Light drag in a left-handed atomic medium via Cross Kerr-like nonlinearity

In this paper, we investigates the Cross Kerr-like nonlinearity effect on the quantum control of the light drag in a negative refractive index media ( NRI). Hence, we consider an atomic system in a four-level Y-type configuration, where a signal field couples the ground state to an upper level. Another weak probe field drives the intermediate transition to the excited state. The Kerr field pumps the excited state to another higher fourth transition. Therefore, we observe that the third-order optical non-linearities drastically contribute to the light drag enhancement of about 11 times. Interestingly, the light drag dynamics can be manipulated to shift from positive to negative, which allows the group delay and advancement to be fully controlled. Typically, an increase in the Kerr field, simultaneously with the detuning, induces an ultra-narrow, sharp peak in the light drag respectively at the resonance and far from the resonance with a group delay ranging from tau = -0.2 to tau = -2. The various interference pathways of light caused by the cross-kerr along with the probe, strong and signal fields not only enhance the light drag but can also be used to shift the light from subluminal to superluminal propagation under negative refraction. These results provide a framework for utilizing the Kerr-cross non-linearity to control the light drag in NRI, which is interesting in applications such as optical trapping.