Resonant two-photon absorption and electromagnetically induced transparency in open ladder-type atomic system

We have experimentally and theoretically studied resonant two-photon absorption (TPA) and electromagnetically induced transparency (EIT) in the open ladder-type atomic system of the 5S$_{1/2}$(F $=$ 1)-5P$_{3/2}$(F' $=$ 0, 1, 2)-5D$_{5/2}$(F'' $=$ 1, 2, 3) transitions in $^{87}$Rb atoms. As the coupling laser intensity was increased, the resonant TPA was transformed to EIT for the 5S$_{1/2}$(F $=$ 1)-5P$_{3/2}$(F' $=$ 2)-5D$_{5/2}$(F'' $=$ 3) transition. We demonstrate the influence of the atomic system openness and the multi-photon interaction on the resonant TPA and EIT in the three-level ladder-type atomic system. From the numerical results, considering all the degenerate magnetic sublevels of the 5S$_{1/2}$-5P$_{3/2}$-5D$_{5/2}$ transition, both the competing EIT and TPA phenomenon could be understood by the decomposition of the spectrum into an EIT component owing to the pure two-photon coherence and a TPA component caused by the mixed term