Giant Kerr nonlinearity in an open V-type system with spontaneously generated coherence

We investigate the Kerr nonlinearity in an open three-level V-type system with spontaneously generated coherence (SGC). It is shown that the giant Kerr nonlinearity with vanishing linear absorption can be obtained with the presence of the SGC effect. While the Kerr nonlinearity is smaller than that in a general closed system due to the existence of the additional term from the open system. The method to enhance the Kerr nonlinearity in the open system is also discussed.