  There is a broad interest in enhancing the strength of light-atom
interactions to the point where injecting a single photon induces a nonlinear
material response. Here, we show theoretically that sub-Doppler-cooled,
two-level atoms that are spatially organized by weak optical fields give rise
to a nonlinear material response that is greatly enhanced beyond that
attainable in a homogeneous gas. Specifically, in the regime where the
intensity of the applied optical fields is much less than the off-resonant
saturation intensity, we show that the third-order nonlinear susceptibility
scales inversely with atomic temperature and, due to this scaling, can be two
orders of magnitude larger than that of a homogeneous gas for typical
experimental parameters. As a result, we predict that spatially bunched
two-level atoms can exhibit single-photon nonlinearities. Our model is valid
for all atomic temperature regimes and simultaneously accounts for the
back-action of the atoms on the optical fields. Our results agree with previous
theoretical and experimental results for light-atom interactions that have
considered only a limited range of temperatures. For lattice beams tuned to the
low-frequency side of the atomic transition, we find that the nonlinearity
transitions from a self-focusing type to a self-defocusing type at a critical
intensity. We also show that higher than third-order nonlinear optical
susceptibilities are significant in the regime where the dipole potential
energy is on the order of the atomic thermal energy. We therefore find that it
is crucial to retain high-order nonlinearities to accurately predict
interactions of laser fields with spatially organized ultracold atoms. The
model presented here is a foundation for modeling low-light-level nonlinear
optical processes for ultracold atoms in optical lattices.
