Using a gradient echo memory, we experimentally demonstrate cross phase modulation (XPM) between two optical pulses; one stored and one freely propagating through the memory medium. We explain how this idea can be extended to enable substantial nonlinear interaction between two single photons that are both stored in the memory. We present semi-classical and quantum simulations along with a proposed experimental scheme to demonstrate the feasibility of achieving large XPM at single photon level.
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