Three-photon coherence of Rydberg atomic states

We investigated three-photon coherence effects of the Rydberg state in a four-level ladder-type atomic system for the 5S$_{\mathrm{1/2}}$ (F$=$3) -- 5P$_{\mathrm{3/2\thinspace }}$(F'$=$4) -- 50D$_{\mathrm{5/2}}$ -- 51P$_{\mathrm{3/2}}$ transition of $^{\mathrm{85}}$Rb atoms. By adding a resonant electric field of microwave (MW) at electromagnetically induced transparency (EIT) in Rydberg state scheme, we observed experimentally that splitting of EIT signal appears under the condition of three-photon resonance in the Doppler-broadened atomic system. Discriminating the two- and three-photon coherence terms from the calculated spectrum in a simple four-level ladder-type Doppler-broadened atomic system, we found that the physical origin of splitting of EIT was three-photon coherence effect, but not three-photon quantum interference phenomena such as three-photon electromagnetically induced absorption (TPEIA).