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

Investigation of robust population transfer using quadratically chirped laser interacting with two-level system