  The propagation of a weak probe field in a four-level N-type quantum system
in the presence of spontaneously generated coherence (SGC) is theoretically
investigated. The optical properties of the system are studied and it is shown
that the group velocity of light pulse can be controlled by relative phase of
applied fields. By changing the relative phase of applied fields, the group
velocity of light pulse changes from transparent subluminal to the transparent
superluminal light propagation. Thus, the phase-controlled absorption-free
superluminal light propagation is obtained without applying an incoherent laser
fields to the system. The propagation of a weak probe light pulse is studied by
solving the Maxwell's wave equation on numerical grid in space and time.
Moreover, we study the third order self- and cross-Kerr susceptibility of probe
field and calculate the nonlinear cross-phase shift for different values of
intensity of applied fields. In addition, we take into account the effect of
Doppler broadening on the light pulse propagation and it is found that a
suitable choice of laser propagation directions allows us to preserve our
results even in the presence of Doppler effect. It is demonstrated that by
increasing the Doppler width of distribution to the room temperature, the
dispersion changes from transparent subluminal to transparent superluminal
light propagation which is our major motivation for this work.
