Rovibrational population transfer is controlled by a two-overlapping- pulse scheme in which the frequency ratio of the two pulses is 1:3. The calculated results show that nearly 100% of the population can be transferred from initial state |0,0to target state |3,1. The probability of population transfer can be controlled by pulse phase. When 1 =1.68 , the two pulses can be increased mutually and the probability of population transfer is also increased. When 1 =0.64 , the two pulses can be offset mutually and the probability of population transfer is reduced. The intensity of the second pulse has a significant effect on the population transfer.

The multiphoton transition is investigated theoretically by using wave packet method for the ground electronic state of HF molecule. A laser field composed of two overlapping infrared pulses is used in our model, and the ratio of their frequencies is 1:2. States |4,0> and |4,2> are chosen as target states. Calculated results show that the population can be transferred to different target states as the corresponding resonant frequency is chosen. The probability of the population transfer can be controlled by the initial phase difference of the two pulses. When the initial phase difference is of an odd number of π/2, the probability of population transfer reaches the maximal value. When the initial phase difference is of an even number of π/2, the probability of population transfer reaches the minimum value. In comparison with the state |4,2>, the initial phase difference has a stronger in fluence on the population of the state |4,0>.

The extended “ladder” transition controlled by two harmonic pulses is investigated by using a time-dependent quantum wave packet method. The molecular population transfers from the state|0, 0> angle to the states|5, 0> angle and|5, 2> angle induced by the fundamental and second-harmonic pulses, and to the states|5, 3> angle and |6, 2> angle induced by the fundamental and third-harmonic pulses. The calculated results show that the two harmonic pulses can induce a nearly 100% of population to transfer to the target state. The relative phase of two pulses can affect the population distribution. The variation of population has a period of π for the fundamental and second-harmonic pulses, and a period of 2π for the fundamental and third-harmonic pulses.

The photoassociation reaction H+D+ induced by two chirped pulses is theoretically studied. The first pulse is employed to accelerate the collision pairs, and the second pulse is used to enhance the yield ratio of HD+. The optimal parameters of the second pulse and the population of product HD+ depend on the chirp rate of the first pulse. The population of the product HD+ can be controlled by the delay time between the two laser pulses.