Deterministic quantum logic with photons via optically induced photonic band gaps

We study the giant Kerr nonlinear interaction between two ultraweak optical fields in which the cross-phase-modulation is not accompanied by spectral broadening of the interacting pulses. This regime is realizable in atomic vapors, when a weak probe pulse, upon propagating through the electromagnetically induced transparency (EIT) medium, interacts with a signal pulse that is dynamically trapped in a photonic band gap created by spatially periodic modulation of its EIT resonance. We find that large conditional phase shifts and entanglement between the signal and probe fields can be obtained with this scheme. The attainable pi phase shift, accompanied by negligible absorption and quantum noise, is shown to allow a high-fidelity realization of the controlled-phase universal logic gate between two single-photon pulses.