Relationship between two-and three-photon coherence in a ladder-type atomic system

We investigated the relationship between two-and three-photon coherence in terms of the transition routes and coupling field intensities in a Doppler-broadened ladder-type atomic system of the 5S$_{1/2}$-5P$_{3/2}$-5D$_{5/2}$ transition in $^{87}$Rb atoms. Three-photon electromagnetically induced absorption (TPEIA) due to three-photon coherence was observed in the only transition route that exhibited a dominant two-photon coherence effect. We showed that two-photon coherence is a necessary condition for three-photon coherence phenomena. A comparison of the relative magnitudes of the electromagnetically induced transparency and TPEIA as a function of the coupling field intensity revealed that three-photon coherence increased twice as rapidly as two-photon coherence. Considering three-photon coherence in a Doppler-broadened ladder-type three-level atomic system, the relation between two-and three-photon coherence was numerically calculated.