Research on resonant (1+1) two photon transition amplitude by shaped ultrashort laser pulses

We theoretically calculate the resonant (1 + 1) two photon transition probability in the Rubidium (Rb) atom by the θ−phase shaped pulses. The results show that the resonant two photon transition probability can be enhanced by the θ−phase shaped pulses. The resonant two photon transition amplitude in complex plane have different distributions for different phase step position, but those distributions meet in a point which corresponds the transition amplitude of transitions-limited pulse and the shaped pulses with θ = 0. Moreover, the transition amplitude of on-resonant and near-resonant part is calculated to explain the two photon transition amplitude distribution and reveal the physical control mechanism.