Systematic vector solitary waves from their linear limits in one-dimensional n-component Bose-Einstein condensates.

Abstract

We systematically construct a series of vector solitary waves in harmonically trapped one-dimensional three-, four-, and five-component Bose-Einstein condensates. These stationary states are continued in chemical potentials from the analytically tractable low-density linear limit of respective states, as independent linear quantum harmonic oscillator states, to the high-density nonlinear Thomas-Fermi regime. A systematic interpolation procedure is proposed to achieve this sequential continuation via a trajectory in the multidimensional space of the chemical potentials. The Bogoliubov-de Gennes spectral analysis shows that all of the states considered herein can be fully stabilized in suitable chemical potential intervals in the Thomas-Fermi regime. Finally, we present some typical SU(n)-rotation-induced and driving-induced dynamics. This method can be extended to higher dimensions and shows significant promise for finding a wide range of solitary waves ahead.