Matter-wave solitons and finite-amplitude Bloch waves in optical lattices with a spatially modulated nonlinearity
arXiv:1006.3839 · doi:10.1103/PhysRevA.82.033614
Abstract
We investigate solitons and nonlinear Bloch waves in Bose-Einstein condensates trapped in optical lattices. By introducing specially designed localized profiles of the spatial modulation of the attractive nonlinearity, we construct an infinite number of exact soliton solutions in terms of the Mathieu and elliptic functions, with the chemical potential belonging to the semi-infinite bandgap of the optical-lattice-induced spectrum. Starting from the exact solutions, we employ the relaxation method to construct generic families of soliton solutions in a numerical form. The stability of the solitons is investigated through the computation of the eigenvalues for small perturbations, and also by direct simulations. Finally, we demonstrate a virtually exact (in the numerical sense) composition relation between nonlinear Bloch waves and solitons.
arXiv comment9 pages, 10 figures
References in corpus (35)
- Discrete Solitons and Breathers with Dilute Bose-Einstein Condensates
- Effective wave-equations for the dynamics of cigar-shaped and disc-shaped Bose condensates
- Tuning the scattering length with an optically induced Feshbach resonance
- Observation of discrete vortex solitons in optically-induced photonic lattices
- Theory of Nonlinear Matter Waves in Optical Lattices
- Landau and Dynamical Instabilities of the Superflow of Bose-Einstein Condensates in Optical Lattices
- Dynamically Stabilized Bright Solitons in a Two-Dimensional Bose-Einstein Condensate
- Controlling collapse in Bose-Einstein condensates by temporal modulation of the scattering length
- Bose-Einstein condensates in standing waves: The cubic nonlinear Schroedinger equation with a periodic potential
- Lie symmetries and solitons in nonlinear systems with spatially inhomogeneous nonlinearities
- Localized nonlinear waves in systems with time- and space-modulated nonlinearities
- Nonlinear Self-Trapping of Matter Waves in Periodic Potentials
- Bose-Einstein Condensates in Optical Lattices: Band-Gap Structure and Solitons
- Dynamics of dark solitons in elongated Bose-Einstein condensates
- Solitons in combined linear and nonlinear lattice potentials
- Stability of Repulsive Bose-Einstein Condensates in a Periodic Potential
- Controllable soliton emission from a Bose-Einstein condensate
- Matter-wave solitons of collisionally inhomogeneous condensates
- Effective mean-field equations for cigar-shaped and disk-shaped Bose-Einstein condensates
- Bloch Waves and Bloch Bands of Bose-Einstein Condensates in Optical Lattices
- Two-dimensional solitons in the Gross-Pitaevskii equation with spatially modulated nonlinearity
- Stability of Attractive Bose-Einstein Condensates in a Periodic Potential
- Stable two-dimensional solitons in nonlinear lattices
- Gap solitons in Bose-Einstein condensates in linear and nonlinear optical lattices
- Qualitative and quantitative analysis of stability and instability dynamics of positive lattice solitons
- Soliton modes, stability, and drift in optical lattices with spatially modulated nonlinearity
- Localized modes of binary mixtures of Bose-Einstein condensates in nonlinear optical lattices
- Gap Solitons and Bloch Waves in Nonlinear Periodic Systems
- Vector solitons in nonlinear lattices
- Trapping and transmission of matter-wave solitons in a collisionally inhomogeneous environment
- Truncated-Bloch-wave solitons in optical lattices
- Power-dependent shaping of vortex solitons in optical lattices with spatially modulated nonlinear refractive index
- Surface solitons at interfaces of arrays with spatially-modulated nonlinearity
- Soliton dynamics at an interface between uniform medium and nonlinear optical lattice
- Multidimensional semi-gap solitons in a periodic potential
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- Instabilities of a Bose-Einstein condensate with mixed nonlinear and linear lattices
- Quantum Scattering States in a Nonlinear Coherent Medium