Few-Photon All-Optical {\pi} Phase modulation Based on a Double-{\Lambda} System

We propose an efficient all-optical phase modulation based on a double-{\Lambda} system and demonstrate a {\pi} phase shift of a few-photon pulse induced by another few-photon pulse in cold rubidium atoms with this scheme. By changing the phases of the applied laser fields, one can control the property of the double-{\Lambda} medium. This phase-dependent mechanism makes the double-{\Lambda} system different form the conventional cross-Kerr-based system which only depends on the applied laser intensities. The proposed scheme provides a new route to generate strong nonlinear interactions between photons, and may have potential for applications in quantum information technologies.