Full quantum solutions to the resonant four-wave mixing of two single-photon wave packets

We analyze both analytically and numerically the resonant four-wave mixing of two co-propagating single-photon wave packets. We present analytic expressions for the two-photon wave function and show that soliton-type quantum solutions exist which display a shape-preserving oscillatory exchange of excitations between the modes. Potential applications including quantum information processing are discussed.