Pulse Propagation in Four-Level Atomic Systems Studied in light of Three-Level Doublets

Based on our understanding of coherent effects such as Electromagnetically Induced Transparency (EIT) and Autler-Townes (AT) in three-level systems (Lambda, Cascade, Vee) we study the propagation of a probe pulse in a variety of four-level systems. Specifically, we study two ``N'' schemes: one in which the probe field couples the ``outer'' levels and one in which the probe couples two of the ``inner'' levels. Surprising, although these systems appear different, they exhibit very similar steady state behavior. The Physics becomes clear in a semi-dressed states picture where each four-level system reduces to two three-level systems. The semi-dressed states picture analysis is complemented with a numerical work that follows from the discretization in time and space of the fields and density matrix elements equations. The systems under study exhibit slow and fast light behaviors with a dramatic transition between two positive and negative group velocity regimes that are explained in the adopted picture.