  We numerically investigate the soliton tunnelling process in double-well
potential trapped Bose-Einstein condensate. Comparing with the usual low energy
few particle tunnelling process, we find that the soliton tunnelling leads to
massive particle transport between two wells. The {population imbalance}
between two wells is not evolving sinusoidally with the time as the Josephson
plasma oscillation, but shows a higher density contrast square-wave pattern due
to the reflections at the trapping potential boundaries. Such unusual behavior
clearly demonstrates the topologically stable, localized nature of solitons
that propagate in a nonlinear medium without spreading. The square-wave
oscillation of soliton also provides measurable dynamics to define a qubit in
cold altom system.
