Spontaneous formation and non-equilibrium dynamics of a soliton-shaped Bose-Einstein condensate in a trap

The Bose-stimulated self-organization of a quasi-two dimensional non-equilibrium Bose-Einstein condensate in an in-plane potential is proposed. We obtained the solution of the nonlinear, driven-dissipative Gross-Pitaevskii equation for a Bose-Einstein condensate trapped in an external asymmetric parabolic potential within the method of the spectral expansion. We found that, in sharp contrast to previous observations, the condensate can spontaneously acquire a soliton-like shape for spatially homogenous pumping. This condensate soliton performs oscillatory motion in a parabolic trap and, also, can spontaneously rotate. Stability of the condensate soliton in the spatially asymmetric trap is analyzed. In addition to the nonlinear dynamics of non-equilibrium Bose-Einstein condensates of ultra-cold atoms, our findings can be applied to the condensates of quantum well excitons and cavity polaritons in semiconductor heterostructure, and to the condensates of photons.