Excitations and dynamics of a two-component Bose-Einstein condensate in 1D

Abstract

We study different solutions and their stability for a two component one-dimensional Bose-Einstein condensate. First of all, we present the spectrum of the ground state in the miscible phase and we identify two families of excitations. Using this spectrum we characterize the transition between the miscible and immiscible phase, and we analyze different solutions which appear in this new phase. With this background, now we study an excited state in the miscible phase, the darkdark soliton. We present its spectrum and we find two different anomalous modes, one of them, the out-of-phase mode, collides with other modes of the ground state and creates unstable regions. In these regions we find an interesting decay process to two new solutions, dark-antidark solitons. Besides, we study the dynamics of the dark-dark soliton in a harmonic trap, and we find that the oscillation frequency is the same as for a dark soliton in one component one-dimensional Bose-Einstein condensate.