Phase control of Kerr nonlinearity due to quantum interference in a four-level N-type atomic system

Linear and nonlinear response of a four-level N-type atomic system for a weak probe field is investigated. It is demonstrated that the giant Kerr nonlinearity with reduced absorption can be achieved by the spontaneously generated coherence. In addition, the effect of a relative phase between coupling fields on linear and nonlinear absorption as well as Kerr nonlinearity is then discussed.