A theoretical study of the group refractive index ng in a four-level inverted Y-type system formed by 87Rb atom – laser radiation interaction

We report a theoretical investigation of the dispersion resulting from electromagnetically induced transparency (EIT) and the associated group refractive index profiles n_g of a four-level inverted Y-type system formed by the interaction of three optical fields (probe, pump and control) with ⁸⁷Rb atoms. The density matrix equations are derived from the semi-classical Liouville's equation and solved both numerically and analytically to study the coherent nonlinear optical properties of the medium. We first present the EIT, dispersion and corresponding group index profiles n_g under the switch-on/off and on/off-resonance conditions of the pump and control lasers. In presence of both pump and control lasers, an enhancement of the EIT window, a sharp EIT spike and related steeper dispersion slopes are obtained at the line centre of the probe frequency detuning. The group index profiles with the variation of the strengths of individual applied optical fields are studied. The effect of the ground state decoherence rates on the group index profile is examined in detail. It is found that the manipulation of n_g values and the corresponding group velocities υ_g of the probe light can be easily controlled from subluminal to superluminal values or vice versa by changing the strengths of the applied fields and the ground state decoherence rates. Besides, the EITbased 'optical switching' phenomenon in the medium is explained by studying the variation of the group index with the pump and control Rabi frequencies.