A theoretical investigation is put forward for obtaining effective cross-Kerr nonlinearity of the four-level atom interacting with three electromagnetic fields. Using density-matrix equations and perturbation iterative method, the variation dependence of the third-order susceptibility on the detunings of the applied electromagnetic fields is derived. The results show that a large cross-Kerr nonlinearity can be generated when the detunings of the two weak probe fields are Raman resonant, and the corresponding linear susceptibility and self-Kerr interactions vanish. The realization of the effective Kerr nonlinearity with vanishing absorption is possible in a Raman resonant four-level system.

nonlinear optics; the third-order susceptibility; cross-Kerr nonlinearity; Raman resonant