  We theoretically demonstrate how the resonant coupling between a pair of
cavity-polaritons and a biexciton state can lead to a large single-photon Kerr
nonlinearity in a semiconductor solid-state system. A fully analytical model of
the scattering process between a pair of cavity-polaritons is developed, which
explicitly includes the biexcitonic intermediate state. A dramatic enhancement
of the polariton-polariton interactions is predicted in the vicinity of the
biexciton Feshbach resonance. Application to the generation of non-classical
light from polariton dots is discussed.
