Study of atomic coherence effects in multi-level V plus Ξ system involving Rydberg state

We present theoretical model to investigate the influence of hyperfine levels on the atomic coherences of V+Xi Rydberg system. Using density matrix formulation, an analytical expression of atomic coherence for weak probe field is derived. The closely spaced hyperfine levels cause asymmetry and red shift while wavelength mismatching induced due to Rydberg state leads to reduction in magnitude and broadening of group index, absorption and dispersion profiles for moving atoms. Our system shows both Rydberg Electro-magnetically induced transparency (EIT) with subluminal behavior and Rydberg Electromagnetically induced absorption (EIA) with superluminal propagation by adjusting the strengths of control and switching fields. Variation of group index with probe detuning reveals anomalous dispersion regions at Autler-Townes doublet positions. Group index for Doppler-broadened atoms at resonance condition has lower magnitude as compared to the stationary atoms and hence the group delay time of the pulse is also reduced. We also explore in-depth non-degenerate four-wave mixing (FWM) which is ignited due to the presence of three electromagnetic (e.m.) fields and concurrently, establish relationship between FWM and multi-photon atomic coherence. The transient behavior is also studied for practical realization of our considered system as optical switch.