Self-trapped spatially localized states in combined linear-nonlinear periodic potentials

Abstract

We analyze the existence and stability of two kinds of self-trapped spatially localized gap modes, gap solitons and truncated nonlinear Bloch waves, in one-and two-dimensional optical or matter-wave media with self-focusing nonlinearity, supported by a combination of linear and nonlinear periodic lattice potentials. The former is found to be stable once placed inside a single well of the nonlinear lattice, it is unstable otherwise. Contrary to the case with constant self-focusing nonlinearity, where the latter solution is always unstable, here, we demonstrate that it nevertheless can be stabilized by the nonlinear lattice since the model under consideration combines the unique properties of both the linear and nonlinear lattices. The practical possibilities for experimental realization of the predicted solutions are also discussed.

arXiv comment7 pages, 6 figures, Accepted for publication

References in corpus (31)

• Many-Body Physics with Ultracold Gases
• Feshbach Resonances in Ultracold Gases
• Nonlinear waves in $\mathcal{P}\mathcal{T}$-symmetric systems
• Solitons in nonlinear lattices
• Theory of Nonlinear Matter Waves in Optical Lattices
• Valley susceptibility of an interacting two-dimensional electron system
• Nonlinear Waves in Bose-Einstein Condensates: Physical Relevance and Mathematical Techniques
• Hybrid photonic-crystal fiber
• Solitons in combined linear and nonlinear lattice potentials
• Matter-wave gap solitons in atomic bandgap structures
• Observation of two-dimensional surface solitons in anisotropic waveguide arrays
• Quantum dynamics with spatiotemporal control of interactions in a stable Bose-Einstein condensate
• Controlling Condensate Collapse and Expansion with an Optical Feshbach Resonance
• Matter-wave gap vortices in optical lattices
• One-dimensional solitons in fractional Schrödinger equation with a spatially modulated nonlinearity: nonlinear lattice
• Superconducting Vortex Lattices for Ultracold Atoms
• Self-localization of polariton condensates in periodic potentials
• Permanent magnetic lattices for ultracold atoms and quantum degenerate gases
• Solitary Waves Bifurcated from Bloch Band Edges in Two-dimensional Periodic Media
• Localized modes in arrays of boson-fermion mixtures
• Band-gap solitons in nonlinear optically-induced lattices
• Three-Dimensional Nonlinear Lattices: From Oblique Vortices and Octupoles to Discrete Diamonds and Vortex Cubes
• Solitonic transmission of Bose-Einstein matter waves
• Excitations of Bose-Einstein condensates in a one-dimensional periodic potential
• Stabilization of one-dimensional solitons against the critical collapse by quintic nonlinear lattices
• Optical gap solitons and truncated nonlinear Bloch waves in temporal lattices
• Delocalizing transition in one-dimensional condensates in optical lattices due to inhomogeneous interactions
• Two-dimensional solitons and vortices in media with incommensurate linear and nonlinear lattice potentials
• Discrete Solitons and Vortices on Anisotropic Lattices
• Statics and Dynamics of an Inhomogeneously-Nonlinear Lattice
• Two-dimensional intra-band solitons in lattice potentials with local defects and self-focusing nonlinearity