  We propose a new method to produce self- and cross-Kerr photonic
nonlinearities, using light-induced Stark shifts due to the interaction of a
cavity mode with atoms. The proposed experimental set-up is considerably
simpler than in previous approaches, while the strength of the nonlinearity
obtained with a single atom is the same as in the setting based on
electromagnetically induced transparency. Furthermore our scheme can be applied
to engineer effective photonic nonlinear interactions whose strength increases
with the number of atoms coupled to the cavity mode, leading to photon-photon
interactions several orders of magnitude larger than previously considered
possible.
