial for its application in MOT.In this paper,we studied the diatomic molecules mentioned above which could be the candidates for laser cooling from a large number of diatomic molecules.Our work outlined here will be necessary in interpreting the spectral data in astrophysics,help design the experimental systems related to laser cooling and trapping,and contribute to further studies about ultracold molecular collisions and fundamental physics measurement.