Atomic coherences of on-resonant and off-resonant two-photon absorptions in ladder-type atomic system

We report the physical origins of the on-resonant and off-resonant two-photon absorption (TPA) in an open ladder-type atomic system of the 5S$_{1/2}$(F $=$ 1)-5P$_{3/2}$(F$^{\prime} =$ 0, 1, 2)-5D$_{5/2}$(F$'' = $ 1, 2, 3) transitions in $^{87}$Rb atoms. When the on-resonant TPA including electromagnetically induced transparency (EIT) was transformed into the off-resonant TPA according to the coupling laser frequency detuning, we clarified the dynamics of the atomic coherences by decomposing into the two-photon coherence (TC) and the crossover coherence (CC) terms mixed between one-photon coherence (OC) and TC terms The physical origins of the two TPAs were completely different; the cause of the on-resonant TPA was the CC term, and that of the off-resonant TPA was the TC term.