Kerr nonlinearity with vanishing absorption in a left-handed three-level atomic system

In this paper, we investigate a theoretical study of the Kerr nonlinearity in a left-handed three-level atomic system. The permittivity and permeability can simultaneously obtain negative values in the same band of frequency range by taking into account the relative phase of the strong control field. We have shown that Kerr nonlinearity with vanishing absorption can be achieved in this left-handed atomic system. Under the numerical simulations, large nonlinearity can be realized in left-hand frequency range due to the effect of quantum coherence and interference.