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We report on the observation of spontaneously drifting coupled spin and quadrupolar density waves in the ground state of laser driven Rubidium atoms. These laser-cooled atomic ensembles exhibit spontaneous magnetism via light mediated interactions when submitted to optical feedback by a retro-reflecting mirror. Drift direction and chirality of the waves arise from spontaneous symmetry breaking. The observations demonstrate a novel transport process in out-of-equilibrium magnetic systems.

Self-organized phases in cold atoms as a result of light-mediated interactions can be induced by coupling to internal or external degrees of the atoms. There has been growing interest in the interaction of internal spin degrees of freedom with the optomechanical dynamics of the external centre-of-mass motion. We present a model for the coupling between magnetic and optomechanical structuring in a $J=1/2 \to J'=3/2$ system in a single-mirror feedback scheme, being representative for a larger class of diffractively coupled systems such as longitudinally pumped cavities and counter-propagating beam schemes. For negative detunings, a linear stability analysis demonstrates that optical pumping and optomechanical driving cooperate to create magnetic ordering. However, for long-period transmission gratings the magnetic driving will strongly dominate the optomechanical driving, unless one operates very close to the existence range of the magnetic instability. At small lattice periods, in particular at wavelength-scale periods, the optomechanical driving will dominate.

The properties of vector vortex beams in vertical-cavity-surface emitting lasers with frequency-selective feedback is investigated. They are interpreted as high-order vortex solitons with a spatially non-uniform, but locally linear polarization state. In contrast to most schemes to obtain vector vortex beams relying on imprinting the polarization structure, vector vortex solitons form spontaneously due to the near polarization degeneracy in vertical-cavity devices. We observe radially, hyperbolic and spiral polarization configurations depending on small residual anisotropies in the system and multi-stability between different states. In addition, we demonstrate flip-flop operation of laser solitons via in principle local electronic nonlinearities. Combining the two themes might open up a route for a simple device enabling fast switching between different vector vortex beams for applications. The investigations connect nicely the fields of nonlinear science, singular optics, structured light and semiconductor laser technology.

A systematic experimental and numerical investigation of the conditions for the spontaneous formation of laser cavity solitons in broad-area vertical-cavity surface-emitting lasers with frequency-selective feedback by a volume Bragg grating is reported. It is shown that the switching thresholds are controlled by a combination of frequency shifts induced by ambient temperature and Joule heating. The gain level has only a minor influence on the threshold but controls mainly the power of the solitons. At large initial detuning and high threshold gain, the first observed structure can be a high order soliton. In real devices spatial disorder in the cavity length causes a pinning of solitons and a dispersion of thresholds. The experimental observations are in good agreement with numerical simulations taking into account disorder and the coupling of gain and cavity resonance due to Joule heating. In particular, we demonstrate that the existence of the traps explain the spontaneous switch on of the solitons,but do not modify the soliton shape significantly, i.e. the observed solitons are a good approximation of the ones expected in a homogenous system., Comment: Accepted for publication 23 December 2015; published 2 February 2016

We study a pattern forming instability in a laser driven optically thick cloud of cold two-level atoms with a planar feedback mirror. A theoretical model is developed, enabling a full analysis of transverse patterns in a medium with saturable nonlinearity, taking into account diffraction within the medium, and both the transmission and reflection gratings. Focus of the analysis is on combined treatment of nonlinear propagation in a diffractively- and optically-thick medium and the boundary condition given by feedback. We demonstrate explicitly how diffraction within the medium breaks the degeneracy of Talbot modes inherent in thin slice models. Existence of envelope curves bounding all possible pattern formation thresholds is predicted. The importance of envelope curves and their interaction with threshold curves is illustrated by experimental observation of a sudden transition between length scales as mirror displacement is varied., Comment: arXiv admin note: substantial text overlap with arXiv:1606.04885

The spontaneous emergence of vector vortex beams with non-uniform polarization distribution is reported in a vertical-cavity surface-emitting laser (VCSEL) with frequency-selective feedback. Antivortices with a hyperbolic polarization structure and radially polarized vortices are demonstrated. They exist close to and partially coexist with vortices with uniform and non-uniform polarization distributions characterized by four domains of pairwise orthogonal polarization. The spontaneous formation of these nontrivial structures in a simple, nearly isotropic VCSEL system is remarkable and the vector vortices are argued to have soliton-like properties.

A stable nonlinear wave packet, self-localized in all three dimensions, is an intriguing and much sought after object in nonlinear science in general and in nonlinear photonics in particular. We report on the experimental observation of mode-locked spatial laser solitons in a vertical-cavity surface-emitting laser with frequency-selective feedback from an external cavity. These spontaneously emerging and long-term stable spatio-temporal structures have a pulse length shorter than the cavity round trip time and may pave the way to completely independent cavity light bullets.

Motionless domains walls representing heteroclinic temporal or spatial orbits typically exist only for very specific parameters. This report introduces a novel mechanism for stabilizing temporal domain walls away from the Maxwell point opening up new possibilities to encode information in dynamical systems. It is based on anti-periodic regimes in a delayed system close to a bistable situation, leading to a cancellation of the average drift velocity. The results are demonstrated in a normal form model and experimentally in a laser with optical injection and delayed feedback., Comment: 6 pages, 5 figures, resubmitted manuscript

Transverse pattern formation in an optical cavity containing a cloud of cold two-level atoms is discussed. We show that density modulation becomes the dominant mechanism as the atomic temperature is reduced. Indeed, for low but achievable temperatures the internal degrees of freedom of the atoms can be neglected, and the system is well described by treating them as mobile dielectric particles. A linear stability analysis predicts the instability threshold and the spatial scale of the emergent pattern. Numerical simulations in one and two transverse dimensions confirm the instability and predict honeycomb and hexagonal density structures, respectively, for the blue and red detuned cases., Comment: submitted to Physical Review Letters

Defects due to growth fluctuations in broad-area semiconductor lasers induce pinning and frequency shifts of spatial laser solitons. The effects of defects on the interaction of two solitons are considered in lasers with frequency-selective feedback both theoretically and experimentally. We demonstrate frequency and phase synchronization of paired laser solitons as their detuning is varied. In both theory and experiment the locking behavior is well described by the Adler model for the synchronization of coupled oscillators., Comment: 5 pages, 5 figures

For highly divergent emission of broad-area vertical-cavity surface-emitting lasers (VCSELs) a rotation of the polarization direction by up to 90 degrees occurs when the pump rate approaches the lasing threshold. Well below threshold the polarization is parallel to the direction of the transverse wave vector and is determined by the transmissive properties of the Bragg reflectors that form the cavity mirrors. In contrast, near-threshold and above-threshold emission is more affected by the reflective properties of the reflectors and is predominantly perpendicular to the direction of transverse wave vectors. Two qualitatively different types of polarization transition are demonstrated: an abrupt transition, where the light polarization vanishes at the point of the transition, and a smooth one, where it is significantly nonzero during the transition.

We consider pattern selection process in a wide aperture VCSEL near threshold. We show that for a square geometry of the laser aperture, the patterns formed at lasing threshold can be very complicated because of a possible misalignment between directions of an intrinsic spatial anisotropy of VCSEL and lateral boundaries of its aperture. The analogy with quantum billiard structures is established, and fingerprints of wave chaos are found. Influence of localized inhomogeneous in the pump current is also considered., Comment: 10 pages, 8 figures, uses REVTEX4