Influence of spontaneously generated coherence on absorption, dispersion, and group index in a five-level cascade atomic system

By solving the density matrix equations in the steady state, we have derived analytical expressions for the absorption, dispersion, and group index of a five-level cascade-type atomic system as functions of laser intensity and frequency, spontaneously generated coherence (SGC), and relative phase of applied fields. The influences of SGC and relative phase on absorption, dispersion, and group index of this system under electromagnetically induced transparency (EIT) are studied. It is shown that the three EIT windows of system become deeper and narrower as the strength of SGC increases. These lead to an increase in the slope and the amplitude of the dispersion curves at three EIT windows. As a result, the amplitude of the group index at these three EIT windows also becomes larger when the strength of SGC increases. In particular, the group index can easily be switched between negative and positive values i.e., the light propagation can easily be converted between superluminal to subluminal modes by adjusting the strength of SGC, relative phase or the coupling laser intensity.