  We propose a method to induce strong effective interactions between photons
mediated by an atomic ensemble. To achieve this, we use the so-called
stationary light effect to enhance the interaction. Regardless of the
single-atom coupling to light, the interaction strength between the photons can
be enhanced by increasing the total number of atoms. For sufficiently many
atoms, the setup can be viable as a controlled-phase gate for photons. We
derive analytical expressions for the fidelities for two modes of gate
operation: deterministic and heralded conditioned on the presence of two
photons at the output.
