Delocalizing transition of multidimensional solitons in Bose-Einstein condensates

Critical behavior of solitonic waveforms of Bose-Einstein condensates in optical lattices (OL) has been studied in the framework of continuous mean-field equation. In 2D and 3D OLs bright matter-wave solitons undergo abrupt delocalization as the strength of the OL is decreased below some critical value. Similar delocalizing transition happens when the coefficient of nonlinearity crosses the critical value. Contrarily, bright solitons in 1D OLs retain their integrity over the whole range of parameter variations. The interpretation of the phenomenon in terms of quantum bound states in the effective potential is proposed.Comment: 12 pages, 19 figures, submitted to Phys. Rev.

Domain walls and bubble-droplets in immiscible binary Bose gases

The existence and stability of domain walls (DWs) and bubble-droplet (BD) states in binary mixtures of quasi-one-dimensional ultracold Bose gases with inter- and intra-species repulsive interactions is considered. Previously, DWs were studied by means of coupled systems of Gross-Pitaevskii equations (GPEs) with cubic terms, which model immiscible binary Bose-Einstein condensates (BECs). We address immiscible BECs with two- and three-body repulsive interactions, as well as binary Tonks--Girardeau (TG) gases, using systems of GPEs with cubic and quintic nonlinearities for the binary BEC, and coupled nonlinear Schr\"{o}dinger equations with quintic terms for the TG gases. Exact DW\ solutions are found for the symmetric BEC mixture, with equal intra-species scattering lengths. Stable asymmetric DWs in the BEC mixtures with dissimilar interactions in the two components, as well as of symmetric and asymmetric DWs in the binary TG gas, are found by means of numerical and approximate analytical methods. In the BEC system, DWs can be easily put in motion by phase imprinting. Combining a DW and anti-DW on a ring, we construct BD states for both the BEC and TG models. These consist of a dark soliton in one component (the "bubble"), and a bright soliton (the "droplet") in the other. In the BEC system, these composite states are mobile too.Comment: Phys. Rev. A, in pres

Matter-wave solitons in radially periodic potentials

We investigate two-dimensional (2D) states of Bose-Einstein condensates (BEC) with self-attraction or self-repulsion, trapped in an axially symmetric optical-lattice potential periodic along the radius. Unlike previously studied 2D models with Bessel lattices, no localized states exist in the linear limit of the present model, hence all localized states are truly nonlinear ones. We consider the states trapped in the central potential well, and in remote circular troughs. In both cases, a new species, in the form of \textit{radial gap solitons}, are found in the repulsive model (the gap soliton trapped in a circular trough may additionally support stable dark-soliton pairs). In remote troughs, stable localized states may assume a ring-like shape, or shrink into strongly localized solitons. The existence of stable annular states, both azimuthally uniform and weakly modulated ones, is corroborated by simulations of the corresponding Gross-Pitaevskii equation. Dynamics of strongly localized solitons circulating in the troughs is also studied. While the solitons with sufficiently small velocities are stable, fast solitons gradually decay, due to the leakage of matter into the adjacent trough under the action of the centrifugal force. Collisions between solitons are investigated too. Head-on collisions of in-phase solitons lead to the collapse; $\pi$-out of phase solitons bounce many times, but eventually merge into a single soliton without collapsing. The proposed setting may also be realized in terms of spatial solitons in photonic-crystal fibers with a radial structure.Comment: 16 pages, 23 figure

Gap-Townes solitons and localized excitations in low dimensional Bose Einstein condensates in optical lattices

We discuss localized ground states of Bose-Einstein condensates in optical lattices with attractive and repulsive three-body interactions in the framework of a quintic nonlinear Schr\"odinger equation which extends the Gross-Pitaevskii equation to the one dimensional case. We use both a variational method and a self-consistent approach to show the existence of unstable localized excitations which are similar to Townes solitons of the cubic nonlinear Schr\"odinger equation in two dimensions. These solutions are shown to be located in the forbidden zones of the band structure, very close to the band edges, separating decaying states from stable localized ones (gap-solitons) fully characterizing their delocalizing transition. In this context usual gap solitons appear as a mechanism for arresting collapse in low dimensional BEC in optical lattices with attractive real three-body interaction. The influence of the imaginary part of the three-body interaction, leading to dissipative effects on gap solitons and the effect of atoms feeding from the thermal cloud are also discussed. These results may be of interest for both BEC in atomic chip and Tonks-Girardeau gas in optical lattices

