Abstract
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.
Highlights
Spontaneous self-organization of near or out-of equilibrium states to ordered spatial structures has attracted considerable attention in many areas of science, technology and natural phenomena due to its appealing beauty, its importance in understanding how non-trivial structures can arise from homogeneous driving and the potential for applications [1,2,3,4,5]
The common feature of these systems is that self-organization occurs in the plane transverse to the propagation direction of the pump beam and that the spatial coupling is mediated by diffraction
For a Kerr nonlinearity this was explicitly calculated in [129], for an optomechanical model including velocity damping via an external molasses in [130]. In the latter model, inversion symmetry is reestablished at a critical coupling strength and a transition from honeycomb to hexagonal via stripe structures is obtained in the atomic density changing the linear phase shift [130]
Summary
Spontaneous self-organization of near or out-of equilibrium states to ordered spatial structures has attracted considerable attention in many areas of science, technology and natural phenomena due to its appealing beauty, its importance in understanding how non-trivial structures can arise from homogeneous driving and the potential for applications [1,2,3,4,5]. [51], respectively, the latter providing a first demonstration of a spontaneously structured atomic coherence In this contribution, we will review the mechanism of diffractive coupling in single mirror feedback systems and provide a unified treatment of the different situations and the requirements on optical density and nonlinear phase shift. This will start with a discussion of structures in cold, but thermal atoms and proceed to quantum degenerate gases. After discussion of the single mirror feedback case, we provide in Section 6 a brief coverage of cold atom structures in longitudinally pumped cavities due to diffractive coupling [52] and hint at potential experimental implementations.
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