Positive- and negative-mass solitons in Bose-Einstein condensates with optical lattices

Hidetsugu Sakaguchi, B. A. Malomed

    Research output: Contribution to journalConference article

    3 Citations (Scopus)

    Abstract

    We study the dynamics of solitons in Bose-Einstein condensates (BECs) loaded into an optical lattice (OL), which is combined with an external parabolic potential. Chiefly, the one-dimensional (1D) case is considered. First, we demonstrate analytically that, in the case of the repulsive BEC, where the soliton is of the gap type, its effective mass is negative. In accordance with this, we demonstrate that such a soliton cannot be held by the usual parabolic trap, but it can be captured (performing harmonic oscillations) by an anti-trapping inverted parabolic potential. We also study the motion of the soliton in a long system, concluding that, in the cases of both the positive and negative mass, it moves freely, provided that its amplitude is below a certain critical value; above it, the soliton's velocity decreases due to the interaction with the OL. Transition between the two regimes proceeds through slow erratic motion of the soliton. Extension of the analysis for the 2D case is briefly outlined; in particular, novel results are existence of stable higher-order lattice vortices, with the vorticity S≥2, and quadrupoles.

    Original languageEnglish
    Pages (from-to)492-501
    Number of pages10
    JournalMathematics and Computers in Simulation
    Volume69
    Issue number5-6
    DOIs
    Publication statusPublished - Aug 5 2005
    EventNonlinear Waves: Computation and Theory IV -
    Duration: Apr 7 2003Apr 10 2003

    Fingerprint

    Optical lattices
    Optical Lattice
    Bose-Einstein Condensate
    Solitons
    Effective Mass
    Motion
    Vorticity
    Trapping
    Trap
    Demonstrate
    Critical value
    Vortex
    Vortex flow
    Harmonic
    Oscillation
    Higher Order
    Decrease
    Interaction

    All Science Journal Classification (ASJC) codes

    • Information Systems and Management
    • Control and Systems Engineering
    • Applied Mathematics
    • Computational Mathematics
    • Modelling and Simulation

    Cite this

    Positive- and negative-mass solitons in Bose-Einstein condensates with optical lattices. / Sakaguchi, Hidetsugu; Malomed, B. A.

    In: Mathematics and Computers in Simulation, Vol. 69, No. 5-6, 05.08.2005, p. 492-501.

    Research output: Contribution to journalConference article

    @article{1e8eb9e4fb7c44e29c587b401739e65f,
    title = "Positive- and negative-mass solitons in Bose-Einstein condensates with optical lattices",
    abstract = "We study the dynamics of solitons in Bose-Einstein condensates (BECs) loaded into an optical lattice (OL), which is combined with an external parabolic potential. Chiefly, the one-dimensional (1D) case is considered. First, we demonstrate analytically that, in the case of the repulsive BEC, where the soliton is of the gap type, its effective mass is negative. In accordance with this, we demonstrate that such a soliton cannot be held by the usual parabolic trap, but it can be captured (performing harmonic oscillations) by an anti-trapping inverted parabolic potential. We also study the motion of the soliton in a long system, concluding that, in the cases of both the positive and negative mass, it moves freely, provided that its amplitude is below a certain critical value; above it, the soliton's velocity decreases due to the interaction with the OL. Transition between the two regimes proceeds through slow erratic motion of the soliton. Extension of the analysis for the 2D case is briefly outlined; in particular, novel results are existence of stable higher-order lattice vortices, with the vorticity S≥2, and quadrupoles.",
    author = "Hidetsugu Sakaguchi and Malomed, {B. A.}",
    year = "2005",
    month = "8",
    day = "5",
    doi = "10.1016/j.matcom.2005.03.014",
    language = "English",
    volume = "69",
    pages = "492--501",
    journal = "Mathematics and Computers in Simulation",
    issn = "0378-4754",
    publisher = "Elsevier",
    number = "5-6",

    }

    TY - JOUR

    T1 - Positive- and negative-mass solitons in Bose-Einstein condensates with optical lattices

    AU - Sakaguchi, Hidetsugu

    AU - Malomed, B. A.

    PY - 2005/8/5

    Y1 - 2005/8/5

    N2 - We study the dynamics of solitons in Bose-Einstein condensates (BECs) loaded into an optical lattice (OL), which is combined with an external parabolic potential. Chiefly, the one-dimensional (1D) case is considered. First, we demonstrate analytically that, in the case of the repulsive BEC, where the soliton is of the gap type, its effective mass is negative. In accordance with this, we demonstrate that such a soliton cannot be held by the usual parabolic trap, but it can be captured (performing harmonic oscillations) by an anti-trapping inverted parabolic potential. We also study the motion of the soliton in a long system, concluding that, in the cases of both the positive and negative mass, it moves freely, provided that its amplitude is below a certain critical value; above it, the soliton's velocity decreases due to the interaction with the OL. Transition between the two regimes proceeds through slow erratic motion of the soliton. Extension of the analysis for the 2D case is briefly outlined; in particular, novel results are existence of stable higher-order lattice vortices, with the vorticity S≥2, and quadrupoles.

    AB - We study the dynamics of solitons in Bose-Einstein condensates (BECs) loaded into an optical lattice (OL), which is combined with an external parabolic potential. Chiefly, the one-dimensional (1D) case is considered. First, we demonstrate analytically that, in the case of the repulsive BEC, where the soliton is of the gap type, its effective mass is negative. In accordance with this, we demonstrate that such a soliton cannot be held by the usual parabolic trap, but it can be captured (performing harmonic oscillations) by an anti-trapping inverted parabolic potential. We also study the motion of the soliton in a long system, concluding that, in the cases of both the positive and negative mass, it moves freely, provided that its amplitude is below a certain critical value; above it, the soliton's velocity decreases due to the interaction with the OL. Transition between the two regimes proceeds through slow erratic motion of the soliton. Extension of the analysis for the 2D case is briefly outlined; in particular, novel results are existence of stable higher-order lattice vortices, with the vorticity S≥2, and quadrupoles.

    UR - http://www.scopus.com/inward/record.url?scp=23144436579&partnerID=8YFLogxK

    UR - http://www.scopus.com/inward/citedby.url?scp=23144436579&partnerID=8YFLogxK

    U2 - 10.1016/j.matcom.2005.03.014

    DO - 10.1016/j.matcom.2005.03.014

    M3 - Conference article

    AN - SCOPUS:23144436579

    VL - 69

    SP - 492

    EP - 501

    JO - Mathematics and Computers in Simulation

    JF - Mathematics and Computers in Simulation

    SN - 0378-4754

    IS - 5-6

    ER -