  We have proposed and demonstrated a fast and robust method of population
transfer between two quantum states using a quadratically chirped laser source.
Incorporating the Jaynes-Cummings in a full quantum description of the
interaction, and numerically solving the time-dependent Schr\"odinger equation,
transition probabilities have been obtained and the condition of the adiabatic
passage is investigated. In this scheme, a laser source has been swept
quadratically in time for arbitrarily engineering the transition probabilities.
The results show that complete and robust population transfer could be
selectively achieved by appropriate adjusting of the laser chirping parameter,
the center frequency and the coupling strength which the time of the complete
transition could be drastically decreased compared to linearly traditional
chirped laser. Furthermore, another feature of using the quadratically chirped
laser is the stimulation of intermediate transitions under the nonadiabatic
passage.
