Gain-assisted giant Kerr nonlinearity in a {\sf \Lambda}-type system with two-folded lower levels

We propose a four-level Λ scheme with a one-mode active Raman gain core and two-folded lower levels to obtain new linear and nonlinear optical responses. We show that this scheme is fundamentally different from that based on electromagnetically induced transparency (EIT). Firstly, it is gain-assisted and thus capable of eliminating all attenuation of probe field. Furthermore, due to the quantum interference effect introduced by a coupling field a gain doublet appears in gain spectrum, and hence the distortion of the probe field during propagation can be effectively avoided. In addition, in such system a large and rapidly responding Kerr nonlinearity can be produced, which is much (more than 10 times) larger than that obtained in the EIT-based scheme with the same energy-level configuration.