  Topological winding and unwinding in a quasi-one-dimensional metastable
  Bose-Einstein condensate are shown to be manipulated by changing the strength
of interaction or the frequency of rotation. Exact diagonalization analysis
reveals that quasidegenerate states emerge spontaneously near the transition
point, allowing a smooth crossover between topologically distinct states. On a
mean-field level, the transition is accompanied by formation of grey solitons,
or density notches, which serve as an experimental signature of this
phenomenon.
