Symmetry Breaking and Enhanced Condensate Fraction in a Matter-Wave   Bright Soliton
  An exact diagonalization study reveals that a matter-wave bright soliton and the Goldstone mode are simultaneously created in a quasi-one-dimensional attractive Bose-Einstein condensate by superpositions of quasi-degenerate low-lying many-body states. Upon formation of the soliton the maximum eigenvalue of the single-particle density matrix increases dramatically, indicating that a fragmented condensate converts into a single condensate as a consequence of the breaking of translation symmetry. 
Rina Kanamoto, Hiroki Saito, Masahito Ueda