With two atoms system drived by external periodic laster field, we have getted the analytic solutions of the centroid quantum state transition probability of the system via the perturbation theory. In the case of two Ca+, the figure of the transition probability of the photon states have simulated, which is vary with the time and the frequency of the laser. The results show that the quantum state of centerofmass collapses and revives,adjusted by external periodical laser frequency and interaction time under feeble field.When the frequency offset is selected from to ,the quantum state of centerofmass transition probabilities achieve 0.98,the longest manipulation cycle is shortened to 0.6×10-6 s,and the manipulation cycle is shortened greatly in theory.When the frequency offset achieve 1.2×107 Hz,quantum state of centerofmass transition probabilities is about 0.49,and the laser can not effectively manipulate the transition of centerofmass quantum states.Accordingly,these results may have some referential values on the realization of twobit quantum logic gate implementation and some other experimental studies.