Giant Kerr nonlinearities obtained by electromagnetically induced transparency

We analyze a cross-phase modulation (XPM) scheme that exhibits a giant, resonantly enhanced nonlinearity, along with vanishing linear susceptibilities. The proposed atomic system uses an electromagnetically induced transparency and is limited only by two-photon absorption. We predict dramatic improvement by several orders of magnitude for conditional phase shifts in XPM, and the system has possible applications in quantum nondemolition measurements and for quantum logic gates.