Bright Gap Solitons Research Articles

Dark matter-wave gap solitons of Bose-Einstein condensates trapped in optical lattices with competing cubic-quintic nonlinearities

• The existence, property and stability of one-dimensional gap solitons and soliton clusters in periodic nonlinear media with competing cubic-quintic nonlinearities are theoretical studied. • The linear-stability analysis and direct perturbed calculations are adopted to identify the stability and instability of the corresponding dark gap modes. • The model can find its realization in periodic optical media with cubic-quintic nonlinear nonlinearities and in Bose-Einstein condensates trapped by an optical lattice. Solitons are nonlinear self-sustained wave excitations and probably among the most interesting and exciting emergent nonlinear phenomenon in the corresponding theoretical settings. Bright solitons with sharp peak and dark solitons with central notch have been well known and observed in various nonlinear systems . The interplay of periodic potentials, like photonic crystals and lattices in optics and optical lattices in ultracold atoms, with the dispersion has brought about gap solitons within the finite band gaps of the underlying linear Bloch-wave spectrum and, particularly, the bright gap solitons have been experimentally observed in these nonlinear periodic systems, while little is known about the underlying physics of dark gap solitons. Here, we theoretically and numerically investigate the existence, property and stability of one-dimensional matter-wave gap solitons and soliton clusters of Bose-Einstein condensates trapped in optical lattices with competing cubic-quintic nonlinearity, the higher-order of which is self-defocusing and the lower-order (cubic) one is chosen as self-defocusing or focusing nonlinearities. By means of the conventional linear-stability analysis and direct numerical calculations with initial perturbations, we identify the stability and instability areas of the corresponding dark gap solitons and clusters ones.

Dark matter-wave gap solitons in dense ultracold atoms trapped by a one-dimensional optical lattice

Optical lattices have been used as a versatile toolbox to control Bose-Einstein condensates (BECs) in recent years, and a wealth of emergent nonlinear phenomena have been found, including bright gap solitons and dark ones, among which the former has been realized in experiments. The latter, however, has only theoretical results and its fundamental properties are still not well understood. Here we theoretically and numerically explore an open issue of creating stable matter-wave dark gap solitons in a one-dimensional optical lattice, onto which the BECs with self-defocusing quintic nonlinearity are loaded. Using linear-stability analysis and direct simulations, the formation, structures, and properties of dark gap solitons in quintic nonlinearity have been compared to those upheld by cubic Kerr nonlinearity. In particular, we uncover that the dark gap solitons and soliton clusters are robustly stable in the first finite band gap of the underlying linear spectrum, and are hard to be stabilized in the second gap. The predicted dark gap solitons are observable in current experiments on dense ultracold atoms, using an optical lattice technique, and in the optics domain for nonlinear light propagation in periodic optical media with quintic nonlinearity.

Gap-type dark localized modes in a Bose–Einstein condensate with optical lattices

Bose-Einstein condensate (BEC) exhibits a variety of fascinating and unexpected macroscopic phenomena, and has attracted sustained attention in recent years--particularly in the field of solitons and associated nonlinear phenomena. Meanwhile, optical lattices have emerged as a versatile toolbox for understanding the properties and controlling the dynamics of BEC, among which the realization of bright gap solitons is an iconic result. However, the dark gap solitons are still experimentally unproven, and their properties in more than one dimension remain unknown. In light of this, we describe, numerically and theoretically, the formation and stability properties of gap-type dark localized modes in the context of ultracold atoms trapped in optical lattices. Two kinds of stable dark localized modes--gap solitons and soliton clusters--are predicted in both the one- and two-dimensional geometries. The vortical counterparts of both modes are also constructed in two dimensions. A unique feature is the existence of a nonlinear Bloch-wave background on which all above gap modes are situated. By employing linear-stability analysis and direct simulations, stability regions of the predicted modes are obtained. Our results offer the possibility of observing dark gap localized structures with cutting-edge techniques in ultracold atoms experiments and beyond, including in optics with photonic crystals and lattices.

Nonlinear waves of Bose-Einstein condensates in rotating ring-lattice potentials

We analyze the dynamics of Bose-Einstein condensates loaded in rotating ring lattices made of a few sites, and show how rotation maps the states found in this finite system into those belonging to a static infinite lattice. Ring currents and soliton states in the absence of a lattice find their continuation in the presence of the lattice as nonlinear Bloch waves and soliton-like states connecting them. Both bright gap solitons and dark-soliton trains are shown to connect continuously to linear solutions. The existence of adiabatic paths upon varying rotation frequency between states with quantized supercurrents suggests highly controllable methods for the experimental generation of persistent currents.

Método variacional aplicado ao estudo de um gás de átomos de Fermi em um estado superfluido aprisionados por uma rede óptica quase periódica

Neste trabalho, nós consideramos um modelo derivado da densidade de um gás de Fermi em um estado superfluido BCS, aprisionado por uma rede óptica quase periódica unidimensional. Reduzindo a equação em 3D para 1D, construímos famílias de gaps sólitons estáveis (GSs) utilizando aproximações variacionais. No limite linear a aproximação variacional prediz exatamente a posição da banda de Bloch que separam os primeiros gaps. Através da aproximação variacional, mostramos a possibilidade de que a não linearidade efetiva atuando em combinação com o potencial de uma rede quase periódica em uma dimensão, permite o surgimento de gaps sólitons iluminados. Variando a amplitude da rede óptica, analisamos a existência e estabilidade dos gaps sólitons iluminados usando um ansatz gaussiano. Os gaps sólitons são estáveis diante de pequenas variações da rede óptica quase periódica. Este artigo pode ser utilizado como um guia de aprendizagem no estudo de átomos frios; estudantes são incentivados a realizarem os cálculos para outros valores de amplitude da rede óptica.

