Dark-soliton states of Bose-Einstein condensates in anisotropic traps - art. no. 053606

Bark soliton states of Bose-Einstein condensates in harmonic traps are stud ied both analytically and computationally by the direct solution of the Gro ss-Pitaevskii equation in three dimensions. The ground and self-consistent excited states are found numerically by relaxation in imaginary time. The e nergy of a stationary soliton in a harmonic trap is shown to be independent of density and geometry for large numbers of atoms. Large-amplitude field modulation at a frequency resonant with the energy of a dark soliton is fou nd to give rise to a state with multiple vortices. The Bogoliubov excitatio n spectrum of the soliton state contains complex frequencies, which disappe ar for sufficiently small numbers of atoms or large transverse confinement. The relationship between these complex modes and the snake instability is investigated numerically by propagation in real time.