Construction Of Analytic Functions And Theoretical Study Of The Laser Cooling For LiRb And XBe(X=Li,Rb,Cs) Molecules

The idea using radiation pressure and gradient force manipulates particles and atoms has become the research focus in the physics since the advent of laser. The emerged technique of laser cooling atoms caused a revolutionary change of optical physics as well as aroused great interest in other traditional fields which are nonintersecting. Because ultracold molecules have the microscopic characteristics, such as internuclear distance, dissociation energy, resonance frequency and vi-rotation, these make molecule cooling have a more profound and significant influence than atom cooling. Because of the complex of molecular properties, it also makes cold molecules have a broader research value and potential applications than cold atoms. Ultracold molecules have provided opportunities for us to study the new physical phenomena, and also will be far more than the traditional molecular science. In 2010, the SrF molecule having been cooled in experiment proved cooling molecule is feasible. However, not all the molecules are allowed to use the laser cooling, which makes it become the first the problem to solve. The original theory established three are three certifications which should be satisfied. The first certification is strong one-photon transitions with highly diagonal Franck-Condon factors（FCFs）. The second criterion is shorter lifetime to ensure high spontaneous-emission rates, which is highly desirable for rapid laser cooling. The third certification is that there are non-intervening electronic states in the cycling transition. However, with the deepening of the research, the intermediate product state can also be used as the laser cooling candidate. What’s more, some studies proved cooling singlet molecule can reach a much more lower temperature than doublet molecules.However, most research follows the above three strict conditions, choicing of molecular state is the transition between binary, and will not be able to have the existence of the intermediate state, which makes the study of other molecules lost the chance.With the deepening of the research and the existing related experiments show that with intermediate state products can also be used as the laser cooling of candidate molecules, and the study found that reach the temperature of the cooling singlet molecular is far lower than the doublet molecules.Unfortunately, these molecules are few research.The starting point of this article is the hotspot in recent years, molecular and state transition between have an intermediate state condition is studied.In addition, for part of singleton molecular properties also did calculations.Based on the calculation results, we forward the comparatively detailed as the study of molecular laser cooling scheme, provide certain theoretical reference for experimentation.Adopting the method of quantum chemistry calculation, i.e., muti-reference configuration interaction（MRCI）, we obtained the analytic function of the diatomic molecules LiRb and BeX（X = Li, Rb, Cs） in the ground state and excited state. Meanwhile, we also made a theoretical study of laser cooling on these molecules.The large basis sets aug-cc-pwCV5 Z and the atomic-natural-orbital-type basis set are used for atoms Li and Rb, respectively. The analytic potential energy functions（APEFs） of the X¹Î£⁺, 2¹Î£⁺, a³Î£⁺, and 2³Î£⁺ states of the LiRb molecule are obtained using Morse long-range（MLR） potential energy function with damping function and nonlinear least-squares method. The reliability of the APEFs is confirmed using the curves of their first and second derivatives. By using the obtained APEFs, the rotational and vibrational energy levels of the states are determined by solving the Schrodinger equation of nuclear movement. The spectroscopic parameters, which are deduced using Dunham expansion, and the obtained rotational and vibrational levels are compared with the reported theoretical and experimental values. The correlation effect of the electrons of the inner shell remarkably improves the results compared with the experimental spectroscopic parameters. For the first time, the APEFs for the dipole moments and transition dipole moments of the states have been determined based on the curves obtained from the MRCI calculations.The LiRb molecule is also studied by the same mothed and basis set, but this time we did a research on the electronic states and spin-forbidden cooling transitions of LiRb. The PECs of the ground state X¹Î£⁺ and the low-lying excited states a³Î£⁺, B¹Î , and b³Î  are performed. The spin-orbit coupling effects for the PECs and transition dipole moments（TDMs） between the X¹Î£⁺ and b³Î  and a³Î£⁺ states are also calculated. The analytical functions for the PECs and TDMs are deduced. The rovibrational energy levels, the spectroscopic parameters and the Franck-Condon factors（FCF） are determined through solving the Schr?dinger equation of nuclear movement with the obtained analytical functions. The b³Î ₀ X¹Î£⁺ and b³Î ¹ X¹Î£⁺ transitions have highly diagonal distributed FCFs and non-zero TDMs, demonstrating that the LiRb molecule could be a very promising candidate for laser cooling. Therefore, a three-cycle laser cooling schemes for the molecule have been proposed based on the two spinforbidden transitions. Using the radiative lifetime and linewidth calculated from the obtained TDM functions, we present a further analysis for the cooling project of LiRb and the corresponding KRb molecule. The transition b³Î ₀ X¹Î£⁺ is found to be a practical transition to cool LiRb molecule, and the sub-microkelvin cool temperature could be reached with the similar laser cooling scheme of KRb molecule.BeAlm（Alm = Li-Cs） molecules are interesting for the investigation of cold molecule recently. However, we fail to find any reports on RbBe and CsBe molecules. the PECs, the curves of dipole moments（DMs） and TDMs for the 1²Î£⁺, 2²Î£⁺, 1²Î  and 2²Î  states of RbBe and CsBe are obtained with the effective basis sets ECP28 MDF for Rb, ECP46 MDF for Cs, and all-electron basis sets Aug-cc-pwCV5 Z for Be. The smallcore approximation is used to obtain the correlation effect of the inner-shell electrons. With the obtained PECs, the APEFs are fitted by using MLR potential energy function with damping function and nonlinear least square method. The rotational and vibrational energy levels of the states are determined by solving Schr?dinger equation of nuclear movement based on the obtained APEFs. The spectroscopic parameters are also determined. The spin-orbit coupling for the four 2Π states is calculated and analyzed. We suppose a new analytical functions for the DMs and TDMs of the states based on the obtained curves. These results are helpful in the photoassociation investigation of the title molecules.The optical scheme to create the simplest heteronuclear metal ultracold LiBe molecule is proposed based on ab initio quantum chemistry calculations. The PECs, DMs and TDMs of ground state 1²Î£⁺, 2²Î£⁺, 1²Î , and 2²Î  states are calculated using large basis sets. The analytical functions deduced from the obtained curves are used to determine the ro-vibrational energy levels, the FCFs and the Einstein coefficients of the states through solving Schr?dinger equation of nuclear movement. The spectroscopic parameters are deduced with the obtained ro-vibrational energy levels. The FCFs（f00: 0.998, f11: 0.986, f22: 0.920） for the 2²Î£⁺（υ = 0）1²Î£⁺（υ’ = 0） transition are highly diagonally distributed, and the calculated radiative lifetime（74.87 ns） of the 22Σ+ state is found to be short enough for rapid laser cooling. The results demonstrate that Li Be could be a very promising candidate for laser cooling and a three-cycle laser cooling scheme for the molecule has been proposed.