We consider the effective coupling of localized spins in a semiconductor quantum dot embedded in a microcavity. The lowest cavity mode and the quantum dot exciton are coupled and close in energy, forming a polariton. The fermions forming the exciton interact with localized spins via exchange. Exact diagonalization of a Hamiltonian in which photons, spins and excitons are treated quantum mechanically shows that {\it a single polariton} induces a sizable indirect exchange interaction between otherwise independent spins. The origin, symmetry properties and the intensity of that interaction depend both on the dot-cavity coupling and detuning. In the case of a (Cd,Mn)Te quantum dot, Mn-Mn ferromagnetic coupling mediated by a single photon survives above 1 K whereas the exciton mediated coupling survives at 15 K.
@article{arxiv.cond-mat/0407639,
title = {Single-photon exchange interaction in a semiconductor microcavity},
author = {G. Chiappe and J. Fernández-Rossier and E. Louis and E. Anda},
journal= {arXiv preprint arXiv:cond-mat/0407639},
year = {2009}
}