Quantum lattice representations for vector solitons in external potentials

George Vahala, Linda Vahala and Jeffrey Yepez

Physica A: Statistical Mechanics and its Applications, 2006, vol. 362, issue 1, 215-221

Abstract: A quantum lattice algorithm is developed to examine the effect of an external potential well on exactly integrable vector Manakov solitons. It is found that the exact solutions to the coupled nonlinear Schrodinger equations act like quasi-solitons in weak potentials, leading to mode-locking, trapping and untrapping. Stronger potential wells will lead to the emission of radiation modes from the quasi-soliton initial conditions. If the external potential is applied to that particular mode polarization, then the radiation will be trapped within the potential well. The algorithm developed leads to a finite difference scheme that is unconditionally stable. The Manakov system in an external potential is very closely related to the Gross–Pitaevskii equation for the ground state wave functions of a coupled BEC state at T=0K.

Keywords: Quantum lattice gas; Solitons; Manakov solitons; Nonlinear Schrodinger equation; Gross–Pitaevskii equation; Optical fibers (search for similar items in EconPapers)
Date: 2006
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:362:y:2006:i:1:p:215-221

DOI: 10.1016/j.physa.2005.09.029

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