Fluctuation- and interaction-induced instability of dark solitons in single and binary condensates

We show that the presence of a soliton in a single-species condensate, at zero temperature, enhances the quantum depletion sufficiently enough to induce dynamical instability of the system. We also predict that for two-species condensates, two Goldstone modes emerge in the excitation spectrum at phase separation. Of these, one is due to the presence of the soliton. We use Hartree-Fock-Bogoliubov theory with Popov approximation to examine the mode evolution, and demonstrate that when the anomalous mode collides with a higher energy mode it renders the solitonic state oscillatory unstable. We also report a soliton-induced change in the topology of the density profiles of the two-species condensates at phase separation.