Effect of spontaneously generated coherence on left-handedness in a degeneracy atomic system

A theoretical investigation is carried out into the effect of spontaneously generated coherence (SGC) on the left-handedness in a four-level $Y$-type atomic system with two highest nearly degenerate lying levels. It is found, with the spontaneously generated coherence intensity enhancing, the atomic system gradually displays left-handedness with simultaneous negative permittivity and permeability. And the refractive index enhances with the increasing intensity of SGC. However, the absorption is suppressed by the SGC effect when the SGC has a large intensity. When the probe field is near-resonant coupled to the atomic system, the appearance of SGC doesn't always change the permeability from positive to negative and allow for left-handed behavior, unless the SGC reaches a large intensity.