Dynamics of positive and negativemass solitons in optical lattices and inverted traps
Abstract
We study the dynamics of onedimensional solitons in attractive and repulsive BoseEinstein condensates (BECs) loaded into an optical lattice (OL), which is combined with an external parabolic potential. First, we demonstrate analytically that, in the repulsive BEC, where the soliton is of the gap type, its effective mass is negative. This gives rise to a prediction for the experiment: such a soliton cannot be held by the usual parabolic trap, but it can be captured (performing slow harmonic oscillations, with a period that is estimated to be ~0.01 s in realistic experimental conditions) by an antitrapping 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 interaction with the OL. At a later stage, the damped motion becomes chaotic. We also investigate the evolution of a twosoliton pulse in the attractive model. The pulse generates a persistent breather, if its amplitude is not too large; otherwise, fusion into a single fundamental soliton takes place. Collisions between two solitons captured in the parabolic trap or antitrap are considered too. Depending on their amplitudes and phase difference, the solitons either perform stable oscillations, colliding indefinitely many times, or merge into a single soliton. Effects reported in this work for BECs can also be formulated for optical solitons in nonlinear photonic crystals. In particular, the capture of the negativemass soliton in the antitrap implies that a bright optical soliton in a selfdefocusing medium with a periodic structure of the refractive index may be stable in an antiwaveguide.
 Publication:

Journal of Physics B Atomic Molecular Physics
 Pub Date:
 April 2004
 DOI:
 10.1088/09534075/37/7/006
 arXiv:
 arXiv:nlin/0401041
 Bibcode:
 2004JPhB...37.1443S
 Keywords:

 Nonlinear Sciences  Pattern Formation and Solitons;
 Nonlinear Sciences  Exactly Solvable and Integrable Systems;
 Condensed Matter  Soft Condensed Matter
 EPrint:
 22pages, 9 figures, submitted to Journal of Physics B