In this paper, we investigate the evolutional dynamics of a Λ-type atomic system of which two branches of transitions are driven by two trains of ultrashort pulse respectively. The accumulating of atomic populations and coherences due to excitations of successive pulses are demonstrated by the numerical simulations. The realization of the coherent population trapping (CPT) effect is verified. When the spontaneous generated coherence (SGC) is considered, the system will evolve to the dark state even when the initial state is not the dark state if the degree of the SGC is not maximal and the degree of the SGC will influence the time needed to reach the atomic steady state. With the maximal degree of SGC, whether the system will evolve into the dark state depends on the initial state. This fact means that the maximal SGC spoils the dark state geometry, which a Λ-type atom driven by light field satisfies. Additionally, we found that the involvement of the phase of the driving field can counteract the destruction stem from the maximal degree of the SGC on the dark state geometry, i.e. the system can be trapped in the dark state even when the initial state is not the dark state. Meanwhile, it is found that the phase can adjust the time needed by the system to reach the steady state in a quite wide range.
Coherent population trapping by dark state formation in a carbon nanotube quantum dot
