The analysis of coherent phenomena for both linear and non-linear interactions in a four-level ladder (Ξ)-type configuration using density matrix formalism in dressed state representation

Abstract

In this paper, we present a theoretical study of Autler-Townes (AT) splitting, electromagnetically induced transparency (EIT) and electromagnetically induced absorption (EIA) phenomena in a four-level ladder (Ξ)-type configuration formed by two coupling and one probe laser fields using density matrix formalism in dressed state representation (DSR). The DSR is followed by the analytical solution of the optical Bloch equations (OBEs) under density matrix formalism in bare state representation (BSR). The density matrix elements are presented in both linear and non-linear interaction regimes under DSR. The concept of transfer of population (TOP) mechanism has been shown by calculating the different transition probabilities in DSR. It has been found that the population in a particular dressed state is greatly enhanced by increasing the strength of coupling field and played a key role to manipulate the induced coherence between different energy levels. The present theoretical model of DSR offers an excellent interpretation of the formation of EIT, EIA and conversion from EIT to EIA in both linear and third order non-linear probe absorption profiles. Besides, the dispersion profiles in both linear and non-linear interaction regimes have also been studied and the conversion of normal to anomalous dispersion profile which drastically modifies the optical responses of the medium has been discussed. We have found that the amplitudes of the coherent signals are more sensitive to the third order non-linear interaction compared to first order linear interaction.