  We investigate the population dynamics of the three-level system in the
two-photon absorption (TPA) process, mainly focusing the influence of pulse
width and Rabi frequency on the population dynamics of the system. We observe
the dependency of the population with the Rabi frequency and the pulse width.
We also show that the arbitrary superposition state consisted in two states,
upper state and lower state, is possible by controlling the pulse width and
Rabi frequency. The results obtained can be used to the case of more complex
multilevel system and they can be valuable for coherent quantum control in
quantum information processing.
