A theoretical study on the laser cooling scheme for the three-energy-level system of the CN molecule

Abstract

The X2Σ+ and B2Σ+ states of the CN molecule are suitable for the closed-loop transition of the optical laser cooling scheme because of the high diagonal Franck-Condon factor. However, the low-lying state of A2Π between X2Σ+ and B2Σ+ states makes the laser cooling scheme for the CN molecule become a three-energy-level system. The treatment of the intervening state is a key issue for laser cooling. To explore the feasibility of the scheme, we calculate the potential energy curves and transition dipole moments of X2Σ+, B2Σ+ and A2Π states of the CN molecule using the multi-reference configuration interaction method and large all-electron basis sets. Based on the obtained potential energy curves, the rotational and vibrational energy levels of the states are obtained by solving the Schrödinger equation of nuclear movement. The calculated spectroscopic parameters for the CN molecule are in good agreement with available theoretical and experimental results. The feasibility of laser cooling for the three-energy-level system of the molecule is examined using the results of the molecular electronic and spectroscopic properties. Based on the examination of the transition dipole moment, Franck-Condon factor, the spectroscopic term and the vibration energy levels, we find that the intervening state A2Π proves to be a significant influence on the closed-loop transition, but a large number of scattering photons are still available. Therefore, the optical schemes for the laser cooling of the three-energy-level system can be designed with a two-energy-level model according to the characteristic of X2Σ+ and B2Σ+ states. Finally, the optical scheme for cooling the CN molecule is constructed with three lasers.