2007/09/13 by A. D. Martin, Charles S. Adams, C. S. Adams +1 · 1 citation
Physics and Astronomy · #Cold Atom Physics and Bose-Einstein Condensates #Nonlinear Photonic Systems #Strong Light-Matter Interactions #cond-mat.other
paper · pdf · doi:10.1103/physreva.77.013620
published as Phys. Rev. A 77, 013620 (2008) · 17 pages, 10 figures
arxiv created 2007/09/13 · openalex publication_date 2008/01/25 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
Systems of solitary waves in the one-dimensional Gross-Pitaevskii equation, which models a trapped atomic Bose-Einstein condensate, are investigated theoretically. To analyze the soliton nature of these solitary waves, a particle analogy for the solitary waves is formulated. Exact soliton solutions exist in the absence of an external trapping potential, which behave in a particlelike manner, and we find the particle analogy we employ to be a good model also when a harmonic trapping potential is present up to a gradual shift in the trajectories when the harmonic trap period is short compared with the collision time of the solitons. We find that the collision time of the solitons is dependent on the relative phase of the solitons as they collide. In the case of two solitons, the particle model is integrable, and the dynamics are completely regular. In the case of a system of two solitary waves of equal norm, the solitons are shown to retain their phase difference for repeated collisions. This phase preservation can be used to find regimes where there is agreement between the wave and particle models. This also implies that soliton regimes may be found in three-dimensional geometries where solitary waves can be made to repeatedly collide out of phase, stabilizing the condensate against collapse. The extension to three particles supports both regular and chaotic regimes. The trajectory shift observed for two solitons carries over to the case of three solitons. This shift aside, the agreement between the particle model and the wave dynamics remains good, even in chaotic regimes.