Two Stages in the evolution of binary alkali Bose-Einstein condensate mixtures towards phase segregation

The quantum analogy of the usual spinodal decomposition is explored for the recently achieved binary alkali Bose-Einstein condensates mixture. We conclude that an analogy is possible within the formulation of coupled nonlinear Schrodinger equations, and find that the quantum spinodal decomposition consists of two stages. The non-equilibrium stage I is dominated by the fastest growth mode, associated with a characteristic length. Expressions for both time and length scales in stage I are obtained. Stage II is a relaxation process of approaching equilibrium, dominated by the slowest mode. We propose that for this state the slow evolution towards the phase segregation is due to the Josephson effect between different domains of the same condensate, and its time scale is estimated.