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We optimize the signal-to-noise ratio of a Mach-Zehnder atom interferometerwith Gaussian squeezed input states, in the presence interactions. For weakinteractions, our results coincide with Phys. Rev. Lett. {\bf 100}, 250406(2008), with optimal initial number-variance $\sigma_o\propto N^{1/3}$ andoptimal signal-to-noise ratio $s_o\propto N^{2/3}$ for total atom number $N$.As the interaction strength $u$ increases past unity, phase-diffusion becomesdominant, leading to a transition in the optimal squeezing from initialnumber-squeezing to initial {\it phase}-squeezing with$\sigma_o\propto\sqrt{uN}$ and $s_o\propto\sqrt{N/u}$ shot-noise scaling. Theinitial phase-squeezing translates into hold-time number-squeezing, which isless sensitive to interactions than coherent states and improves $s_o$ by afactor of $\sqrt{u}$.

Optimal Gaussian squeezed states for atom-interferometry in the presence of phase diffusion