  We propose a scheme for a deterministic controlled-phase gate between two
photons based on the strong interaction between two stationary collective
Rydberg excitations in an atomic ensemble. The distance-dependent character of
the interaction causes both a momentum displacement of the collective
excitations and unwanted entanglement between them. We show that these effects
can be overcome by swapping the collective excitations in space and by
optimizing the geometry, resulting in a photon-photon gate with high fidelity
and efficiency.