Multidimensional semi-gap solitons in a periodic potential

The existence, stability and other dynamical properties of a new type of multi-dimensional (2D or 3D) solitons supported by a transverse low-dimensional (1D or 2D, respectively) periodic potential in the nonlinear Schr\"{o}dinger equation with the self-defocusing cubic nonlinearity are studied. The equation describes propagation of light in a medium with normal group-velocity dispersion (GVD). Strictly speaking, solitons cannot exist in the model, as its spectrum does not support a true bandgap. Nevertheless, the variational approximation (VA) and numerical computations reveal stable solutions that seem as completely localized ones, an explanation to which is given. The solutions are of the gap-soliton type in the transverse direction(s), in which the periodic potential acts in combination with the diffraction and self-defocusing nonlinearity. Simultaneously, in the longitudinal (temporal) direction these are ordinary solitons, supported by the balance of the normal GVD and defocusing nonlinearity. Stability of the solitons is predicted by the VA, and corroborated by direct simulations.Comment: European Physical Joournal D, in pres

Multidimensional solitons in a low-dimensional periodic potential

Using the variational approximation(VA) and direct simulations, we find stable 2D and 3D solitons in the self-attractive Gross-Pitaevskii equation (GPE) with a potential which is uniform in one direction ($z$) and periodic in the others (but the quasi-1D potentials cannot stabilize 3D solitons). The family of solitons includes single- and multi-peaked ones. The results apply to Bose-Einstein condensates (BECs) in optical lattices (OLs), and to spatial or spatiotemporal solitons in layered optical media. This is the first prediction of {\em mobile} 2D and 3D solitons in BECs, as they keep mobility along $z$. Head-on collisions of in-phase solitons lead to their fusion into a collapsing pulse. Solitons colliding in adjacent OL-induced channels may form a bound state (BS), which then relaxes to a stable asymmetric form. An initially unstable soliton splits into a three-soliton BS. Localized states in the self-repulsive GPE with the low-dimensional OL are found too.Comment: 4 pages, 5 figure

Dal quadro al modello virtuale: una ricostruzione tridimensionale interattiva dell'Albergheria di Palermo nel 1749

This study suggests a virtual three-dimensional reconstruction of a large urban portion of Palermo Historical Centre modelled on an isometrical view of the 17th century entitled Descrizzione del distretto parrocchiale dell’Albergheria fatta l’anno 1749. It is a painting on canvas that has been kept inside the parish of S.Nicolò all’Albergheria, and which in latter days has been taken by the Museum of Palermo Diocese where it is presently exposed to the public. The work presents different levels of interest for the reading of urban ancient morphology which now has disappeared and for the right information of road textures, blocks and monuments represented there. The digital elaboration that has been made has been overlayed to a second three-dimensional model that has been got from the present maps of Palermo Historical Centre which describe the present configuration of the quarter: thus the model which derives from the 17th century representation has been referred to the real quotes of the ground and to the elevations of the existing buildings which are illustrated and described in the picture. Then all the proposed material has been used to make a new reading of the work and to propose its transformation in a “visual hypertext”. All the elements of the picture have been “translated” as file folders, links about the town history and of its monuments, either disappeared or still existing

Gap-Townes solitons and delocalizing transitions of multidimensional Bose-Einstein condensates in optical lattices

We show the existence of gap-Townes solitons for the multidimensional Gross-Pitaeviskii equation with attractive interactions and in two- and three-dimensional optical lattices. In absence of the periodic potential the solution reduces to the known Townes solitons of the multi-dimensional nonlinear Schr\"odinger equation, sharing with these the propriety of being unstable against small norm (number of atoms) variations. We show that in the presence of the optical lattice the solution separates stable localized solutions (gap-solitons) from decaying ones, characterizing the delocalizing transition occurring in the multidimensional case. The link between these higher dimensional solutions and the ones of one dimensional nonlinear Schr\"odinger equation with higher order nonlinearities is also discussed.Comment: 14 pages, 6 figure

Multidimensional solitons in periodic potentials

The existence of stable solitons in two- and three-dimensional (2D and 3D) media governed by the self-focusing cubic nonlinear Schr\"{o}dinger equation with a periodic potential is demonstrated by means of the variational approximation (VA) and in direct simulations. The potential stabilizes the solitons against collapse. Direct physical realizations are a Bose-Einstein condensate (BEC) trapped in an optical lattice, and a light beam in a bulk Kerr medium of a photonic-crystal type. In the 2D case, the creation of the soliton in a weak lattice potential is possible if the norm of the field (number of atoms in BEC, or optical power in the Kerr medium) exceeds a threshold value (which is smaller than the critical norm leading to collapse). Both "single-cell" and "multi-cell" solitons are found, which occupy, respectively, one or several cells of the periodic potential, depending on the soliton's norm. Solitons of the former type and their stability are well predicted by VA. Stable 2D vortex solitons are found too.Comment: 13 pages, 3 figures, Europhys. Lett., in pres

Shock waves in one-dimensional Heisenberg ferromagnets

We use SU(2) coherent state path integral formulation with the stationary phase approximation to investigate, both analytically and numerically, the existence of shock waves in the one- dimensional Heisenberg ferromagnets with anisotropic exchange interaction. As a result we show the existence of shock waves of two types,"bright" and "dark", which can be interpreted as moving magnetic domains.Comment: 10 pages, with 3 ps figure