In this study, we introduced a model utilizing a plasmonic nanostructure to modulate the entanglement between atoms and photons within a V-type atomic medium. This system is influenced by composite optical vortex light (COVL) and two incoherent pumping fields. The plasmonic nanostructure comprises dielectric nanospheres, which have been thoroughly investigated (Phys. Rev. B 106, 035419, 2022). By adjusting the orbital angular momentum (OAM) of COVL, we demonstrate that the nanostructure induces significant spatial variations in the degree of entanglement (DEM). Additionally, incorporating a weak incoherent pumping field affects the DEM profile within the hybrid system. Our findings reveal that the OAM of structured light can govern the spatial dependence of DEM, particularly when quantum interference from the nanostructure and pumping fields surpasses a specific threshold. Furthermore, our results suggest that analyzing the DEM profile's spatial regions can be employed to determine the OAM number of the structured light.
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