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

We optimize the signal-to-noise ratio of a Mach-Zehnder atom interferometer with Gaussian squeezed input states in the presence interactions. For weak interactions, our results coincide with those of Huang and Moore, with an optimal initial number variance σ_oN1^/3 and an optimal signal-to-noise ratio s_oN2^/3 for the total atom number N. As the interaction strength u increases past unity, phase diffusion becomes dominant, leading to a transition in the optimal squeezing from initial number squeezing to initial phase squeezing with σ_ouN and s_oN/u shot-noise scaling. The initial phase squeezing translates into hold-time number squeezing, which is less sensitive to interactions than coherent states and improves s_o by a factor of u.