Study of multi-window electromagnetically induced transparency (EIT) and related dispersive signals in V-type systems in the Zeeman sublevels of hyperfine states of ⁸⁷Rb-D₂ line

We have theoretically studied the multi-window electromagnetically induced transparency (EIT) and the related dispersive signals in multi-level V-type systems which are formed by the co-propagating circularly polarized pump (σ ⁻) and probe (σ ⁺) laser fields in the Zeeman sublevels of hyperfine states of ⁸⁷Rb-D₂ line. The optical Bloch equations (OBEs) are derived and numerically solved under the steady-state condition to obtain the probe absorption and dispersion spectra. We present the study of a single-window EIT for the three-level, double-window EIT for the four-level and triple-window EIT for the five-level V-type systems under both Doppler-free and Doppler-broadened conditions. The dispersive signals corresponding to the multi EIT windows for each system are also observed separately. From the knowledge of the slopes of the probe dispersion signals, we have calculated group index (n _g) of the medium considering three different V-type schemes. The effect of temperature on the EIT, dispersion and group index profiles is also studied in detail. It is found that the amplitudes of EIT and dispersion signals and also the positive and negative values of n _g are decreased as the temperature of the medium increases. To understand the Doppler-broadening effect on the group index profiles, we have considered three different velocity groups of atoms in the calculation of group index profiles. Moreover, the effects of probe intensity variation on the Doppler-broadened EIT and dispersive signals are studied extensively, and the conversions of EIT to EIA and dispersive positive slope to negative slope are observed under strong probe regime. Also, we have investigated the variation of dispersive slope and group index with the variation of probe intensity and probe frequency, respectively, at the multi-frequency position of the multi-window EIT. Finally, the switching between subluminal (slow light) to superluminal (fast light) propagation of light with the variation of both probe intensity and probe frequency is discussed in detail. (paper)