Decoherence in cross-Kerr nonlinearity based on electromagnetically induced transparency

The effects of decoherence due to dephasing and incoherent population exchange on the cross-Kerr nonlinearity are investigated. In the linear optical behavior, the incoherent population exchange suppresses the linear resonance such as the Autler-Townes absorption and the electromagnetically induced transparency in the same manner as the dephasing. While in the cross-Kerr optical responses these two decoherence mechanisms affect the nonlinearity in different ways. The dephasing enhances the nonlinear absorption at resonance, while the incoherent population exchange leads to cross-nonlinear gain and also broadens its spectrum. In particular, the large cross-Kerr nonlinearity without nonlinear absorption can be realized by suitably adjusting the incoherent population exchange. Additionally, the dependence of y-intercepts of absorption or dispersion curves without control field on the population exchange rate can be used to estimate the incoherent population exchange rate of the system. The results provided here are useful not only for illustrating distinct physical mechanisms of these two kinds of decoherence in nonlinear optics, but also for potential applications of cross-Kerr nonlinearity in quantum information processing