Matter-wave solitons in nonlinear optical lattices

Hidetsugu Sakaguchi, Boris A. Malomed

    Research output: Contribution to journalArticle

    156 Citations (Scopus)

    Abstract

    We introduce a dynamical model of a Bose-Einstein condensate based on the one-dimensional (1D) Gross-Pitaevskii equation (GPE) with a nonlinear optical lattice (NOL), which is represented by the cubic term whose coefficient is periodically modulated in the coordinate. The model describes a situation when the atomic scattering length is spatially modulated, via the optically controlled Feshbach resonance, in an optical lattice created by interference of two laser beams. Relatively narrow solitons supported by the NOL are predicted by means of the variational approximation (VA), and an averaging method is applied to broad solitons. A different feature is a minimum norm (number of atoms), N=Nmin, necessary for the existence of solitons. The VA predicts Nmin very accurately. Numerical results are chiefly presented for the NOL with the zero spatial average value of the nonlinearity coefficient. Solitons with values of the amplitude A larger than at N=Nmin are stable. Unstable solitons with smaller, but not too small, A rearrange themselves into persistent breathers. For still smaller A, the soliton slowly decays into radiation without forming a breather. Broad solitons with very small A are practically stable, as their decay is extremely slow. These broad solitons may freely move across the lattice, featuring quasielastic collisions. Narrow solitons, which are strongly pinned to the NOL, can easily form stable complexes. Finally, the weakly unstable low-amplitude solitons are stabilized if a cubic term with a constant coefficient, corresponding to weak attraction, is included in the GPE.

    Original languageEnglish
    Article number046610
    JournalPhysical Review E - Statistical, Nonlinear, and Soft Matter Physics
    Volume72
    Issue number4
    DOIs
    Publication statusPublished - Oct 1 2005

    Fingerprint

    Optical Lattice
    Nonlinear Lattice
    Solitons
    solitary waves
    Variational Approximation
    Gross-Pitaevskii Equation
    Breathers
    Coefficient
    coefficients
    Unstable
    Decay
    Bose-Einstein Condensate
    Averaging Method
    decay
    Dynamical Model
    Term
    approximation
    Bose-Einstein condensates
    norms
    Laser Beam

    All Science Journal Classification (ASJC) codes

    • Statistical and Nonlinear Physics
    • Statistics and Probability
    • Condensed Matter Physics

    Cite this

    Matter-wave solitons in nonlinear optical lattices. / Sakaguchi, Hidetsugu; Malomed, Boris A.

    In: Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, Vol. 72, No. 4, 046610, 01.10.2005.

    Research output: Contribution to journalArticle

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