Bright soliton dynamics in confining and expelling potentials

Abstract

This work presents an exploration of the dynamics of a Bose-Einstein Condensate (BEC) with a focus the bright soliton solution for the 1D Gross-Pitaevskii equation. The Crank-Nicolson algorithm is used to study the soliton trapped in a harmonic oscillator potential well, a case which can be used to test the solver. Two vibration modalities are revealed: Oscillations, with frequency ωosc = ω, and squeezing, with ωsq = 1 + 0.055 × ξ−2.49. Then the soliton is placed in an inverted harmonic oscillator potential, on which different dynamical regimes are discussed, which depend on the healing length and the oscillator length scale, presenting a transition at ξ ≈ 0.30 ± 0.05a0.