Optical transparency and nonlinearity for a five-level tripod system involving a Rydberg state

We demonstrate electromagnetically-induced transparency and giant Kerr nonlinearity in a five-level atomic system where the upper level is a Rydberg-state coupled coherently to a four-level tripod subsystem. Since the high Rydberg states exhibit rather long lifetimes, the system evolves into a dark state that is a superposition of all long-lived states resulting in an optical transparency for the probe field. We solve the relevant density matrix equations for the atomic system in steady-state and utilize the perturbation approach to obtain the expressions for the linear and nonlinear susceptibility. It is shown that depending on the system parameters, the system can exhibit triple, double or single, optical transparency. Therefore, there is a resulting change in the sign of linear dispersion for different parametric situations giving, rise to switching in the group velocity of the probe pulse from superluminal to subluminal or vice versa. We also identify the existence of giant third-order Kerr nonlinearities within regions of optical transparency and under the slow light condition.