  We investigate the {\em nonlinearity-assisted quantum tunneling} and
formation of nonlinear collective excitations in a matter-wave interferometer,
which is realised by the adiabatic transformation of a double-well potential
into a single-well harmonic trap. In contrast to the linear quantum tunneling
induced by the crossing (or avoided crossing) of neighbouring energy levels,
the quantum tunneling between different nonlinear eigenstates is assisted by
the nonlinear mean-field interaction. When the barrier between the wells
decreases, the mean-field interaction aids quantum tunneling between the ground
and excited nonlinear eigenstates. The resulting {\em non-adiabatic evolution}
depends on the input states. The tunneling process leads to the generation of
dark solitons, and the number of the generated dark solitons is highly
sensitive to the matter-wave nonlinearity. The results of the numerical
simulations of the matter-wave dynamics are successfully interpreted with a
coupled-mode theory for multiple nonlinear eigenstates.

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