Phase-dependent high refractive index without absorption in a four-level inverted-Y atomic system

We consider a closed four-level inverted-Y system in the presence and the absence of a microwave field. It is found that due to the quantum coherence between the two lower levels, either induced by the spontaneous decay or by the microwave field, the refraction – absorption properties of the system can be modulated by controlling the relative phase of the applied fields in both driven ways. In particular, by properly setting the values of the relative phase, the desirable high index of refraction without absorption can be achieved.