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Averaging for solitons with nonlinearity management.

D E Pelinovsky1, P G Kevrekidis, D J Frantzeskakis

  • 1Department of Mathematics, McMaster University, Hamilton, Ontario, Canada L8S 4K1.

Physical Review Letters
|December 20, 2003
PubMed
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We developed an averaging method for solitons in Bose-Einstein condensates, which accurately describes their behavior under periodically changing conditions. This new technique aligns well with experimental Feshbach resonance management methods.

Area of Science:

  • Atomic, molecular, and optical physics
  • Quantum optics
  • Condensed matter physics

Background:

  • Solitons in Bose-Einstein condensates are crucial for quantum information and simulation.
  • Controlling soliton properties requires managing the nonlinearity coefficient.
  • Feshbach resonance management offers a novel approach to control these properties.

Purpose of the Study:

  • To develop an effective averaging method for solitons in Bose-Einstein condensates with periodically varying nonlinearity.
  • To analyze the behavior of matter-wave bright and dark solitons using this method.
  • To validate the accuracy of the averaging method against full numerical solutions.

Main Methods:

  • Development of a local averaged equation for solitons.

Related Experiment Videos

  • Application of the averaging method to the nonlinear Schrödinger equation with a time-dependent nonlinearity coefficient.
  • Numerical simulations of both averaged and full equations for comparison.

    • Main Results:

    • The derived averaging method effectively describes soliton dynamics.
    • Accurate predictions for both bright and dark solitons were achieved.
    • Excellent agreement was found between the averaged and full equation solutions.

    Conclusions:

    • The averaging method provides a powerful and efficient tool for studying solitons in Bose-Einstein condensates.
    • This method is particularly relevant for systems utilizing Feshbach resonance management.
    • The findings pave the way for enhanced control and manipulation of matter-wave solitons.