Quantum fluctuations of coupled dark solitons in a trapped Bose-Einstein condensate

We examine the quantum fluctuations associated with the Bogoliubov quasiparticle vacuum of coupled dark solitons in a quasi-one-dimensional Bose-Einstein condensate. We show that the quantum fluctuations appear in the form of incoherent atoms strongly concentrated near the notches. We identify a finite number of collective modes that are responsible for such quantum phenomena. These collective modes describe the particle-like oscillations of coupled dark solitons.