Orbital angular momentum swapping of light via biexciton coherence

In this paper we study orbital angular momentum (OAM) transfer between applied lights via biexciton coherence and exciton spin coherence. The quantum dot derives by two control fields that couple to a biexciton state which leads to the destructive interference, while a weak probe light interacts by one of the ground-level exciton transitions. In this scenario, a new weak signal light can be generated via the four-wave mixing (FWM) mechanism in a second ground-level exciton transition. We will study the role of exciton spin relaxation as well as intensity of coupling lights on the exchange efficiency of FWM mechanism. We will also discuss the spatially dependent optical effects via OAM state and azimuthal angle of vortex light.