  We theoretically analyze a Mach-Zehnder interferometer with trapped
condensates, and find that it is surprisingly stable against the nonlinearity
induced by inter-particle interactions. The phase sensitivity, which we study
for number squeezed input states, can overcome the shot noise limit and be
increased up to the Heisenberg limit provided that a Bayesian or
Maximum-Likelihood phase estimation strategy is used. We finally demonstrate
robustness of the Mach-Zehnder interferometer in presence of interactions
against condensate oscillations and a realistic atom counting error.
