skip to main content
OSTI.GOV title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: Self-Trapped Nonlinear Matter Waves in Periodic Potentials

Abstract

We demonstrate that the recent observation of nonlinear self-trapping of matter waves in one-dimensional optical lattices [Th. Anker et al., Phys. Rev. Lett. 94, 020403 (2005)] can be associated with a novel type of broad nonlinear state existing in the gaps of the matter-wave band-gap spectrum. We find these self-trapped localized modes in one-, two-, and three-dimensional periodic potentials, and demonstrate that such novel gap states can be generated experimentally in any dimension.

Authors:
; ;  [1]
  1. Nonlinear Physics Centre and ARC Centre of Excellence for Quantum-Atom Optics, Research School of Physical Sciences and Engineering, Australian National University, Canberra ACT 0200 (Australia)
Publication Date:
OSTI Identifier:
20776998
Resource Type:
Journal Article
Resource Relation:
Journal Name: Physical Review Letters; Journal Volume: 96; Journal Issue: 4; Other Information: DOI: 10.1103/PhysRevLett.96.040401; (c) 2006 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; BOSE-EINSTEIN CONDENSATION; FOCUSING; MATTER; NONLINEAR PROBLEMS; ONE-DIMENSIONAL CALCULATIONS; PERIODICITY; POTENTIALS; THREE-DIMENSIONAL CALCULATIONS; TRAPPING

Citation Formats

Alexander, Tristram J., Ostrovskaya, Elena A., and Kivshar, Yuri S. Self-Trapped Nonlinear Matter Waves in Periodic Potentials. United States: N. p., 2006. Web. doi:10.1103/PhysRevLett.96.040401.
Alexander, Tristram J., Ostrovskaya, Elena A., & Kivshar, Yuri S. Self-Trapped Nonlinear Matter Waves in Periodic Potentials. United States. doi:10.1103/PhysRevLett.96.040401.
Alexander, Tristram J., Ostrovskaya, Elena A., and Kivshar, Yuri S. Fri . "Self-Trapped Nonlinear Matter Waves in Periodic Potentials". United States. doi:10.1103/PhysRevLett.96.040401.
@article{osti_20776998,
title = {Self-Trapped Nonlinear Matter Waves in Periodic Potentials},
author = {Alexander, Tristram J. and Ostrovskaya, Elena A. and Kivshar, Yuri S.},
abstractNote = {We demonstrate that the recent observation of nonlinear self-trapping of matter waves in one-dimensional optical lattices [Th. Anker et al., Phys. Rev. Lett. 94, 020403 (2005)] can be associated with a novel type of broad nonlinear state existing in the gaps of the matter-wave band-gap spectrum. We find these self-trapped localized modes in one-, two-, and three-dimensional periodic potentials, and demonstrate that such novel gap states can be generated experimentally in any dimension.},
doi = {10.1103/PhysRevLett.96.040401},
journal = {Physical Review Letters},
number = 4,
volume = 96,
place = {United States},
year = {Fri Feb 03 00:00:00 EST 2006},
month = {Fri Feb 03 00:00:00 EST 2006}
}
  • We study the motion of bright matter-wave solitons in nonlinear potentials, produced by periodic or random spatial variations of the atomic scattering length. We obtain analytical results for the soliton motion, the radiation of matter wave, and the radiative soliton decay in such configurations of the Bose-Einstein condensate. The stable regimes of propagation are analyzed. The results are in remarkable agreement with the numerical simulations of the Gross-Pitaevskii equation with periodic or random spatial variations of the mean field interactions.
  • The new classes of periodic solutions of nonlinear self-dual network equations describing the breather and soliton lattices, expressed in terms of the Jacobi elliptic functions have been obtained. The dependences of the frequencies on energy have been found. Numerical simulations of soliton lattice demonstrate their stability in the ideal lattice and the breather lattice instability in the dissipative lattice. However, the lifetime of such structures in the dissipative lattice can be extended through the application of ac driving terms.
  • We study the nonequilibrium dynamics of cold atoms held in an optical lattice subjected to a periodic driving potential. The expansion of an initially confined atom cloud occurs in two phases: an initial quadratic expansion followed by a ballistic behavior at long times. Accounting for this gives a good description of recent experimental results and provides a robust method to extract the effective intersite tunneling from time-of-flight measurements.
  • Exact nonlinear plane periodic traveling acoustic waves with steady profile are discovered for a Newtonian self-gravitating perfect fluid. This demonstrates that self-gravity as a dispersive force can counterbalance hydrodynamic nonlinearity to produce persistent structures. These periodic waves do not admit a solitary wave limit. Galactic scale (M approx. = 10/sup 12/ M/sub sun/) nonlinear waves can have amplitude deltarho/rho/sub 0/ < or approx. = 1% only at recombination in a high-density universe, allowing for photon dissipations.
  • We apply the dynamical systems tools to study the linear dynamics of a self-interacting scalar field trapped in the braneworld, for a wide variety of self-interaction potentials. We focus on Randall-Sundrum and on Dvali-Gabadadze-Porrati braneworld models exclusively. These models are complementary to each other: while the Randall-Sundrum brane produces UV) corrections to general relativity, the Dvali-Gabadadze-Porrati braneworld modifies Einstein's theory at large scales, i e., produces IR modifications of general relativity. This study of the asymptotic properties of both braneworld models, shows - in the phase space - the way the dynamics of a scalar field trapped in the branemore » departs from standard general relativity behavior.« less