Multiple self-organized phases and spatial solitons in cold atoms mediated by optical feedback

We study the transverse self-structuring of a cloud of cold atoms with effective atomic interactions mediated by a coherent driving beam retro-reflected by means of a single mirror. The resulting self-structuring due to optomechanical forces is much richer than that of an effective-Kerr medium, displaying hexagonal, stripe and honeycomb phases depending on the interaction strength parametrized by the linear susceptibility. Phase domains are described by real Ginzburg-Landau amplitude equations. In the stripe phase the system recovers inversion symmetry. Moreover, the subcritical character of the honeycomb phase allows for light-density feedback solitons functioning as self-sustained dark atomic traps with motion controlled by phase gradients in the driving beam.