The effects of the incoherent pumping field on the phase control of group velocity

This paper studies the effects of the incoherent pumping field and the spontaneously generated coherence (SGC) on the phase control of group velocity. The effects of a relative phase between probe and coupling fields on the absorption and the dispersion are then discussed. It is shown that the phase dependence of the group velocity not only depends on the existence of the SGC, but also depends on the existence of the incoherent pump field. We show that for the weak probe field, and in the presence of SGC, the existence of the incoherent pump field is a necessary condition for the phase control of the dispersion, the absorption and the group index.