Quantum processing photonic states in optical lattices

In a quantum network, transmission of quantum states is performed by photonic channels, which distribute them between remote locations. However, the storage and manipulation of the photons is more problematic. Recently, several schemes have been proposed to store photons efficiently by interfacing the photonic channel with an atomic system, i.e. an atomic ensemble. In those schemes, the photonic input state is transferred to a collective atomic state. But the manipulation of photonic states requires the ability to perform entangling operations. We show how to do this manipulation and perform a deterministic entangling gate between photons. To this order, we interface a system of cold neutral atoms in an optical lattice with the photonic channel, such that now the atoms are not only used to store information, but also to process it by means of cold controlled collisions in the lattice.