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We propose a scheme to exchange optical vortices of slow light using thephenomenon of electromagnetically induced transparency (EIT) in a four-leveldouble-$\Lambda$ atom-light coupling scheme illuminated by a pair of probefields as well as two control fields of larger intensity. We study thelight-matter interaction under the situation where one control field carries anoptical vortex, and another control field has no vortex. We show that theorbital angular momentum (OAM) of the vortex control beam can be transferred toa generated probe field through a four-wave mixing (FWM) process and withoutswitching on and off of the control fields. Such a mechanism of OAM transfer ismuch simpler than in a double-tripod scheme in which the exchange of vorticesis possible only when two control fields carry optical vortices of oppositehelicity. The losses appearing during such OAM exchange are then calculated. Itis found that the one-photon detuning plays an important role in minimizing thelosses. An approximate analytical expression is obtained for the optimalone-photon detuning for which the losses are minimum while the intensity ofgenerated probe field is maximum. The influence of phase mismatch on theexchange of optical vortices is also investigated. We show that in presence ofphase mismatch the exchange of optical vortices can still be efficient.

Exchange of optical vortices using an electromagnetically induced transparency based four-wave mixing setup