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 ν _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 EIT-based ‘optical switching’ phenomenon in the medium is explained by studying the variation of the group index with the pump and control Rabi frequencies.

我们报告了由电磁感应透明度 (EIT) 产生的色散的理论研究，以及由三个光场（探针、泵浦和控制）相互作用形成的四级倒 Y 型系统的相关群折射率分布n _g有^{87 个}Rb 原子。密度矩阵方程源自半经典刘维尔方程，并通过数值和解析求解，以研究介质的相干非线性光学特性。我们首先展示了 EIT、离散度和相应的组指数分布n _g在泵浦和控制激光器的开/关和开/关谐振条件下。在同时存在泵浦激光器和控制激光器的情况下，在探头频率失谐的线中心获得了 EIT 窗口的增强、尖锐的 EIT 尖峰和相关的更陡峭的色散斜率。研究了随着单个应用光场强度变化的群指数分布。详细检查了基态退相干率对群指数分布的影响。发现操纵n _g值和相应的群速度ν _g通过改变外加场的强度和基态退相干率，可以很容易地控制探测光从亚光速到超光速值，反之亦然。此外，通过研究群指数随泵浦和控制 Rabi 频率的变化，解释了介质中基于 EIT 的“光切换”现象。