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The light propagation of a probe field pulse in a four-level double-lambda type system driven by laser fields that form a closed interaction loop is studied. Due to the finite frequency width of the probe pulse, a time-independent analysis relying on the multiphoton resonance assumption is insufficient. Thus we apply a Floquet decomposition of the equations of motion to solve the timedependent problem beyond the multiphoton resonance condition. We find that the various Floquet components can be interpreted in terms of different scattering processes, and that the medium response oscillating in phase with the probe field in general is not phase-dependent. The phase dependence arises from a scattering of the coupling fields into the probe field mode at a frequency which in general differs from the probe field frequency. We thus conclude that in particular for short pulses with a large frequency width, inducing a closed loop interaction contour may not be advantageous, since otherwise the phase-dependent medium response may lead to a distortion of the pulse shape. Finally, using our time-dependent analysis, we demonstrate that both the closed-loop and the non-closed loop configuration allow for sub-and superluminal light propagation with small absorption or even gain. Further, we identify one of the coupling field Rabi frequencies as a control parameter that allows to conveniently switch between sub-and superluminal light propagation.

This paper studies the effects of the incoherent pumping field and the spontaneously generated coherence (SGC) on the phase control of group velocity. The effects of a relative phase between probe and coupling fields on the absorption and the dispersion are then discussed. It is shown that the phase dependence of the group velocity not only depends on the existence of the SGC, but also depends on the existence of the incoherent pump field. We show that for the weak probe field, and in the presence of SGC, the existence of the incoherent pump field is a necessary condition for the phase control of the dispersion, the absorption and the group index.

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