  Mach-Zehnder atom interferometry requires hold-time phase-squeezing to attain
readout accuracy below the standard quantum limit. This increases its
sensitivity to phase-diffusion, restoring shot-noise scaling of the optimal
signal-to-noise ratio, $s_o$, in the presence of interactions. The
contradiction between the preparations required for readout accuracy and
robustness to interactions, is removed by monitoring Rabi-Josephson
oscillations instead of relative-phase oscillations during signal acquisition.
Optimizing $s_o$ with a Gaussian squeezed input, we find that hold-time number
squeezing satisfies both demands and that sub-shot-noise scaling is retained
even for strong interactions.
