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Hole-burning in an Autler-Townes doublet and in superluminal (subluminal) Electromagnetically induced transparency of a light pulse via a joint nonlinear coherent Kerr effect and Doppler broadening

We investigate the behavior of light pulse propagation in a 4-level double Lambda atomic system under condition of electromagnetically induced transparency. The Fano type interference effect and spectral hole burning appears in the the dynamics of the absorption-dispersion spectra caused by the joint nonlinear coherence Kerr effect and Doppler broadening. The coherent Kerr effect exhibits an enhancement (reduction) in superluminal (subluminal) in negative (in positive) group index while the Doppler broadening generates multiple hole burning in the Autler-Townes like spectra of this system. The hole burning in addition with coherent Kerr effect on the spectral profile influences the dynamics of subluminal and superluminal of the probe pulse through the medium. The characteristics of superluminality and subluminality modified by considering cold-Kerr-free medium and hot-Kerr-dependent mediums. The light pulse delays and advances in different regions of dispersion medium with the Doppler broadening and coherent Kerr effect. Consequently, the pulse delays by $49μs$, while advance by $-91μs$, for a same set of parameters [note: a revised version is under preparation