Transient optical properties of coherent four-level atoms without undepleted ground-state approximation

We present a theoretical method for studying the transient linear and nonlinear optical property of a four-level atomic system with electromagnetically induced transparency. We start from equations of motion of density matrix that describe the response of atoms to probe and signal fields. We solve these equations by means of a method of multiple-scales. Different from previous studies, in our approach undepleted ground-state approximation is not used and significant differences from previous results are found.