Light propagation through closed-loop atomic media beyond the multiphoton resonance condition

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. The finite frequency width of the probe pulse requires a time-dependent analysis beyond the multiphoton resonance assumption. We apply a Floquet decomposition to the equations of motion to solve this time-dependent problem and to identify the different scattering processes contributing to the medium response. We find that the response oscillating in phase with the probe field is phase-independent. 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. In particular for short pulses with a large frequency width, inducing a closed loop interaction contour may lead to a distortion of the pulse shape via this phase-sensitive scattering. Finally, we demonstrate that both the closed loop and the nonclosed loop configuration allow for sub- and superluminal light propagation with small absorption or even gain, where one of the coupling field Rabi frequencies acts as a control parameter that enables one to switch between sub- and superluminal light propagation.