Uma abordagem variacional ao estudo de condensados de Boso-Einstein aprisionados por redes ópticas

Nós investigamos as soluções de uma equação hidrodinâmica de campo médio unidimensional utilizando aproximações variacionais. Modelamos analiticamente e comparamos dois condensados de Bose-Einstein que podem ser usados para criar gaps sólitons iluminados experimentalmente, um deles aprisionado por uma rede óptica duplamente periódica e o outro aprisionado por uma rede óptica simples. Nesses dois casos não utilizamos um confinamento harmônico adicional. Através da aproximação variacional nós estudamos a possibilidade de que o coeficiente de não linearidade atuando em uma combinação com o potencial da rede óptica duplamente periódica, ou com o potencial de uma rede óptica simples, permite o surgimento de gaps sólitons iluminados em uma dimensão. Em ambos os casos, nós analisamos a existência e estabilidade de gaps sólitons iluminados usando um ansatz gaussiano. Este artigo pode ser utilizado como um guia de aprendizagem no estudo de átomos frios; incentivando os alunos a realizarem cálculos variacionais para outros tipos de redes ópticas.

Anomalous interactions of spatial gap solitons in optically induced photonic lattices

We demonstrate coherent interactions between spatial gap solitons in optically induced photonic lattices. Because of the "staggered" phase structures, two in-phase (out-of-phase) bright gap solitons can repel (attract) each other at close proximity, in contrast to soliton interaction in homogeneous media. A reversal of energy transfer direction and a transition between attractive and repulsive interaction forces can be obtained solely by changing the initial soliton separation relative to the lattice spacing.

SOLITON ON THE SEMI-INFINITE BAND GAP OF BEC IN AN OPTICAL LATTICE

By developing a multiple-scale method, we study analytically the dynamics of the soliton inside the semi-infinite band gap (SIBG) of quasi-one-dimensional Bose–Einstein condensates trapped in an optical lattice. In the linear case, a stable condition of soliton formation is obtained. For a weak nonlinearity, whether there occurs a spatially propagating or localized gap soliton is determined by the lattice depth. Meanwhile, we predict the existence of the dark (bright) gap solitons for the repulsive (attractive) interactions in the SIBG, different from that of the gap solitons in other energy gaps. And the collision of two dark (or bright) solitons is nearly elastic under a safe range of atomic numbers. An experimental protocol is further designed for observing these phenomena.

Discrete Diffraction and Spatial Self-Action of Light Beams in One-Dimensional Photonic Lattices in Lithium Niobate

Features of the behavior of light beams in one-dimensional photonic lattices in iron-doped lithium niobate have been experimentally studied. It is demonstrated that bright discrete spatial solitons and bright gap solitons can be formed in this system using 633 nm radiation on a microwatt power level. © 2005 Pleiades Pub- lishing, Inc.

Nonlinear atom optics and bright-gap-soliton generation in finite optical lattices

We theoretically investigate the transmission dynamics of coherent matter wave pulses across finite optical lattices in both the linear and the nonlinear regimes. The shape and the intensity of the transmitted pulse are found to strongly depend on the parameters of the incident pulse, in particular its velocity and density: a clear physical picture of the main features observed in the numerical simulations is given in terms of the atomic band dispersion in the periodic potential of the optical lattice. Signatures of nonlinear effects due to the atom-atom interaction are discussed in detail, such as atom-optical limiting and atom-optical bistability. For positive scattering lengths, matter waves propagating close to the top of the valence band are shown to be subject to modulational instability. A scheme for the experimental generation of narrow bright gap solitons from a wide Bose-Einstein condensate is proposed: the modulational instability is seeded starting from the strongly modulated density profile of a standing matter wave and the solitonic nature of the generated pulses is checked from their shape and their collisional properties.

Gap solitons in asymmetric dual-core nonlinear optical fibers

We demonstrate that an asymmetric dual-core fiber, with opposite signs of the dispersion in its two cores, supports bright gap solitons. Such a fiber is a new nonlinear optical medium, the fabrication of which is technologically feasible. There are three nontrivial features of these new gap solitons: (i) Their exponential tails may oscillate as they decay; (ii) the energy in the normal-core component may be equal to or larger than the energy in the anomalous-core one, despite the obvious fact that the normal-dispersion core, in isolation, cannot support any bright solitons; and (iii) a part of the finite gap available for soliton solutions remains empty, having no solitons inside it. In addition, we show that such fibers can also support weakly delocalized solitons, which sit on a small-amplitude, nonvanishing, continuous-wave background. We also investigate the case in which the dispersion in both cores is anomalous but in which the cores are asymmetric and have different magnitudes of dispersion. In this case the general picture of the soliton solutions, including their bifurcations and stability, is qualitatively the same as when one has equal dispersions in the two cores, but with an asymmetry produced by a phase-velocity mismatch. These studies have been carried out by a combination of an analysis of the dispersion relation for the linearized system, the variational approximation for the full nonlinear one, and direct numerical methods.