“…For ( 3 w w + ) pulse scheme, the phase of 3rd-harmonic pulse has no effect on the symmetry and the final population distribution has a period of 2p. Besides the Brumer-Shapiro transition scheme, the two harmonic pulses can also control the population transfer through a ladder transition scheme, in which the initial, intermediate, and target states are respectively coupled by two harmonic pulses and population is transferred to the target state via the intermediate state [27,32]. If the Brumer-Shapiro and ladder transition schemes occur simultaneously in a process of population transfer, the two transition schemes will affect each other, which can increase the effect of pulse phases on population distribution.…”