Dynamics in direct two-photon transition by frequency combs

Based on the proposed theoretical model of a three-level system, the optical Bloch equations including the direct two-photon transition (DTPT) process using the optical frequency comb (OFC) were derived and the population distribution of particles in the upper states varying with the velocity of the atoms was obtained. Comparing to the resonance two-photon transition process, that population was increased by a factor of 1.4 without the Doppler shift, which is consistent with our previous experimental results. Simultaneously, the relationship between momentum transfers, and atomic velocity and pulse number were analyzed. When applied to a multi-level system it was found the population of particles in the excited states increased by a few percentages. The novel approach of DTPT using OFC improved the utilization of comb teeth and atoms, increased the momentum transfer path, reduced the reachable Doppler temperature limit, and encouraged us to use OFC to cool multiple elements simultaneously through the DTPT process. By analyzing the Doppler temperature of 133Cs and 87Rb in one dimension, it was found that this process can lower a temperature below 100 mK and generate dipolar molecules 133Cs87Rb via photoassociation, which provides us a new tool to create dipolar molecules and to investigate their complex rovibrational spectra in ultra-cold chemistry.