  The study of transverse optical pattern formation has been studied
extensively in nonlinear optics, with a recent experimental interest in
studying the phenomenon using cold atoms, which can undergo real-space
self-organization. Here, we describe our experimental observation of pattern
formation in cold atoms, which occurs using less than 1 microWatt of applied
power. We show that the optical patterns and the self-organized atomic
structures undergo continuous symmetry-breaking, which is characteristic of
non-equilibrium phenomena in a multimode system. To theoretically describe
pattern formation in cold atoms, we present a self-consistent model that allows
for tight atomic bunching in the applied optical lattice. We derive the
nonlinear refractive index of a gas of multi-level atoms in an optical lattice,
and we derive the threshold conditions under which pattern formation occurs. We
show that, by using small detunings and sub-Doppler temperatures, one achieves
two orders of magnitude reduced intensity thresholds for pattern formation
compared to warm atoms.
