FIG. 4: Real (a) and imaginary (b) parts of susceptibility versus probe field detuning for the parameters γ = 1, r$_{1}$ = 1 . 5, r$_{2}$ = 0 . 0, Ω c = 0 . 7 (solid), 1 . 7 (dashed), 4 . 0 (dot-dashed), and 6 . 0 (dotted). | 1 〉 is split into two symmetric dressed levels | d $^{+}$〉 and | d $^{−}$〉 with frequency differences of ± Ω$_{c}$ from the original level. When the coupling field is weak, there still seems to be one gain deep and the dressed levels are indistin- guishable. By strengthening the coupling field, the gain deep is transformed to two gain deeps (see Fig.4). This is proportional to changing the normal slope of disper- sion to anomalous (negative) dispersion which leads to exceeding the group velocity from c (speed of light in vac- uum) or even may cause its becoming negative. When the dressed levels are partly distinguishable, system may still exhibits a considerable gain around zero detuning, which corresponds to existence of noise in the medium for a probe pulse with a middle frequency of ω$_{31}$ . By choosing a larger Rabi frequency for the coupling field, the gain becomes lesser and the anomalous region becomes wider. Then to achieve a transparent medium with anomalous dispersion, i.e. superluminal light propagation, a strong enough coupling field should be applied while the popu- lation is inverted for the probe field transition [26, 27]. If r$_{2}$ = 0, as Fig.3a shows, Ω$_{c}$ > 1 is the sufficient condition to switch the probe pulse propagation from subluminal to superluminal by application of the indirect incoherent pump of strength r$_{1}$ . For Ω$_{c}$ ≫ 1, r$_{1}$ = 1 is the thresh- old value at which the slope of dispersion changes from a lighter color is used to illustrate the more transpar- ent region. Finally, the contour lines of χ ′′ = − 0 . 15, − 0 . 11, − 0 . 07, − 0 . 03, − 0 . 012, and − 0 . 005, are plotted in black-dashed style. As Fig.3a illustrates, there are two regions of anomalous dispersion and one region of normal dispersion. As determined by Fig.3b, the first region of negative dispersion is due to the existence of an absorption line around zero probe field detuning and occurs where Ω$_{c}$ , r$_{1}$ < 1. The solid lines of Fig.2 can be regarded as an example of this region. The other re- gion of negative dispersion happens where Ω$_{c}$ , r$_{1}$ > 1, while according to Fig.3b it accompanies by gain. For the region of normal dispersion, as Fig.3b demonstrates, the absorption property can take either a small positive or a large negative value, proportional to negligible at- tenuation or strong amplification of the probe field, re- spectively. Fig.4 and Fig.5 are presented to clarify how positive and negative dispersions can occur in the gain region of Ω$_{c}$ and r$_{1}$ plane. By the indirect incoher- ent pump of strength r$_{1}$ > γ (see Eq.5c), the inversion of population between levels | 1 〉 and | 3 〉 is established. In this situation the system shows amplification for the probe field. Then there exists a gain deep with positive slope of dispersion around zero detuning (see the red- solid lines of Fig.4). By applying the coupling field level FIG. 5: Real (a) and imaginary (b) parts of susceptibility versus probe field detuning for the parameters γ = 1, Ω c = 1 . 69, r$_{2}$ = 0, r$_{1}$ = 1 . 2 (solid), 1 . 5 (dashed), and 3 . 0 (dot- dashed). 4 GLYPH<Minus> 6 GLYPH<Minus> 4 GLYPH<Minus> 2 0 2 4 6 GLYPH<Minus> 0.05 0.00 0.05 GLYPH<CapDelta>$_{p}$ Re GLYPH<LParen1> Χ GLYPH<RParen1> GLYPH<Minus> 6 GLYPH<Minus> 4 GLYPH<Minus> 2 0 2 4 6 GLYPH<Minus> 0.15 GLYPH<Minus> 0.10 GLYPH<Minus> 0.05 0.00 GLYPH<CapDelta>$_{p}$ Im GLYPH<LParen1> Χ GLYPH<RParen1> a b GLYPH<Minus> 6 GLYPH<Minus> 4 GLYPH<Minus> 2 0 2 4 6 GLYPH<Minus> 0.05 0.00 0.05 GLYPH<CapDelta>$_{p}$ Re GLYPH<LParen1> Χ GLYPH<RParen1> GLYPH<Minus> 6 GLYPH<Minus> 4 GLYPH<Minus> 2 0 2 4 6 GLYPH<Minus> 0.15 GLYPH<Minus> 0.10 GLYPH<Minus> 0.05 0.00 GLYPH<CapDelta>$_{p}$ Im GLYPH<LParen1> Χ GLYPH<RParen1> a b