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We consider the effective coupling of localized spins in a semiconductorquantum dot embedded in a microcavity. The lowest cavity mode and the quantumdot exciton are coupled and close in energy, forming a polariton. The fermionsforming the exciton interact with localized spins via exchange. Exactdiagonalization of a Hamiltonian in which photons, spins and excitons aretreated quantum mechanically shows that {\it a single polariton} induces asizable indirect exchange interaction between otherwise independent spins. Theorigin, symmetry properties and the intensity of that interaction depend bothon the dot-cavity coupling and detuning. In the case of a (Cd,Mn)Te quantumdot, Mn-Mn ferromagnetic coupling mediated by a single photon survives above 1K whereas the exciton mediated coupling survives at 15 K.Comment: 4 pages, 3 figure

Anisotropic exchange interaction induced by a single photon in semiconductor microcavities