Electromagnetically induced transparency and enhanced self-Kerr nonlinearity in a four-level scheme

We analyze the interaction of three laser fields with a four-level quantum system in a tripod configuration. We obtain an analytical expression for the linear susceptibility and nonlinear susceptibility of a weak-probe field and show that the properties of double electromagnetically induced transparency and the self-Kerr nonlinearity can be modified significantly by changing the ratio of the two coupling fields. We also show that a coherently prepared tripod scheme can be used for a giant self-Kerr nonlinearity generation with vanishing absorption in the case of optimal ratio. We present a physical understanding of our numerical results using the dressed-state approach and analytical explanation.