Competition between attractive and repulsive interactions in two-component Bose-Einstein condensates trapped in an optical lattice

We consider effects of inter-species attraction on two-component gap solitons (GSs) in the binary BEC with intra-species repulsion, trapped in the one-dimensional optical lattice (OL). Systematic simulations of the coupled Gross-Pitaevskii equations (GPEs) corroborate an assumption that, because the effective mass of GSs is negative, the inter-species attraction may \emph{split} the two-component soliton. Two critical values, $\kappa_{1}$ and $\kappa_{2}$, of the OL strength ($\kappa$) are identified. Two-species GSs with fully overlapping wave functions are stable in strong lattices ($\kappa >\kappa_{1}$). In an intermediate region, $\kappa_{1}>\kappa >\kappa_{2}$, the soliton splits into a double-humped state with separated components. Finally, in weak lattices ($\kappa <\kappa_{2}$%), the splitting generates a pair of freely moving single-species GSs. We present and explain the dependence of $\kappa_{1}$ and $\kappa_{2}$ on thenumber of atoms (total norm), and on the relative strength of the competing inter-species attraction and intra-species repulsion. The splitting of asymmetric solitons, with unequal norms of the two species, is briefly considered too. It is found and explained that the splitting threshold grows with the increase of the asymmetry

Spontaneous symmetry breaking of gap solitons in double-well traps

We introduce a two dimensional model for the Bose-Einstein condensate with both attractive and repulsive nonlinearities. We assume a combination of a double well potential in one direction, and an optical lattice along the perpendicular coordinate. We look for dual core solitons in this model, focusing on their symmetry-breaking bifurcations. The analysis employs a variational approximation, which is verified by numerical results. The bifurcation which transforms antisymmetric gap solitons into asymmetric ones is of supercritical type in the case of repulsion; in the attraction model, increase of the optical latttice strength leads to a gradual transition from subcritical bifurcation (for symmetric solitons) to a supercritical one.Comment: 6 pages, 5 figure

Light Bullets in Nonlinear Periodically Curved Waveguide Arrays

We predict that stable mobile spatio-temporal solitons can exist in arrays of periodically curved optical waveguides. We find two-dimensional light bullets in one-dimensional arrays with harmonic waveguide bending and three-dimensional bullets in square lattices with helical waveguide bending using variational formalism. Stability of the light bullet solutions is confirmed by the direct numerical simulations which show that the light bullets can freely move across the curved arrays. This mobility property is a distinguishing characteristic compared to previously considered discrete light bullets which were trapped to a specific lattice site. These results suggest new possibilities for flexible spatio-temporal manipulation of optical pulses in photonic lattices.Comment: 7 pages, 4 figure

Statistical region based active contour using a fractional entropy descriptor: Application to nuclei cell segmentation in confocal microscopy images

We propose an unsupervised statistical region based active contour approach integrating an original fractional entropy measure for image segmentation with a particular application to single channel actin tagged fluorescence confocal microscopy image segmentation. Following description of statistical based active contour segmentation and the mathematical definition of the proposed fractional entropy descriptor, we demonstrate comparative segmentation results between the proposed approach and standard Shannon’s entropy on synthetic and natural images. We also show that the proposed unsupervised statistical based approach, integrating the fractional entropy measure, leads to very satisfactory segmentation of the cell nuclei from which shape characterization can be calculated

Computer-Assisted Segmentation of Videocapsule Images Using Alpha-Divergence-Based Active Contour in the Framework of Intestinal Pathologies Detection

Visualization of the entire length of the gastrointestinal tract through natural orifices is a challenge for endoscopists. Videoendoscopy is currently the “gold standard” technique for diagnosis of different pathologies of the intestinal tract. Wireless Capsule Endoscopy (WCE) has been developed in the 1990's as an alternative to videoendoscopy to allow direct examination of the gastrointestinal tract without any need for sedation. Nevertheless, the systematic post-examination by the specialist of the 50,000 (for the small bowel) to 150,000 images (for the colon) of a complete acquisition using WCE remains time-consuming and challenging due to the poor quality of WCE images. In this article, a semiautomatic segmentation for analysis of WCE images is proposed. Based on active contour segmentation, the proposed method introduces alpha-divergences, a flexible statistical similarity measure that gives a real flexibility to different types of gastrointestinal pathologies. Results of segmentation using the proposed approach are shown on different types of real-case examinations, from (multi-) polyp(s) segmentation, to radiation enteritis delineation

Fully three dimensional breather solitons can be created using Feshbach resonance

We investigate the stability properties of breather solitons in a three-dimensional Bose-Einstein Condensate with Feshbach Resonance Management of the scattering length and con ned only by a one dimensional optical lattice. We compare regions of stability in parameter space obtained from a fully 3D analysis with those from a quasi two-dimensional treatment. For moderate con nement we discover a new island of stability in the 3D case, not present in the quasi 2D treatment. Stable solutions from this region have nontrivial dynamics in the lattice direction, hence they describe fully 3D breather solitons. We demonstrate these solutions in direct numerical simulations and outline a possible way of creating robust 3D solitons in experiments in a Bose Einstein Condensate in a one-dimensional lattice. We point other possible applications.Comment: 4 pages, 4 figures; accepted to Physical Review Letter