Polychromatic Kerr nonlinearity within electromagnetically induced transparency window

We study the nonlinear effect in a three-level atomic system in Lambda configuration. As two or more fields are confined within the common electromagnetically induced transparency (EIT) window, they directly disturb EIT dark state at the same time, which leads to the self-and cross-Kerr nonlinear interactions. Our scheme is different from the existed schemes based on three-level or multilevel systems only existing single type of nonlinear interactions. In the common EIT windows, the self-and cross-Kerr nonlinearities are established with suppressed linear absorption and our scheme can be generalized polychromatic Kerr nonlinearity. Because the atoms are almost trapped in the ground states and the atom population becomes unchanged, the scheme is robust to the atomic spontaneous emission. Our scheme is a promising avenue for preparation of squeezing and entanglement.