Nonlinear optics with polar molecules in optical lattices

We explore the feasibility of ultracold polar molecules in optical lattices for realization of efficient photon-photon interactions in quantum information processing. Photon-photon interaction is implemented by converting photons into collective molecular excitations using dark-state polaritons via the electromagnetically induced transparency effect. As a result of dipole-dipole interaction between polar molecules in the lattice the polaritons acquire a nonlinear phase shift, which allows one to realize a photonic phase gate. We discuss major decoherence mechanisms, such as decay from symmetric molecular collective excited states, and explore doubly occupied lattices as a means to avoid this difficulty.