  In the present paper we investigate the influence of measurements on the
quantum dynamics of degenerate Bose atoms gases in a symmetric double-well. We
show that continuous measurements enhance asymmetry on the density distribution
of the atoms and broaden the parameter regime for self-trapping. We term this
phenomenon as nonlinear quantum Zeno effect in analog to the celebrated Zeno
effect in a linear quantum system. Under discontinuous measurements, the
self-trapping due to the atomic interaction in the degenerate bosons is shown
to be destroyed completely. Underlying physics is revealed and possible
experimental realization is discussed.
