Localized modes in the Gross-Pitaevskii equation with a parabolic trapping potential and a nonlinear lattice pseudopotential
arXiv:1802.05181 · doi:10.1016/j.cnsns.2018.06.019
Abstract
We study localized modes (LMs) of the one-dimensional Gross-Pitaevskii/nonlinear Schrödinger equation with a harmonic-oscillator (parabolic) confining potential, and a periodically modulated coefficient in front of the cubic term (nonlinear lattice pseudopotential). The equation applies to a cigar-shaped Bose-Einstein condensate loaded in the combination of a magnetic trap and an optical lattice which induces the periodic pseudopotential via the Feshbach resonance. Families of stable LMs in the model feature specific properties which result from the interplay between spatial scales introduced by the parabolic trap and the period of the nonlinear pseudopotential. Asymptotic results on the shapes and stability of LMs are obtained for small-amplitude solutions and in the limit of a rapidly oscillating nonlinear pseudopotential. We show that the presence of the lattice pseudopotential may result in: (i) creation of new LM families which have no counterparts in the case of the uniform nonlinearity; (ii) stabilization of some previously unstable LM species; (iii) evolution of unstable LMs into a pulsating mode trapped in one well of the lattice pseudopotential.
arXiv commentto be published in Commun. Nonlin. Sci. Numer. Simul
References in corpus (29)
- Production of cold molecules via magnetically tunable Feshbach resonances
- Solitons in nonlinear lattices
- Effective wave-equations for the dynamics of cigar-shaped and disc-shaped Bose condensates
- Tuning the scattering length with an optically induced Feshbach resonance
- Controlling collapse in Bose-Einstein condensates by temporal modulation of the scattering length
- Solitons in combined linear and nonlinear lattice potentials
- Nanometer-scale spatial modulation of an inter-atomic interaction in a Bose-Einstein condensate
- Matter-wave solitons of collisionally inhomogeneous condensates
- Quantum dynamics with spatiotemporal control of interactions in a stable Bose-Einstein condensate
- Bright solitons from defocusing nonlinearities
- Effective mean-field equations for cigar-shaped and disk-shaped Bose-Einstein condensates
- Nonlinear Coherent Modes of Trapped Bose-Einstein Condensates
- Improved numerical approach for time-independent Gross-Pitaevskii nonlinear Schroedinger equation
- States without linear counterpart in Bose-Einstein condensates
- Permanent magnetic lattices for ultracold atoms and quantum degenerate gases
- Excited states in the Thomas-Fermi limit: a variational approach
- Stability of stationary states in the cubic nonlinear Schroedinger equation: applications to the Bose-Einstein condensate
- Nonlinear modes for the Gross-Pitaevskii equation -- demonstrative computation approach
- Oscillations of dark solitons in trapped Bose-Einstein condensates
- Matter-wave solitons with a periodic, piecewise-constant nonlinearity
- Stability of excited states of a Bose-Einstein condensate in an anharmonic trap
- Bose-Einstein condensation: Twenty years after
- Localized dark solitons and vortices in defocusing media with spatially inhomogeneous nonlinearity
- Solitons and vortices in nonlinear potential wells
- Stationary states of Bose-Einstein condensates in single- and multi-well trapping potentials
- Dark solitons near potential and nonlinearity steps
- Dark Solitary Waves in a Class of Collisionally Inhomogeneous Bose-Einstein Condensates
- Stability of single and multiple matter-wave dark solitons in collisionally inhomogeneous Bose-Einstein condensates
- Small-amplitude nonlinear modes under the combined effect of the parabolic potential, nonlocality and symmetry