Square wave oscillation of soliton in double-well potential trapped BEC.

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.