This article discusses self-organization in cold atoms via light-mediated interactions induced by feedback from a single retro-reflecting mirror. Diffractive dephasing between the pump beam and the spontaneous sidebands selects the lattice period. Spontaneous breaking of the rotational and translational symmetry occur in the 2D plane transverse to the pump. We elucidate how diffractive ripples couple sites on the self-induced atomic lattice. The nonlinear phase shift of the atomic cloud imprinted onto the optical beam is the parameter determining coupling strength. The interaction can be tailored to operate either on external degrees of freedom leading to atomic crystallization for thermal atoms and supersolids for a quantum degenerate gas, or on internal degrees of freedom like populations of the excited state or Zeeman sublevels. Using the light polarization degrees of freedom on the Poincaré sphere (helicity and polarization direction), specific irreducible tensor components of the atomic Zeeman states can be coupled leading to spontaneous magnetic ordering of states of dipolar and quadrupolar nature. The requirements for critical interaction strength are compared for the different situations. Connections and extensions to longitudinally pumped cavities, counterpropagating beam schemes and the CARL instability are discussed.

We investigate numerically a one-dimensional Bose-Einstein Condensate illuminated by offresonant laser light which is retroreflected by a single feedback mirror. Studying the ground states of the system, we find density structures which are self-trapped via the optomechanical action of the diffracted light. We show that these structures are stable and exhibit Newtonian dynamics. We propose that these results allow continuous, non-destructive monitoring of condensate dynamics via the optical intensity and may offer new opportunities for optical control and transport of coherent matter via gradients in optical phase alone.I.

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We investigate the interplay between two mechanisms for magnetic self-organization in a cloud of cold rubidium atoms subjected to a retroreflected laser beam. The transition between two different phases, one linked to a spontaneous spatial modulation of the m = 2 ground-state coherence and the other to that of the magnetic orientation (spin), can be induced by tuning either a weak transverse magnetic field or the laser intensity. We observe both first-and second-order transitions depending on the presence of the magnetic field. The experimental observations are successfully compared to extended numerical simulations based on a spin-1 model.

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