Electromagnetically induced transparency in degenerate ladder-type system

We study the effect of the electromagnetically-induced transparency on the 3-level ladder-type atomic system, with the middle level being three-fold degenerate, and show the influence of the degeneracy on the shape of both the transparency window and dispersion curve. In the theoretical description of the model, the density matrix formalism is used, with decoherence effects described by the spontaneous emission coefficients from higher to lower energy levels. The corresponding optical Bloch equations are numerically solved in the stationary regime, and the obtained results are interpreted with the help of the theoretical dressed-state analysis. The influence of the control Rabi frequency and spontaneous emission coefficients on the occurrence and properties of the transparency window, as well as the properties of the dispersion curve are also investigated. Finally, using the dressed-state analysis, together with the approximate analytical results from the perturbation theory, we show that the system with the degenerate middle level can be treated as the system without degeneracy, with the modified decay rate from the highest to the middle energy level.