Interaction of four level closed loop atomic systems in the presence of two vector beams

In this manuscript, we have theoretically studied the four level closed loop atomic systems in the presence of two vector beams. A spatially dependent transparency for the probe vector beam is obtained based on the semiclassical model. We have explicitly shown that the number of petals formed for probe absorption depends on the value of orbital angular momentum (OAM) of the constituting beams. A detailed study for absorption and dispersion of right circularly polarized (RCP) and left circularly polarized (LCP) components of the probe beam is carried out and the importance of the polarization state of the beams on Higher Order Poincare Sphere (HOPS) is highlighted. An explicit effect of the interferometer phase of the vector beam which is geometric in nature, is shown for probe beam response. Three types of four level closed loop atomic system is studied with particular emphasis given for double ? and Diamond atomic system. A dark state analysis of the atomic system is carried out which facilitate a physical understanding of the obtained results. Our study has explored the effects of inhomogeneity in both polarization and intensity for probe and coupling beam in a closed loop atomic system which is phase dependent.