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We propose a procedure to achieve a complete energy conversion between laserpulses carrying orbital angular momentum (OAM) in a cloud of cold atomscharacterized by a double-\Lambda atom-light coupling scheme. A pair ofresonant spatially dependent control fields prepare atoms in aposition-dependent coherent population trapping state, while a pair of muchweaker vortex probe beams propagate in the coherently driven atomic medium.Using the adiabatic approximation we derive the propagation equations for theprobe beams. We consider a situation where the second control field is absentat the entrance to the atomic cloud and the first control field goes to zero atthe end of the atomic medium. In that case the incident vortex probe beam cantransfer its OAM to a generated probe beam. We show that the efficiency of suchan energy conversion approaches the unity under the adiabatic condition. On theother hand, by using spatially independent profiles of the control fields, themaximum conversion efficiency is only 1/2.

physical review. a/physical review, a

Complete energy conversion between light beams carrying orbital angular  momentum using coherent population trapping for a coherently driven  double-\Lambda atom-light coupling